1. No category

Near-Field Acousto Monitoring Shear Interactions Inside a Drop of

Portland State University
PDXScholar
Physics Faculty Publications and Presentations
Physics
5-2016
Near-Field Acousto Monitoring Shear Interactions Inside a Drop
of Fluid: The Role of the Zero-Slip condition
Xiaohua Wang
Portland State University
Rodolfo Fernandez Rodriguez
Portland State University, [email protected]
Nan Li
Bronx Science High School
Hsien-Chih Hung
Portland State University
Anuradha Venkataraman
Portland State University, [email protected]
See next page for additional authors
Let us know how access to this document benefits you.
Follow this and additional works at: http://pdxscholar.library.pdx.edu/phy_fac
Part of the Fluid Dynamics Commons
Citation Details
Wang, Xiaohua; Fernandez Rodriguez, Rodolfo; Li, Nan; Hung, Hsien-Chih; Venkataraman, Anuradha; Nordstrom, Richard; and La
Rosa, Andres H., "Near-Field Acousto Monitoring Shear Interactions Inside a Drop of Fluid: The Role of the Zero-Slip condition"
(2016). Physics Faculty Publications and Presentations. 251.
http://pdxscholar.library.pdx.edu/phy_fac/251
This Post-Print is brought to you for free and open access. It has been accepted for inclusion in Physics Faculty Publications and Presentations by an
authorized administrator of PDXScholar. For more information, please contact [email protected].
Authors
Xiaohua Wang, Rodolfo Fernandez Rodriguez, Nan Li, Hsien-Chih Hung, Anuradha Venkataraman, Richard
Nordstrom, and Andres H. La Rosa
This post-print is available at PDXScholar: http://pdxscholar.library.pdx.edu/phy_fac/251
Near-field
N
ea
acousto monitoring shear interactions inside a drop of fluid: The role of
the zero-slip condition
Xiaohua Wang,1 Rodolfo Fernandez,1 Nan Li,2 Hsien
Hsien-Chih
Chih Hung,1 Anuradha Venk
Venkataraman,1
Richard Nordstrom,1 and Andres H. La Rosa1, a)
1
1
2
Department of Physics, Portland State University, P.O. Box 751; Port
Portland,
rttland
nd, Oregon
O ego 97207
Or
Bronx Science High School, 75 West 205th Street, Bronx, NY 10468
68
68
A full understanding of nanometer-range (near-field)
(neaar-ffiieelld)
d) interactions
iin
nteeraactions between
betw
mesoscopic
two sliding solid boundaries, with a mesoscop
oppic
ic fluid
id
d layer sandwiched
sandwiche in
particular,
between, remains challenging. In particu
ccuuularr, the
the origin
th
orrigin of the blue-shift
ori
blue-s
when
resonance frequency experienced byy a laterally
l tera
la
rall
ra
lly oscillating probe w
problem
approaching a substrate is still a matter
m ttteerr of
ma
of controversy.
co
ontroversy. A simpler prob
with a
is addressed here, where a laterally
lateera
rall
rall
lly os
ooscillating
scciillllatting solid probe interacts wi
rests
identifying
more sizable drop of fluidd that
that
th
at res
sts
ts on
o a substrate, aiming at identify
interaction mechanisms
mss that
t att could
th
coouuld
ld also be present in the near-field
near-f
interaction case. It iss fo
ffound
ounnd th
haatt th
he inelastic component of the probe-f
that
the
probe-fluid
interaction does not constitute
co
ons
nsti
titute
tuttee the main energy-dissipation channel and
tu
has a weak ddependence
eep
pende
ende
en
denc
n e on fluid’s viscosity, which is attributed to the
signal
zero-slip hydrodynamic
hydroddyn
hy
ynami
am
mic condition. In contrast, the acoustic sig
engendered
viscosity
engender
eerred
ed by
by the
the fluid
ffllui
u d has a stronger dependence on the fluid’s visco
(attributed
also
(attri
ibuute
t d aal
lso
s to
to the zero-slip hydrodynamic condition) and correlates
correl
well
we
w
ell
ll with
witth the probe’s resonance frequency red-shift. We propose a similar
sim
mechanisms
m
ech
chan
nis
isms happens in near field experiments, but a blue-shift in the
probe’s
molecules
prob
obbee’’s resonance results as a consequence of the fluid molec
((subjected
suubbjjected to the zero-slip condition at both the probe and substrate
subst
boundaries) exerting instead a spring type restoring force on the probe.
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
II.. INTRODUCTION
IIN
N
Quartz tuning forks (QTF) have been successfully incorporated into scanning probe
microscopy (SPM).1,2 Upon electrical excitation, the piezoelectric property of the QTF allows
setting its two tines into lateral oscillations, one of which carries an attached probe (typically few
millimeters long, ~100 Pm wide but tapered to an apex of nanometer-sized
nanomeeter
ter-si
te
s zed radius).
ra
A probe
approaching a sample (referred here as a substrate with its nat
tuurrally
ally ad
al
dso
sorbe
rb fluid layer3)
rb
naturally
adsorbed
experiences near-field “shear-forces” that significantly affectt the
the TF
th
TF oscillations
oscillati
(near-field
refers here to the nanometer probe-substrate separation ddistance).
isttaanc
is
n e)
e). Th
The
he perception
perc
that an
strong
adsorbed fluid layer of few nanometer thickness can exert
exer
errt such
ssuuch
uchh a st
trong
ro effect oon a millimeter
ro
confined
size probe springs from the fact that, as it is well known,
know
ow
wn, co
onnffin
fiin
ned
e mesoscopic fluids display
relaxation
properties quite different than the bulk (namely, enhanced
en
nhhaanc
n eed
d shear
she
heaarr viscosity, prolonged
prolon
transformation).
time, confinement-induced phase transformation
n).4 However,
Howev
veerr,
r the exact nature of
o the near-field
“shear forces” and the involved striking pproperties
roope
pert
r iess of
o mesoscopic fluids are not yet well
understood.
The dynamic behavior of mesoscop
mesoscopic
opic
op
ic ffluids
luid
lu
ds trapped
ttrr
between the boundaries of a probe and
involving a more
substrate is indeed complex. But if
if we
w focused
foc
ocused instead on the interaction inv
sizeable volume of fluid (few P
PL
L)),, the
tth
he complexity
comp
co
mplexity will be reduced considerably, sstill we may be
able to identify a subset of characte
characteristics
teeri
teri
rissttics
ics also present in the mesoscopic-volume near-field case.
ic
Herein we describe a sys
systematic
various sizes and
ste
tematiic im
iimplementation
mplementation of such tests, using probes of va
fluid droplets of vario
various
viscosities.
ouuss visco
coosi
siti
ties
es. What type of responses from the probe and the
t fluid would
we see by inserting
the fluid in these
ngg tthe
he probe
prro
obbee tto
o various immersion lengths? What is the role of th
interactions, an
and
the
parameters (shift in
nd how
how
ho
o does
ddooes
oe th
he fluid response relates to the probe’s physical para
resonance fr
volume affect the
ffrequency
req
req
quenc
uueennccy
c for example)? Would a change of the droplet volu
results? Up
Upon
pon
on pperforming
erfo
orm
rming these tests, what responses could we infer if an actual
actua surface were
placedd closer
the results from
clo
loser to
to tthe
he probe? Could these insights be extrapolated to interpret th
mesoscopic
meeso
sossccop
coppiicc fluid
flu
luid cases? These are the questions addressed herein.
lu
A new
typical QTF-SPM)
n w feature in the measurements reported here (but no present in a typi
ne
involves
iin
nvolv
voolv
ves using an acoustic transducer to monitor the droplet fluid response (in addition to the
QTF
QT
TF signal that monitors the probe’s oscillation amplitude). The combined QTF
QT and acoustic
5
sensing strategy has been called Shear
Shear-force
force Acoustic Near-field
Near field Microscopy (SANM).
(S
From
near
nne
ear field measurements6,7 it is known that typically the acoustic signal strengthens as the QTF
signal weakens, however the vertical range of comparison is obviously limited. By using instead
a drop of water one has the ability to achieve deeper immersion into the fluid and, thus, could
allow making a clearer correlation, if exists, between the QTF and acoustic signals.
si
Possible
factors such as damping, mass loading, and energy transfer, will be discussed
dis
di
issccus
u sed in the context of
synchronous measurements of changes in amplitude, resonance frequency
freq
eeq
que
uennccy shift,
shiiffft,
sh
t and
a in response
to variations in probe diameter and fluid viscosity.
II. EXPERIMENTAL DETAILS
A. Control variables
Table 1 shows the set of variables investigated too ev
eevaluate
valua
uate
ua
te ttheir
hheeir influence in the probe-fluid
interaction. The primary variables, namely the pr
pprobe
roobbe ddiameter,
iam
meter, probe’s immersi
immersion length, and
fluid’s viscosity, were chosen as they were a pr
ppriori
riio
oori es
sttiima
m ted to have the best chance
ch
estimated
to exhibit
parameters
volume and water
tangible consequences. The secondary pa
ara
r am
meete
terrss li
llike
lik
ikkee driving force, fluid volu
reproducibility of the
evaporation time were investigated inn or
oorder
deer to
der
to verify the stability and reprodu
results.
Each test followed a preparation
n of
of tth
he ssa
am
mp
ple surface, adding a water droplet, submersion
sub
the
sample
of the
probe into the droplet, and measur
urrem
emen
nt with the SANM system. The hydrophilic
hydrophil character of
measurement
atomically flat mica allowed
allow
wed
ed aan
n eea
asy spread of the fluid on the surface (still formi
easy
forming droplet-type
geometry). The fiber pr
pprotruding
rotrudi
dinngg ffrom
di
rroom one of the QTF’s tines is dipped into a droplet
drop of glycerol
aqueous solution ((~5
~5 P
~5
L in
n vvolume)
olume) placed on a mica disk. The submersion
submersi
PL
length was
controlled using
ngg a sset
e of
et
of fi
ffine-pitch
ine-pitch
i
screws (100 TPI precision, 7 Pm travel per 10o turn, AJS1002 from Newport),
New
ew
wppoort)
rt),
rt
), complemented
complemented with the nanopositioning stage (Nano-OP65, 65 Pm range
linear motion,
mot
ottio
otio
ionn,, 0.13
0.133 nm precision; from Mad City Labs, Inc.) built into the
th SANM. All
experiments
reported
experi
iments rre
epo
port
rted herein were performed under ambient temperature ~23 °C
° and relative
humidity
hu
um
miiddiity
y of
of ~45%.
~445
~
45%.
Table
Ta
T
a
ab
1. Test Program
Figure
Fi
Control Variable
Tests series
Fig 2
Depth of probe in water droplet
Fig 3, 4
Probe diameter
Fig 5, 6
Viscosity
Fig 7
Fig 8
Fig 9
Driving force
f
dependence
Water evaporation time
Water volume.
Table 2. Baseline Parameters
Probe diameter
Probe mounting
Nominal QTF AC voltage excitation
Glycerol concentration
Spectra recording time
Depth 0-, 0+, 10, 20, 30, 40, 80,
120, 160, 200, 240, 280 Pm
125, 114, 98, 81 Pm
m
Water droplet of 00%
0%,
%, 30%, 440%,
50% glycerin cco
concentration
onnccen
c nttrraattion
t
125 Pm cy
cylindrical,
ylliind
n rica
caal,
l optical glass fiber
fib
Outside
Outsid
iidde one
one of
of the
the
he QTF prongs
400 m
mV
Vrm
amplitude
a
am
m
mpl
pl
p
l
itude
rms
ms
ms
0%
%w
w.t.
.t. (i.e.,
.t
(i.
i.e.,., 1100%
00% distilled water)
20 s
20
B. Probe Fabrication
(520-TFC3X8-X,
12.5
We use commercial QTF (520-TF
FC3
C33X8
X88-X
X
X,, 12
2.5 pF, from Mouser Electronics) with nominal
frequency of 32768 Hz, and with
wiith
h a calculated
caallccu
ullaatteeedd spring constant Kstat
(E/4)
(E/4)w(t/L)
E w(t/
t/L)3 = 26 u 103 N/m
prong’s
dimensions
(the value obtained using the prong’
g’’s ddi
ime
m nsions L = 3.8 mm, t = 0.6 mm, and w = 0.35 mm, and
modulus
E=
the quartz elastic modulu
uuss E
= 7.
77.87
.87
87 1010 N/m2). After mounting the probe, the mec
mechanical quality
factor Q fall around 11003. For
Foor cco
constructing
onstructing the complete probe, the QTF is rem
removed from its
vacuum lid and a ccleaved
leav
le
a ed
d ooptical
ptica
pt
iccal fiber (SMF-28 Corning) of ~ 3 mm in length and 125 Pm initial
mm beyond the
diameter, is glued
glu
lu
ued
d to
to one
onne of
o the QTF prongs; the fiber purposely protrudes ~1 m
can
prong so it cca
an bbee ppartially
artially immersed into a drop of liquid. For the purpose of additional tests
etching
presentedd herein,
here
he
ere
rein
in,
n we
we also
also prepared glass fibers of reduced diameters through a chemical
ch
process
that
proces
ss th
hat uuses
sees bbuffered
uffered hydrofluoric acid (BHF) solution.8 By using BHF ssolution with a
vo
volume
olu
um
mee ratio
raattio
tio
io of
of NH4F: HF: H2O
2:1:1, the fiber becomes uniformly thinner.
C.
Liquid
preparation
C Li
L
iqu
quiid
dp
reparation
Glycerol-water
calculated weights of
Glyc
Gl
ycer
ero -water solutions of different viscosities were prepared by mixing calcula
erol
glycerol
glyc
yccer
e ol and distilled water as followed from the literature.9,10 For pure water (0% glycerin
concentration): density U 0
997.34 kg/m3; dynamic viscosity J 0 1.005 centipoise, where 1
centipoise
cce
ent
= (cP) =10-3 N s/m 2 . For 50% glycerin concentration: U50 1129.65 Kg/m3 and
J 50 6.000 cp.
D. Description of the Experimental Measurements
5,6
6
em
m5,6
ccombines
co
om ine synchronous
omb
The Shear-force Acoustic Near-field Microscopy (SANM) system
detection of two signals, i) the electrical QTF signal (the current measured
measur
me
assur
ured by th
the lock-in #1 in
oscillation
in Results
Fig. 1) from which one can retrieve the probe’s amplitude of osc
s il
illa
lattiion
ionn ((as
a described
as
descr
section below), and ii) the acoustic signal (the current from
m tthe
he acoustic
he
acco
ouusstiic tr
ttransducer
ansduce monitored by
droplet. Both are
the lock-in #2) that measures the acoustic signal generated
gene
neraate
ne
ted at
at tthe
h liquid dro
he
partially-immersed
acquired simultaneously while a cleaved optical fiber
fibeer os
ooscillates
ciillllat
at s llaterally
ates
aterally and part
aqueous
mixture
in the fluid. Here the fluid is a droplet of glycerol aqu
aq
quueeou
ous mi
m
ixture (~5 PL) placed on a mica disk
film
involved
measurements.)
substrate (which contrasts with a “mesoscale” fluid
f uiid ffi
fl
illm
m iin
nvolved in near-field m
The configuration of the experimental setup iss shown
ssh
how
wn in
in figure
figure 1.
The most general observed behavior
oorr ((as
ass w
will
iilll
l be
be shown in more detail in the nnext sections) is
amplitude
signal
a QTF signal (the probe’s amplit
ittud
u e of
of ooscillations)
sscciilllations) decreasing while the acoustic
a
(response from the fluid) gainingg strength
stre
reength
ngth
ng
th aass th
tthee probe progressively gets immerse
immersed into the bulk
liquid. At a given immersion length,
leeng
ngtth
ngth
h, bo
bboth
oth
t signals are recorded across the frequ
frequency spectrum
while driving the QTF with
th a hharmonic
th
ar
armoni
ar
ic voltage of constant amplitude. The individual
individ spectra are
then analyzed for peak
k ffrequency,
reequ
quen
e cy
y, mechanical quality factor Q, and resonance frequency
fr
shifts
relative to baselinee conditions.
coonndi
dittiiions.
ss.. S
ince the electrical detection of the probe’s amplitude
am
Since
has a
drawback in the QTF’s
QT
TF’
F’s inhe
in
nhe
herent capacitance (which modifies the spectral response
respo
inherent
and, thus,
does not refle
leect
ct aan
n accu
urraate measurement of the QTF’s prongs oscillation am
reflect
accurate
amplitude),11 the
RLC
spectrum is
is ffit
it to
t aan
n RL
R
C equivalent circuit in order to separate out the capacitance
capacitan contribution
more
and thus
us ccalculate
us
a cu
al
ula
latee m
ore accurately the probe’s amplitude of oscillation.12,13 This procedure
p
gives
a curren
current-to-amplitude
eennt-to-am
am
mppllitude calibration factor of 2.5 nA/nm.5
Sensing the fiber’s
lateral oscillations
amplitude
Z coarse
positioner
Fiber
glass
Frame
Lock-in #1
125 Pm
Z nanopositioner
Tuning
fork.
Ref.
Liquid
ddroplet
l t
Lock-in #2
Interface
Water
W
Sensiingg tth
Sensing
the
he
acoustic em
misssion
emission
liqquuiid
from the liquid
Mica
disk.
Fraame
Frame
a)
b)
Near-field
setup. b) Optical
Fig. 1 a) Schematic of the Shear-force Acoustic
Acoust
sticc N
st
ear-fi
ea
fiielld Microscope (SANM) setup
immersion
image of a cleaved fiber probe right after its
itts im
mmeerrssiio
on in
int the the fluid.
into
Due to the lateral motion of the
he probe,
pro
robe
ro
be, an
be,
an acoustic signal is generated insi
inside the droplet,
which couples to the substrate aand
ndd rreaches
eeaach
ches
hes
es tthe
he acoustic transducer (SE32-Q sen
sensor of 10 mm
diameter sensitive area, and cust
tom
miz
ized
d ffor
o maximum response near 32 kHz; from Score Atlanta
or
customized
Inc.) The substrate and the
he aacoustic
he
cous
co
ustic se
ensor are in intimate mechanical contact. It iis observed that
sensor
the response from both
th
h sensors,
sen
en
nssoors, the
the QTF and the acoustic transducer, vary lin
linearly with the
amplitude of the ac driving
drivin
dr
iv
ving
ing voltage,
in
volt
lttag
age, as described in more detailed in the Results section
se
below.
III. The ADDITIONAL
ADDI
AD
DITION
ONAL INERTIAL MASS MODEL
ONA
A. Sim
mple harmonic
haarrm
moon
nic oscillator model of the QTF probe
Simple
A ttu
tuning
uni
ning
ng fork
foorrk vibrating with limited or negligible interaction with an external environment is
us
usually
sua
uall
lly well
lly
well
we
l described by analyzing the motion of just one of its prongs as a cantilever
c
beam
vibrating
vvi
ibr
brat
atin
atin
i ng
2S f n
in
flexure.
The
eigen-frequencies14,15 of
such
a
system
aare
given
by
(D n / L) 2 ( EI//UA)1/ 2 , where the cantilever dimensions are T, W, and L (th
(thickness, width,
length of the individual prong), A=WT is the individual prong’s cross section area, E and U are
tthe
th
he elastic
e
constant and density of quartz respectively, and I the areal momentum of inertia. The
values of
D n are determined by the expression imposed by the boundary condition
(cos D n L)(cosh D n L) 1 0 .
B. Interaction of the probe with a fluid described in terms of an additional
inertial mass
addi
ditional
di
ti
ti
ine
However the purpose here is not to ignore the environmental surr
surrounding
but rather
rrrrou
ound
ndin
ing the
tthhe QTF,
Q
to characterize the interaction of the probe with a droplet. It turns
that the
turrns
ns out,
out, nonetheless,
noneth
frequency response of an elastic beam immersed in a viscous
constitutes
visccoouus fl
ffluid
lui
uid co
onstitute a formidable
problem.16 Even for very simple structures like beams and plates,
pla
late
tess,, an
an analytical
aan
nalytical solution
so
involves
rather complicated functions of the wavelength, freque
frequency
ency an
and
nd dim
ddimensional
di
imensional sha
shape factors.17,18
However, given the fact that the experimental results
resul
ulltss reported
repor
orte
or
ted below
bel
e ow reveal sign
signatures that can
model,
justified
be accounted by a simple harmonic motion mod
del
el, iitt iiss jju
usttiiffied then to attempt a much simpler
description as follows.
motion
When a solid body undergoes oscillatoryy m
ottio
ion in
iinside
nside a fluid medium, the
th extra energy
taken
“additional inertial
needed to keep the fluid in motion can be ta
ake
ken in
iinto
nto
o aaccount
ccount by an equivalent “add
mass 'm ” added to the cantilever oscillations,
osci
ciillllatio
attiio
ons
ns, which
which has an effect in the value of the probe’s
resonant frequencies. Assuming tha
haat the
the added
th
add d inertia is much smaller than the
ad
adde
th mass of the
that
prong, the modified eigen-frequencies
eigen-freq
eq
quenc
uenc
ue
nciiees are given by f n
| f on (1 EI/ [UA P ])1/ 2
(1 / 2S ) (D n / L) 2 ( E
1 P
) , wheree f oonn stands
stan
an
nds
ds for the eigen-frequencies outside the fluid, and P is the added
2 UA
geometry P | 2mo /L ,
mass inertia per unit
unniit length.
lleeng
ngth. IItt turns out that for a body of cylindrical geomet
where mo is thee m
mass
ass off tthe
as
hhee fluid volume displaced by the QTF prong (the factor 2 in front of this
expression
n is
is aassociated
ssocciiaate
ss
ted to a cylindrical geometry).17,18 This gives f n | f oon (1 mo
) , where
M Prong
M PProngg is
is thee mass
mass of one of the QTF’s prongs.
ma
However,
Howeeve
v r, the description above assumes that the prong is fully immersed in tthe fluid, while
in
considered a mass
in our
uurr case
caasse only part of the attached probe is immersed. Hence, if we cons
mo
'm fluid (the mass of the fluid volume displaced by the partially submerged
submerge probe) as an
th change in the
added mass whose location is concentrated at the end of the prong, its effect on the
cantilever’s resonance frequency would be greater compared to a similar mass distributed over
tthe
th
he full
f length of the QTF prong. On the other hand, it has been pointed out in the literature that,
when describing the dynamics of a QTF, the coupling between the two prongs should also to be
taken into account;19 so a mass greater than the mass of a single prong M Prong should be
considered, whose effect would be to lower the resonance frequency value.
vaalu
l e. Thus,
Thu the influence
of these two factors on the resonance frequency tend to cancel each oother;
ther
th
er; still w
we will take the
expression
f n | f on
o (1 'm fluid
M PProng
) as a cautious approximation, whose
who
hose
se accuracy
accuracy w
will have to be
verified experimentally (as we do below); for
f simplicity we
we will
willl co
cconsider
onsid
iid
der only th
the fundamental
resonance mode. But first, in anticipation to the experime
experimentally
non-linear variation of
ment
me
nta
tally
y oobserved
bbsser
e ved non-line
the resonance frequency f with the immersion length
and to emphasize
h d (t
((to
to be
b sshown
hown below), an
for
small
(compared to the length
that the approximations employed above are valid
d fo
or ssm
mal
all vvalues
alues of 'd (compare
of the TF), it is convenient to rewrite the expression
expres
essi
es
s onn aabove
bboovee iin
n the following form,
'm fluid
M Prong
'ff (d )
'
f (d )
(1)
In this expression, at a given imm
immersion
mersi
siioonn length
len
nggtth d the resonance frequency is f
f (d ) ;
an
additional immersion length ' d (c
(controlled
con
ontrol
trroollle
led by the user) produces an additio
additional fluid mass
displacement 'm fluid , which givess rise
rissee tto
ri
o a corresponding change in the resonance frequency ' f
' f ((d
d)
detected in th
the
he SA
SANM;
ANM;
NM all the quantities are subsequently updated for the next
NM
approximation. Given
Giveen tthe
he rationale
r ti
ra
tion
onal
ale and approximations that led to obtain expression
expr
(1), the
additional mass in
inertia
model
harmonic oscillator
ner
erti
t a mo
m
oode
ddeel
el is
i then basically the description of a simple harm
(SHO).
For a cylind
cylindrical
ndri
nd
r caal probe
pprrobe of radius r immersed in a fluid of density U fluid , an increase in the
immers
immersion
sio
ion le
length
eng
ngth
t by
by ' d , produces an additional displacement of fluid mass given by,
' m fluid
U flflluid ' V fluid U fluid S r 2 ' d
(2)
From
Fr
F
om
m ((1)
1) and
1)
and (2), one obtains,
M Prong
P
'm fluid
f
'
'ff
U flfluid
S r2 f
l
'd
'f
'f
(3)
All
A
Al
ll the quantities on the right side of (3) are under experimental control within the SANM
system, which provides an opportunity to verify the validity of the SHO model being used. For
measurement taken at different immersion length, we should expect to obtain a constant value
for M PProng . This is verified in the Analysis section below.
IV. RESULTS
Table 3 shows a summary of order of magnitude changes
chan
nggees in
in the
the
he probe’s
p obe’ amplitude of
pr
oscillations (an indicator of damping effects), the probe’s resonance
shift (an indicator
reeso
sona
nanc
nce frequency
nc
freq
fr
quency shi
of elastic effects) and acoustic signal (sound engender byy th
fluid
tthe
hhee flui
id an
aand
nd monitored by
b the SANM),
which were obtained from systematic measureme
measurements
meennttts pe
m
pperformed
erfor
rfoorrmed with probes
rf
probe of different
diameters and using droplets of different viscosities.
viscos
osittiiees. The
The partial results quoted
Th
quote in the table
correspond to behavior of the signals near the,
immersion length,
th
he, arbitrarily
arbi
bbiitr
traril
trar
ily selected, 160 Pm imm
among
them.
Notice
just to obtain first a rough comparison amon
onng tth
hem
em. N
otice that the values of the “resonance
“acoustic”
frequency shift” in column-3 and the “acou
ouusstttic
i ” si
ic
ssignal
sign
iggnnal in column-5 are somewhat
somewha close to each
oscillation”). This
other, but both are quite different than the
the values
th
vvaallu
ues
es in column-4 (“amplitude of osc
these
correlation (or lack of it) among th
hes
ese three
th
hrreee signals turns out to be consistent across the full
Pm,
range of immersion length, 0 to 280
22880 P
m, aass will be shown below.
m,
Table
T
Ta
ab 3. Test Results
Figure
Fig
Fi
Fig
g2
Figs.
3, 4
Figs.
5, 6
Fig. 7
Fig. 8
Fig. 9
Control
Variable
Increasing
“immersion
eso
length d” of the
probe in water
droplet.
Probe diameter
Droplet
viscosity.
Driving force
Water
evaporation
time
Water volume
Resonant
Frequency Shift
QTF resonance freq.
aand
d acoustic
acous c pea
peak
freq. shift together.
Oscillation amplitude
Acoustic
Resonance amplitude
p
Peak amplitude
At d = 160 Pm:
45% rate reduction
in frequency shift
per immersion
length due to a 58%
decrease of probe
cross section area.
At d = 160 Pm:
m::
Amplitude decr
decreases
reeaasees
2% more per
peer
p
immersion len
le
length
ength
h duee
to a 35% de
decrease
d
eccrrease
easee in
ea
n
probe
prob
be diameter.
diameter
dia
di
eteerr.
et
At d = 160 Pm:
At
67% rate reduction in
aacoustic
ac
oustic signal per
iimmersion
im
mersion length due
to a 58% decrease of
probe’s ccross section
area.
ar
At d = 160 Pm:
10% rate increase of
frequency shift
caused by
a 500 % increase in
n
viscosity.
y.
At d = 16
At
160
60 Pm:
Pm:
Am
A
mp
plliittudde decreases
decreases
Amplitude
2% less
2%
le s p
le
per
pe
er iimmersion
mmersion
length
le
eng
ngth
t when the
viscosity
visc
vi
sco
ossit
sit
ity increases by
500%.
At d = 160 Pm:
20% rrate increase
in acou
acoustic signal
due to
du
a 500% increase in
viscosity.
visc
None.
Non
nnee.
None.
None
N
None.
N
No
onneee.
None.
None.
N
None
No
N
one
ne
None.
None
N
A. P
A.
Probe immersed in a droplet of pure water
Fig. 2 shows few representative spectral responses from the QTF and the acoustic sensor,
both acquired simultaneously with the probe immersed in a drop of water.
Mica Disk
Fig. 2 Effects
Effe
Ef
fects off probe immersion in a drop of water. a) Few representative
repre
electrical
QTF
elec
cttrricall Q
QT
TF spectra, and b) corresponding SANM acoustic response from the
fluid,
immersion
flui
uiid, for
uid
fo a probe
fo
probe of 125 Pm diameter at 40, 120, 200, and 280 Pm im
pr
lengths
respectively.
frequency. c)
lle
ennggthss rre
esp
spectively. Notice that both signals peak at the same frequ
Calculated
Ca
C
alc
l ullat
at
ated
mechanical oscillation-amplitude spectra obtained from a) after
removing
re
emo
m vviing the effect of the QTF’s intrinsic capacitance (as described in the text); the
right
righ
ri
gghht vertical axis uses a 2.5 nA/nm calibration factor.
Notice
the same
N tice that at each immersion length the peak frequency of both signals experience
No
exper
m
negative shift
shift. (A similar feature is also observed in near-field measurements of mesoscopic
fluid
films using a SANM system, except that the frequency-shift is positive).5 The figure also shows
tthat
th
haatt at deeper immersion lengths the QTF peak amplitude decreases while the peak of the
acoustic signal increases. For comparison, in the near field case a similar trend is observed at
large probe-sample distances, but at smaller separation distances both decrease;6 the latter can be
attributed then to effects caused by the substrate.
The results presented in Figures 3 and 4 confirm further that the signals
siign
gnals vary monotonically
and with smooth variations in the slope (i.e. non-linearly) over the entire
ent
ntirre 0 to
ntir
o 2280
8 Pm immersion
80
range. For comparison, in the near field case the variation in sslope
loppee iiss not
lo
not that predictable
p
and,
occasionally, abrupt changes are observed.20
B. Effects of Probe Diameter
Figures 3 and 4 show the changes in resonan
resonance
frequency
resonance oscillation
nce fr
nc
reque
eeq
quueenccy shift and resona
positioned
lengths inside a
amplitude for probes of different diameter posit
ittio
ione
n d at
at vvarious
a ious submersion le
ar
pure-water droplet. Each of the four traces corresponds
c rr
co
rreesspo
p ndds to a new probe attached to a different
correspondingly
QTF, which in general resulted in corr
respo
ponndding
in
ngly
ly different
different initial resonance frequency and
resonance peak amplitude. For each aapproaching
pppprrooacchhiinngg step, a CCD camera allowed observing the
contact
instant when the fiber probe gets iin
n cco
onttac
act with
act
wiitth
h the water boundary (as shown iin Fig. 1b); this
the
vertical position is defined as th
he d
iimmersion
mme
m rsion length.
0 im
One parameter of interest is the negative
neeg
gattive resonance frequency shift (colloquial
(colloquially referred here
also as “red shift”) experienced
expper
erienced
ie ed
ie
d bby
y the probe as it gets progressively immersed into a ~5 PL
water droplet. The shift
tracked
when the probe
shi
hiift
ft is ttr
raccke
rac
ked relative to the resonance frequency measured w
ked
is completely withdrawn
with
th
hdr
draw
a n from
froom
fr
m droplet (a location referred to as d
0 ). The slope
sl
of a given
frequency-shitt trace
trace
ce changes
cha
haang
nges
e with immersion length. At d~160
d
Pm, the rates of change
ch
are 20 Hz
and 11 Hzz per
per every
ev
veerry 100 Pm immersion length for the 125 Pm diameter and 81
8 Pm diameter
probes,, respectively.
resp
re
speecctiveelly
y. This represents a 9/20 45% rate reduction in frequency
freque
shift per
immer
immersion
rsio
rs
ion length
leength
ngth
ng
h caused by a 58% decrease in probe’s cross section area. Figur
Figure 3 also shows
th
that
hat
at the
the
he rat
rate
atte at
ate
at which the probe’s frequency redshift changes per immersion length is the same as
thee rra
rate
which
tth
attee aatt w
ate
hich the corresponding acoustic signal peak frequency changes.
Immersion Length (Pm))
Immersion Length (Pm)
(
Fig. 3 Effects of probe diameter oon
n tth
the
he ma
m
magnitude
agn
gnitudde of the probe’s resonant frequ
frequency shift
the acoustic
(left) and on the corresponding
g magnitude
maag
gn
nit
itud
itud
ude of
ude
of the peak frequency shift of th
response (right), at various immersion
imme
meers
rsiioon length
rsio
leen
ng
gth in a pure-water droplet.
In Figure 4, the diagram on the
he lleft
he
eefft shows
s ows the mechanical resonance amplitude
sh
amplitu at different
resonance-amplitude
immersion lengths for probes
prrob
obess of
of different diameters. Notice the rate of reson
reduction per immersion
immersio
io
on length
leng
nggth
th iss practically
practically the same for each probe. Indeed, at d ~ 160 Pm the
thinnest probe decreases
deccrreeasseess bbarely
arreelly 2% more in amplitude than the thicker probe
prob per 100 Pm
immersion depth.
dept
pptth.
h. In
In contrast,
con
ontr
nt astt, the rate at which the acoustic signal changes has a much stronger
the
dependence oon
n tth
he pprobe
robe diameter, as revealed by the diagram on the right side of Fig. 4. One
observes a 67%
67% rate
tee increase
increase in acoustic signal per immersion length when comp
comparing the cases
for th
the
he thin
tth
thinnest
hinnest
stt (8
((81
81 Pm diameter) and the thickest (125 Pm diameter) probe. There
81
T
is then a
ma
markedly
ark
rkeed
dly
y difference
difffe
ference between the light damping effects on the probe (which
(which, in a simple
harmonic
amplitude) and the
ha
armonic
rrm
m c motion
motion model, is revealed by the changes in the probe’s oscillation amp
strong
interaction.
stro
st
tro
rong
ong
ng acoustic
accou
o stic response from the fluid, both caused by the probe-fluid interaction
IInn the reported acoustic traces, each value (output current from the acoustic transducer) has
been normalized with the corresponding probe’s oscillation amplitude (output current
cu
from the
tuning fork sensor), hence giving values in “normalized acoustic units (A/A)”. This
normalization
nno
orrm
m
procedure allows comparing the strength of the acoustic signal obtained at
different immersion lengths as if the probe were oscillating with the same amplitude in each
single measurement. (The experimentally observed linear response of the acoustic sensor with
the probe’s oscillation amplitude, addressed in Sections IV.D below, justifi
justifies further this
normalization procedure).
Immersion
Immersio
on L
Length
ength (Pm)
Immersion Length (Pm)
diameter
Fig. 4 Effects of pprobe’s
robe’s
ro
’ss dia
iam
ia
metteer on the probe’s resonance amplitude (left) and on the
me
t acoustic
signal responsee ffrom
pure
water
rom p
pu
ure w
ure
aatter droplets (right) at different immersion lengths.
C. Effectss of
of flu
fluid
uid
d vviscosity
iscosity
is
Figu
gure
gu
re 5 shows
sshhow
ws an increase in the the magnitude of the shift in the probe’s
pro
Figure
resonance
frequency
freque
ennccy (diagram
(diiag
agram on the left) and in the fluid’s peak frequency acoustic response
respon (diagram on
th
he right)) when
whhen the viscosity of the droplets increases. The results were obtained using
w
u
the
a probe of
Pm
1125
12
25 P
m di
ddiameter.
iameter. At d = 160 Pm the changes in frequency are approximately 20 Hz and 25 Hz
pper
pe
er every
ev
very 100 Pm immersion length for the droplets of 0% and 50% glycerin concentration
respectively.
resp
pectively. In the latter case we have to factor out the frequency increase due
du to the larger
density of the more viscous fluid, which results in a net 22 Hz increase instead (just due to
21
vviscosity)
vi
isscco
. The 2 Hz difference reflects a 10% difference in frequency-shift due to a change
from 0% and 500% glycerin concentration. Changes in the peak frequency for the acoustic signal
are shown in the right side diagram of Fig. 5; notice it is practically a replica of the diagram on
the left.
Immersion Length
Leng
gth ((Pm)
Pm)
Immersion Length (P
(Pm)
Fig. 5 Effects of droplet
drop
op
ple
let viscosity
viisc
scos
o ity on the magnitude of the probe’s resonant ffreque
frequency shift
(left) and on the co
corresponding
in its
orressp
po
ond
n in
ng frequency at which the acoustic signal registers a peak
p
fu
un
ncttio
ion
on off the
the submersion length. The diameter of the probe is 1125 Pm in
th
amplitude, as a function
all the cases..
In Fig. 6,
6, th
the
he ddi
diagram
iagram on the left shows the changes in the probe’s resonance amplitude for
droplets of
of different
difffferen
di
f eennt glycerin concentrations. Notice, the rate of amplitude reduction per
immers
immersion
rrssion length
leng
ngth
ng
th is
is practically independent of the viscosity; near d =160 Pm imm
immersion length,
there
th
heerre is
i a 2%
2% ddifference
ifference when comparing the traces corresponding to 0% and 500% glycerin
concentration.
co
onc
ncen
e trat
attiio
on. In contrast, the diagram on the right side of Fig. 6 shows a much stronger
dependence
Pm immersio
immersion length, there
ddeeppeend
nden
e ce of the acoustic signal strength on viscosity. Near d=160
d
is a 20%
2 % change in acoustic signal due to a 500% increase in viscosity, indicating that there is an
20
effective contribution from the viscous nature of the fluid to the production of sou
sound. Again, the
quoted
qqu
uot acoustic signal values are given in “normalized acoustic units (A/A)” as described in the
previous section.
Immersion Lengt
Length
th ((Pm)
Pm)
Immersion Length (Pm)
(Pm
Fig. 6 Viscosity effect oon
n the
th
he probe’s
probe’s resonance amplitude (left) and on the
corresponding acoust
acoustic
tic
ic rresponse
e ponsee fr
es
ffrom
rom the fluid (right) as a function of the immersion
imm
length using the sa
same
ame
me probe
be di
be
ddiameter
ameter in liquids of different viscosities.
D. Effect of the
th
he driving
driv
dr
i in
ing vvoltage
olta
t ge
Figure shows
show
show
sh
ows th
tthe
he response from the QTF (top graph) and the acoustic sensor (center graph)
as a function
funct
cttio
ion of
of thee driving
driving voltage set by the signal generator (see also Fig. 1).
1) The observed
linear response
resppoonsee adds
adds reliability to normalization processes of the acoustic signal ((bottom graph),
ad
where
wh
her
ere the
th
he output
oouutp
tpu
put current from the acoustic transducer has been divided by the corresponding
probe’s
pr
rob
obe s oscillation
obe’
ossci
c llation amplitude; this results in “normalized acoustic units (A/A)”.
Fig. 7 Linear rre
response
esppo
on
nse from
om
m the QTF (top) and acoustic (center) sensor
sensors to
values
increasing val
lu
uees of tthe
he ex
he
eexcitation
citation source driving voltage amplitude.
E. The effect of lliquid
iqui
iq
uid eevaporation
vaapo
poration during experiments
The result
results
ltts iin
nF
Fig.
ig. 6 ev
ig
evaluate
valuate whether or not the liquid evaporation was a det
detrimental factor
measurements.
during thee m
eassurreem
men
e ts. As the drop of liquid evaporates, the amount of liquid in contact with
which
the probe
prob
obe would
ob
wouulld decrease
wo
decrease and thus cause an increase in the probe’s resonance frequency,
de
fre
spectra of
wouldd co
cconvolute
onv
n ollut
ut the reported results. To evaluate this effect, we recorded the vibration
ute
vibr
the
and
immersion length into
th
he QTF aan
nd acoustic signals with a probe kept at fixed position (80 Pm immers
the
water
traces is 1 minute.
tth
hhee initial
in
nit
itia
ial w
ater droplet). In Figure 6, the time interval between consecutive trac
time employed to
The entire
Th
The
en
nti
tire recording lasted ~5 minutes, which is much longer than the average tim
significant change in
run a given subset of the experiments described in the sections above. No signif
the resonance frequency shift due to the evaporation during this interval of time is observed.
32100
32110
3
32
2110
Fig. 8 Multiple recordings of the QTF frequency
freq
eq
qu
ueenc
n y re
response
esp
spponse while keeping the late
laterally
oscillating probe at a fixed immersion le
length
interval
leng
eng
ngth
h in
in distilled
dis
i tilled water. The time int
between two traces next to each othe
other
heer is
is 1 min,
miin
n, and
a d the entire process lasted ~5 min.
an
A more detailed position of the rresonance
eesson
onan
a cee ppeaks
e ks is shown in the inset.
ea
F. Effects of the Liquid Droplett V
Vo
Volume
olume
lum
lu
mee
The baseline test condition
use
But we wanted to
conddit
itio
tion
ion is
io
is to us
se a droplet of consistent 5 PL volume. Bu
explore whether the ex
volume
frequency shift of the
eexact
xact vvo
o m could have an effect on the peak frequenc
olume
acoustic response, aan
and
nndd hence,
hheenncce, affect
affffect the reproducibility of the results reported above.
abo Also, using
droplets of differ
different
volumes
distances from the
eren
er
ent vvo
olu
um
mees places the air-fluid interface at different dista
substrate, which
whi
hiich
ch allows
alllo
lo evaluating
lows
evaluating a potential influence, if any, of the substrate oon the reported
results. Figure
responses when using
Fiig
guure 9 sh
sshows
how
ows the reproducibility of the QTF and acoustic respons
different
volumes
differen
ent
en
nt dr
ddroplet
ropple
let vvo
olumes (5 PL, 7.5 PL, 10 PL. 12.5 PL and 15 PL). In each case a 125 Pm
diameter
diam
aam
meetter
er pprobe
robe
bee was submerged 80 Pm into the droplets. No effect of the droplet volume on the
resonance
re
essooonancce fr
ffrequency
equency is observed.
Fig. 9 QTF electrical response and fluid’ss ac
aacoustic
oust
ou
stic res
response
essponse from droplets of different
differ volumes.
V. ANALYSIS
A. Signatures of simple harmo
mo
on
niic ooscillatory
ssccil
illa
lla
attoory motion in the probe’s response
harmonic
Figure 10 shows response
ses from
se
m tthe
he Q
he
TF sensor, which reveal the probe behaves
beha
responses
QTF
as a simple
harmonic oscillator (SHO
O). Figure
F guure
Fi
re 10a shows that the rate at which the mechanica
(SHO).
mechanical quality factor
Q changes with imm
mer
ersionn llength
en
nggtth iiss practically the same whether the probe is in a droplet of pure
immersion
water (1.005 centi
tiipo
pois
i e visc
vviscosity)
vi
issccos
osit
ity) or in a droplet of 50% glycerin concentration ((6.00 centipoise
centipoise
viscosity). Thee results
resu
resu
re
sult
ul s suggest
suuggggest that viscosity does not play a significant role as energy
ene
dissipation
channel in tthe
hhee pprobe-fluid
robe-fluid interaction. A plausible explanation considers the liq
ro
liquid molecules
adhering to
to the
tth
he surface
surf
rrffac
a e of the laterally oscillating probe upon its entrance into the droplet (a
manife
feestationn of
of the
tth
he zero-slip hydrodynamic condition effect, which happens to be
b valid also on
manifestation
hy
yddrrop
ophoobic
bic ssu
bi
ubstrates22). In consequence, the amount of liquid set into motion ((and eventually
hydrophobic
substrates
constituting
co
onssttiituti
i inngg a wave traveling in a direction transverse to the lateral oscillations) resides mainly
inside
iin
nsiidee a boundary layer surrounding the probe. That layer has a viscosity-dependent
viscosity-depende thickness of
just
ju
ust
st a few micrometers (as estimated in Section V.E below). The small value oof the boundary
layer’s thickness (compared
m
slidin motion at the
to the probe diameter) and the lack of relative sliding
solid-liquid
sso
olliid
interface (which otherwise would affect the probe’s amplitude more strongly)
diminishes the damping effects of viscosity.
p
p to pput in context the role of microscopic
p friction in the
This interpretation
also helps
implementation of the zero-slip condition. As currently accepted, the energy
ene
neerrg
gy dissipation
dissip
raised by
the viscous resistance is at the mesoscale (of the order of the bounda
ary
ry layer’s
layyeer’s thickness),
la
th
boundary
while
that raised by the molecular friction, i.e. liquid molecules adsorb/desorb
adsorb/de
ddeessooorb
b oon
n sol
lliid atoms, is at the
solid
microscale.23,24 First, the independence of amplitude dampingg per
p r immersion
pe
iim
mm
meersio
rrssion
io length
io
leng on viscosity
indicates that the zero-slip condition is strictly in place; oot
otherwise
thheerw
e wisse (a
((as
as argued aabove) a higher
change in amplitude
viscosity would cause a higher damping rate. Second, th
tthe
he ob
oobserved
serv
rvved
ed larger chang
when the probe just gets immersed into a fluid of hhigher
igghe
her viscosity
vviisc
s oossity (as indicated by the arrows
the
microscopic friction.
along the horizontal axis in Fig. 10b) illustrates
illustratees fu
ffurther
urt
rrtthe
her tth
he
h effects of micros
Notice, more energy is dissipated on the 50% gl
gglycerin
lyc
y errin
in fluid
flu
luiidd (amplitude deceases ddown to ~30%)
(amplitude
decreases
compared to the immersion in pure water (am
mpplliittud
de dec
dde
ecr
creases down to 50%).
damping
The weak effect of viscosity on dampin
in
ng on
oonce
nce
ce tthe
he probe is immersed into the few micro-liter
he
volume fluid (as reported here) contrasts
contrast
stts with
with
wi
th iits,
ts,
ts
s, cu
ccurrently
rrently controversial, role on tthe dynamics of
some
reports
mesoscopic fluids. On one hand, so
ome
me re
epo
ports suggest that viscosity increases as
a the fluid gets
progressively more confined.255 Two
Tw
woo re
rrelated
elaate
ted mechanisms may contribute to th
this increase in
viscosity. First, the small probe-substrate
pprrob
obe-subsstr
traatte gap (< 15 Pm) compared to the 125 Pm diameter of the
Ref.
causes
probe (as in the case of Re
R
eff.. 25
225)) cca
aus
u es constrains in the motion of the confined fluid.
flu Also, since
the
thickness
such a small gap falll iin
n th
he th
hicckn
knness range of the fluid boundary layer, the probe
prob and substrate
adhesion
boundaries may have
hhaavvee a significant
siiggnnif
ifiiccant
c
effect of the dynamics of the trapped fluid. Second,
Se
molecules
forces attract the
th
he fl
ffluid
luuiid
i mo
m
olleecules
e
towards the probe and substrate solid boundaries (imposing the
inside the gap. Both
zero-slip hydrodynamic
hyd
yyddrody
dynnaamic condition), which results in larger velocity gradients insid
viscosity” much larger
mechanisms
mss may
maay contribute
m
co
onnttribute to have a mesoscopic fluid with an “effective viscosit
than the
thhee viscosity
visccos
o itty of bulk fluid. On the other hand, there also exist reports claiming that
confinement
does
co
onnffin
nem
men
ent ddo
ent
oes not affect the viscosity of mesoscopic fluids at all.26 A res
resolution of this
cont
nttrroove
v rssy has been presented more recently based on experiments that test tthe behavior of
controversy
mesoscopic
probe) at different
me
m
eso
sosc
ossccop
o ic fluids (confined between a mica surface and a silicon-oxide prob
confinement
co
onnffin
fi ement speeds.27 No variation in viscosity is observed due to both co
confinement and
molecular ordering near an atomically flat surface when the mesoscopic fluid is probed at high
sspeed
sp
peeee (1.5 nm/s confinement rate). At this high speeds, when molecules are in an ordered state
cannot easily move out of the gap as a group, thus becoming ‘‘stuck’’ and responding elastically
to external shears; i.e. the mesoscopic fluid behaves solid-like. 27 Higher viscosities are however
measured when the fluid is probed at lower speed (< 0.6 nm/s) and due to the re
restricted motion
imposed by confinement (as described at the beginning of this paragraph);
paragr
grap
gr
rap
aph); the liquid behaves
liquid-like, but with enhanced viscosity 27
Q vvss A
Amplitude
mplitud
Mechanical quality factor
6000
600
00
6000
125 Pm D
Dia
00%
% Glyy
Q
4000
40
000
Q
4000
1255 P
Pm
m Dia
0%
% Glyy
2000
0
50% G
Glyy
0
90
180
270
Immersion Length ((Pm)
Pm)
a)
50%
Gly
Gl
22000
000
0
0
0.3
0.6
0.9
1.2
Normalized resonance aamplitude
b)
Fig. 10 Variation of the mechanical
meecchanicaal qu
qquality
uality factor Q with a) probe’s immersion le
length, and b)
amplitude
probe’s resonance ampl
pllit
itude ((at
at ddifferent
at
ifferent immersion length). Two cases are presented,
presented pure water
(open circles trace)) aand
nd
n
d 550%
0%
0
% gglycerin
lycerin (solid circles trace) droplets; in both case
ly
cases the probe
diameter is 125 P
m.. The
m
Th
he arrows
arrrro
ows along the horizontal axis in 10b) indicated the normalized
Pm.
behavior in both
probe’s amplitude
amplitud
udde right
u
righht after
ri
afte
af
ter the
the tip immerses into the corresponding fluid. The beha
graphs display
displaay signatures
sign
si
g atur
attu
urrres
es off a simple harmonic oscillator motion (as described in the text).
t
amplitude (measured
Fig.
gg.. 10b
10b disp
10
ddisplays
di
isp
spllaays the mechanical Q factor as a function of the probe’s amplit
different immersion
with the
he probe
he
probe
bee first completely outside the droplet and then at a series of differ
positions)
po
ositions)
s)) corresponding to two different droplets of 0% and 50% glycerin concentration,
respectively.
rre
esp
specti
eccti
tive
vel
ely
ly. Notice the linearity between Q (~1/(damping constant)) and the probe’s
pro
resonance
amplitude
ampl
am
mpl
plituudde is maintained whether the probe is immersed or not in the droplet. That is, as far as the
probe
prob
obbe is maintained at resonance, we observe that the net damping force (F
FD ~ damping
da
constant
u amplitude ~ amplitude/Q) remains constant at different immersion lengths. It is as if the
aamplitude
am
mp
and corresponding damping constant confabulate to keep the total damping force the
same while the probe gets immersed into the droplet.14 The latter is a signature of a simple
harmonic oscillator motion (SHO). This further justifies the use of the SHO, adopted below, to
describe the additional experimental results.
B. Validation of the additional inertial mass model
Fig. 11 shows calculated values for M PProng predicted
predictted
d by
by eex
expression
xpressio (3) above,
M Prong
P
U fluid S r f
2
'd
'f
'f
, where we have used values forr 'd aan
and
nd 'f measured with the probe
water.
Calculations
placed at different immersion lengths in a droplet of pu
ppure
ure
r w
ater
at
e .C
alculations were performed for
probes of three different diameters. Notice that ffor
orr tthe
hhee pprobes
robe
ro
robe
bes of 125 Pm diameter
diame (“rhombus”
lie around
trace) and 98 Pm diameter (“triangles” trace)
tracce)
e) the
hee ccalculated
aallcu
ulated values consistently
consisten
M Prong (2 r 0.5) u 106 Kg . The case for the
he 881
1 Pm
Pm di
ddiameter
iam
ameter (“open circles” trac
trace) shows more
discrepancy, but still with a tendency
discrepancy may be
y tto
o fit ar
aaround
roou
undd a constant value. (The discre
due to the fact that, being the thinnest
prong, that fiber
thin
nnneest
e t pprobe
rroob
obbee protruding
protruding ~1 mm beyond the pr
be din
be
bend
ing, a situation
ssiituation that departs from the the assu
section may undergo additional bending,
assumed oscillation
of a fully stiff prong.)
measurement of
The calculated value ooff M PPr
Prong
Pro
ro n g turns out to be very sensitive to the precise m
ro
rong
the immersion length.
length
h. This
Thiss sensitivity
seens
nsit
siittivity is exposed by the three “rhombus” traces in Fig 11; they
purposely
were obtained byy ppu
urpos
oossel
ely in
iintroducing
ntroducing 1 Pm
uncertainty in the immersion le
length d, which
leads to an unce
uncertainty
cert
ce
rtai
aint
n y of
of 0.2 PK
Kg (see error bar segment at the bottom-left side of the figure as
values accumulate
a reference).
reference)
e). In
e)
I spite
spi
pite
te of this sensitivity, it is remarkable that all the calculated valu
around the
the
he 2 PK
Kgg mark
maark for each submersion length and for three different probes. An alternative
m
proced
duurre to eestimate
stimate the value of M PProng is to calculate the slope of the curve '
st
procedure
'ff vs 'd in Fig.
'f
11.
Forr th
the
11
1. Fo
F
he case of pure water, at d = 160 Pm the slope is equal to 'd / 'f
wh
w
which
hhic
ich
ic
ch expression
eex
xpression (3) gives M Prong
U fluid S r f
2
200 Pm
40 Hz
comparis
the mass of
2 u 106 Kg . For comparison,
one prong of the QTFs used here [of dimensions L= (3.8 r 0.01) mm, W
(0.6 r 0.01) mm; quartz density U quartz
200 P m/40 Hz , for
(0.35 r 0.01) mm, T =
2650 kg/m3] has a mass equal to M Prong
(2.1 r 0.1)
PK
P
Kg.
g Thus the value obtained from the hydrodynamic measurement matches very well the
actual mass of one tine. Beyond this surprising accuracy predicting the value for M Prong (given
the approximations made though our calculations), what we highlight here is the consistent
constant value obtained for M PProng (at different probe’s submersio
submersion
on lengths and for three
-6
Mass (x 10 Kg )
different probes), which validates the use of a harmonic oscillator mode
mo
model,
ode
dell,, eexpression
xprreessio (1).
xp
4
Estimated
t
e
TF
T
F mass
mass
3
2
1
0
0
900
180
118
80
2270
27
7
70
Immersion
Immer
rsion depth
deppth (Pm)
Fig. 11 Calculated valuee ooff the
th
he Q
QT
TF m
ass M TTF predicted by expression (1) usin
using
QTF
mass
the experimental values of tthe
hee ffrequency
h
r quency shifts measured at different immersio
re
immersion
distances. Data in
ncl
clud
de re
rresults
esu
s lts for three probes of different diameters, 125 P
include
Pm
left
(rhomboids), 998
8 Pm
m (t
((triangles),
tri
r an
ngles), 81 Pm (circles). The symbol on the lower le
indicate
that
side is to ind
nddic
icaatte
te tth
ha a 1 Pm uncertainty in the immersion length d, produces an
hat
uncertainty
uncertaint
ntty of
n
of 0.2
2 PK
Kg
g in the calculated mass. The horizontal line drawn at 22.1
PKgg is
i tto
o in
iindicate
ndica
caattee tthe
he actual mass of the TF prong.
C. Fre
Frequency
equen
e cy
y sshift
hift
hif
hi
ft values expected from the observed changes in the mechanical
mechani factor Q
In
In addition
add
ddit
itio
ion to
to the mass loading effect, a change in the probe’s resonance frequency
frequ
can occur
also
oscillator model, the
al
lssoo as a consequence of damping effects. From a simple harmonic oscilla
amplitude
amppllit
am
itud
tuudde peaks at f
'f |
'f
f o (1 1 1/ 2
) , which for fo = 32,000 kHz and Q = 2500 gives
2Q 2
'Q
Hz . Fi
H
Figure 10
10a shows
h
a change
h
ffrom Q2
106
22,500
500 tto Q1 11,500
500 when
h the probe is
submerged
ssu
ubm
from d = 0+ to d = 280 Pm. For the observed change of 'Q 1,000 , the expression
above predicts a frequency shift 'f in the order of 10-3 Hz , much smaller than the observed 10s
of Hz reported in Fig. 3. This indicates that the damping effect is not the main source for the
observed changes in the resonance frequency. Similar changes in the value
val
allue
u of Q are observed in
near-field experiments (measured before and after the tip starts to iinteract
nntter
erac
ract
c wit
with the sample’s
28
adsorbed layer) but the frequency shift is positive and of the orde
er of
of 10
10 Hz;28
this
th suggests that
order
mesoscopic
damping is not the origin of the frequency shift. In short, for thee bu
bbulk
ulk
lk aand
nd m
nd
esosco fluid cases
to the
(both treated within the SHM model), a large change in Q does
do
oes not
not
ot contribute
conntr
tri ute significantly
trib
sign
observed change in the probe’s resonance frequency.
viscosity
D. Effects of probe diameter and droplet viscosit
ty
1. Impact of probe diameter
immersion length is
Fig. 3 shows that the rate at which the
he frequency-shift
ffrreeq
que
uency
nnccy-shift changes per imme
straightforward;
greater for thicker probes. The interpretation
interpretati
tiion
on is
is st
traaig
ightforward; for larger cross section areas, a
mass
the inertial mass
larger amount of water volume and m
ass will
as
wiillll bbee driven and, according to th
w
frequency
will
volume of water
model, a larger decrease in frequenc
ncy sh
nc
sshift
hifft wi
w
ll be observed. Driving a larger vo
other hand, Fig. 4
would also cause a stronger acoustic
acou
ouust
sticc signal,
sig
iggna
n l, which is verified in Fig. 3. On the oth
na
damping effects) is
shows the rate of change inn os
ooscillation
sci
c llatio
ion am
aamplitude
plitude (which is associated to the dam
tendency
probes tested. A rate
much less pronounced, with
wiith
w
h a ten
nddeency to be practically the same for all the probe
independent
of amplitude change almost
aallmo
most
st in
nde
dependent of the probe diameter can be explained by the fact that
shaken
the probe is shake
keen la
llaterally;
ate
t raall
lly; he
hhence
ence the damping effects are caused mainly by the probe’s lateral
deeper
submerged lateral wall
walls. As the pr
pprobes
obeess get
obe
ob
ett dde
eeper immersed, all the probes increase their submerg
size in the same
ssaame aamount,
mount, hence contributing to the damping independent of their thickness.
mo
th
increase
shifts per
In short,
shoortt, an
an inc
nccre
r ase in the probe diameter produces a larger rate of frequency
frequ
immersion
invariant resonance
immers
rrssio
si n length,
leennggth
gth
h, a larger rate in increasing acoustic signal, and an almost inva
amplitude.
am
mppllit
lit
itudde.
Effects
22.. Ef
E
Effe
ffe
fec s off fluid viscosity
fect
Figures
Fi
F
gures 9 and 10 show that increasing values of fluid viscosities produce i) very small
changes in the rate at which the oscillation amplitude decreases with immersion llength, ii) large
variation
vva
arriia
in the rate at which the frequency-shift decreases with immersion length, and iii) a
stronger acoustic signal. These results provide further indication that the damping forces inside
the droplets play a weak role in the probe’s motion. The minor change in amplitude despite the
500% change in viscosity can again be explained by considering an absence of relative
rel
sliding at
the solid-water interface (the zero-slip condition). The dissipation occurs
ooccc
ccurs inst
instead within the
boundary layer that extends just a few microns from the solid probe
pro
robbee boundary
bou
ound
n a (for all the
viscosities considered here). This region is small enough that ann iincrease
nnccre
reas
ase of viscosity
visco
by 5 times
does not change the rate at which the oscillation amplitude vva
aries
rriieess. In
In ccontrast,
oonnttrrast, the larger change
varies.
in frequency-shift indicates that a greater amount of ffl
llui
uuiid is
is ddragged
ragged by th
ra
fluid
the probe when
immersed in droplets of higher viscosities. Such a featur
re is very
ry re
ry
eev
vealing. It inv
feature
revealing.
invites to consider
that a similar mechanism could also be present in tthe
he ca
he
assee ooff nnear-field
ear-field (probecase
(probe-fluid-substrate)
interactions, except that in the latter case one hass to
to ta
tak
kkee into
int
ntto account that the flui
take
fluid is not free to
move (like in the bulk state) but restricted in its
itts mo
m
tiion
on by their stronger attraction
attractio to the probe
motion
zero-slip
and substrate boundaries (fulfilling the zze
ero
r -sslllip
iip
p bo
bboundary
bou
oundary condition). When the two solid
other
restoring force on
boundaries become very close to each oot
the
h r (n
((nanometer
naan
nometer separation distances) a res
and,
frequency.
the probe could then take place and
d, he
hhence,
ncee,, ca
nc
ccause
auusse a blue-shift in the probe’s resonance
resona
Further, the reaction force on tthe
he ((viscous)
viisc
v
scoouuss)) fluid would engender an acoustic signal. Such a
correlation between the probe’s freq
ffrequency
fr
req
equenc
eque
uennccy shift and the acoustic signal from the fluid in nearue
field experiments has been
en aaddressed
en
ddre
dd
r ssed
d bbefore.
efore.5 The more systematic tests, reported
repor
here, using
fluids of different viscosities
viscos
oossiittie
ies (although
(al
a th
hough with a more sizable volume of fluid) support
supp such earlier
underscore
then
the
findings. We under
rsc
scor
cor
ore tth
hen
n tth
he effective contribution to the production of ssound from the
viscous nature off the
the ffl
th
fluid
lui
u d (t
((the
thhee higher the viscosity, the greater the volume of the dragging fluid,
acoustic
and the greater
greateer the
the aac
th
cousttiicc signal).
signal is
In summary
summ
mmarry when
mm
when
wh
heen
n the probes get immersed into a fluid droplet the acoustic
aco
consistently
greater viscosity;
consiste
tteent
ntly
ly sstronger
ttrronge
onggeer when using either probes of larger diameter or fluids of gr
on
probe’s
resonance
the ppr
rob
obe’
e s re
esonance frequency shift follows a similar trend. The resonance amplitude of
oscillation,
os
scillatio
onn,, hhowever,
owever, is weekly dependent on the probe diameter and fluid viscosity.
viscosit
E.. T
The
boundary
E
Th
he b
oundary layer effect
Ass argued above, an additional contribution to the negative frequency shift ccomes from the
A
motion of water molecules contained in the boundary layer neighbor to the probe’s walls. The
vvelocity
ve
ello
o
field induced by a probe oscillating at frequency Z / 2S establishes a wave that
propagates in the direction perpendicular to the oscillations. They are, however, rapidly damped.
The dampening is exponential, with a depth of penetration being given by,15,29
§ 2J / U ·
¨
¸
© Z ¹
1/ 2
G
(4)
where J is the dynamic viscosity and U is the density of the fl
ffluid.
lui
uid. Fo
F
For
or the 32 kHz operating
frequency in these experiments, G varies from 3 Pm to 77.5
.5 P
.5
Pm
m ffo
for
or th
the
he 0% and 50% glycerin
water
the probe a bit
concentration respectively. The motion of this extra llayer
ayer
e off w
wa
ater makes th
factor
“thicker”. The displaced mass increases by a fac
cto
or 2S rG / S r 2
wh
causes an
2G / r , which
frequency
according
additional inertial mass
increase in the change of the resonance freque
enc
ncy aac
ccorddin
i g to the additiona
model. In Section IV.C above we report 20 Hz
Hz andd 25
25 Hz
Hz increases in frequency shift, per 100
respectively, when
Pm immersion length, for the droplets of 0%
% aand
nd 550%
nd
0% gglycerin
0%
lycerin concentration resp
concentration
using a probe of 125 Pm diameter. Forr the 0%
0% co
onccentration case, the factor 2G / r is equal to 2
u 3/62.5
0.1, which gives a 20 H
Hzz u 00.
0.1
.1
2 Hz
Hz contribution to the frequency sh
shift per 100 Pm
immersion length. For the 50% glycerin
g ycceerrin
gl
rin
n cco
onc
ncentration droplet that factor is 2 u 7.
7.5/62.5
concentration
which gives 25 u 0.24
0.24,
6 Hz
H
Hz.
z. Th
The
he es
eestimated
timated 4 Hz difference matches well
w
the 5 Hz
reported
Section
experimental results repor
rte
ted
ed in
in S
ectionn IV.C.
(in
probe’s resonance
In short, the contribution
contrrib
ibuttion
ion (i
io
in the order of Hz) to the change in the prob
frequency from a bboundary
oouunnddaarry layer
laye
yyeer (whose thickness depends on the viscosity) is ddefinitely much
order of mHz, as
higher than the co
ccontribution
ont
ntri
trriibu
b tiion expected from the damping effects (in the orde
Section
estimated in S
eecc onn V.C
ection
C ab
aabove).
bbove).
Correlation
between
response
F. Corr
rrrrelat
elat
el
a io
ion be
b
etween
tw
tw
the probe’s frequency shift and the fluid’s acoustic re
The
hee results
r sult
re
ltts above
lts
ab
bove indicate that for probes of increasing diameter and fluids
fluid of increasing
viscosity
vi
issccosityy ii)) th
th rate of changes in resonance frequency and the acoustic signal with
the
w immersion
length
amplitude (ascribed to
lleng
le
enggtth
h consistently
connssistently become larger, but ii) the rate of change in resonance amplitu
co
cons
dissipative
further examine how
diss
ddi
issssipattive effects) remain approximately constant. These findings invite to furthe
close
clos
se a given pair of any of these signals correlates with each other. Such a comparison is
presented in Figure 12, which displays our attempts to a) linearly fit the decreasing amplitude of
oscillation
oos
scciil
to the decreasing frequency-shift, as well as b) linearly fit the increasing acoustic
signal to the increasing magnitude of the frequency-shift, as a function of the immersion length.
To implement this comparison, the signals were simply multiplied by a corresponding constant
factor (optimized for the best fitting) and then shifted so that the four traces could be displayed in
a single graph. The fitting process was performed for probes of three different
diiff
fferent diameters.
diam
ive ef
iv
eeffects
ff ctts sh
ffe
sshould
shou
h
According to the SHO model, signatures of increasing dissipativ
dissipative
be revealed
by a decrease in the probe’s resonance amplitude, as well as
as by
by a linear decrease
d
of the
mechanical factor Q with decreasing resonance amplitudes; tth
he la
llatter
latt
attter
er is
is indeed
indeed observed
in
o
the
in Fig.
10b above. Here we also observe that, as the probe imme
mers
r es
es ddeeper
eepe
ee
per into the droplet,
dr
immerses
both the
resonance frequency and the resonance amplitude decrease
deccr
crea
e se (Figs.
(Fig
(Fig
(F
gs. 3 and 4). But
B the results
displayed in Fig. 12 show that the frequency and am
mppllit
itudde variations
itud
vari
va
riat
ations are not relat
amplitude
related linearly (the
concavity of their corresponding traces are actual
lly
ly opposite).
oppposite)
e).
e)
). In contrast, the chan
actually
changes in acoustic
signal fit remarkably close to the changes iin
n fr
ffrequency
freque
r ueennccy shift for each of the three different
frequency shift and the
probes. Incidentally, such a correlation bbetween
etwe
et
w en
n tthe
hee probe’s
probe’s resonance frequenc
reported
with
fluid’s acoustic response has been previously
preevviiou
o slly rre
epo
p rtted in near-field experiments performed
p
the SANM system.5
-40
68
-60
A
Acoustic
cou
u i
fittin
ng
n
fitting
51
0
80
160
-80
Res. Amplitude
Amplitud (nm)
-20
85
132
0
Amplitude
fitting
110
-15
-30
88
Acoustic
Aco
coust
coust
ussti
tic
fi
itttin
ing
n
fitting
66
-45
-60
240
0
80
8
160
1 0
16
Frequency shift (Hz)
Amplitude
fitting
102
Probe Dia. 98 Pm
0
Frequency
ncy Shift (Hz)
Res. Amplitude
Amplitud (nm)
Probe Dia. 125 Pm
240
24
Immersion
Im
mmerssio
ion Length ( Pm)
Immersion Length ( Pm)
a)
b)
0
Amplitude
Am
mplitud
li ud
ude
fitting
fitt
ffi
iitt
ttin
tt
ing
140
-10
120
-20
100
80
-30
Acoustic
Aco
ou
usstic
ffitting
fi
ttiin
tt
tti
ng
60
0
0
80
160
Freq shift (Hz)
Res. amplitude (nm)
Probe Dia. 8
81
1 Pm
Pm
160
-40
240
IImmersion
Im
Imme
mm rsion Length ( Pm)
c)
Fig. 12 Traces ooff th
tthe
he probe’s
prrobe’s resonance frequency shifts (open rhombus and
p
an
well
response
open circles) fit
ffiit we
w
ellll to a llinear
i ear fitting process with the fluid’s acoustic respon
in
trace)
amplitude
(solid rhombus
rhomb
mb
bus tra
raace
c ) bu
but nnot
but
ot to the changes in the probe’s resonance amplitu
circles).
(solid circ
rccles).
le )
le
The resu
result
experimental confirmation
ultt described
des
e cr
cribed in
in the previous paragraph, together with the experimenta
of express
expression
sssio
ion (1)
(1) that
(1
th
hat
at relates the change in displaced fluid mass to the frequency shift (Fig. 11),
offers a cclear
mechanical energy
lleearr picture
pic
ictu
t re about the generation of acoustic signal: conversion of mec
from
then couples into
m the
he oscillating
he
o cill
os
llating probe into fluid motion (sound) inside the droplet (which the
ll
the
Fig. 12 indicates
th
he sample
s mp
sa
ple
le substrate and reaches the acoustic sensor, as shown in Fig. 1 above). F
that
mechanical-to-acoustic
that
th
at tthis
his m
hi
echanical-to-acoustic energy conversion is linear. It is remarkable that this linear
relationship
re
elat
lationship occurs across the full immersion length range, even at the early stages of immersion
la
(close to d
0+), where the generation of sound comes from a much (small) localized fluid
volume,
vvo
olu
and thus many other factors no directly related to fluid volume change (including
surface tension) could have also affected the frequency shift.
In the liquid droplet experiments reported here the change in the probe’s resonance frequency
is negative because the surrounded water molecules, being in their bulk state, ar
are compliant to
follow the probe’s lateral motion. We conjectured that a similar transfer
err ooff energy may happen in
near field experiments when testing the response from confined m
esos
es
oscopiic fluids.
ffllui
lu d In the latter
mesoscopic
case, however, the molecules in the fluid are not as compliant too move
movve along
alo g with the probe since
al
alon
they are instead more tightly attached to the substrate (zero-slip
(zero
(zer
(z
ero-sl
er
sllip
slip
ip condition
con
o dition effect). As a
consequence there will be a restoring force on the probe,, wh
w
hic
ich wo
w
ould
uld lead to an increase in the
ul
which
would
observed resonance frequency (instead of a negative one,
onee, li
llike
ike inn bu
bbulk
ulk
lk fluid).
VI. CONCLUSIONS
We have addressed the interaction betwee
between
een a lla
een
laterally
atera
a alllly oscillating cylindrical ffiber-probe and
a sizable (few Pl) volume of fluid. A quartz
quarrtz
tz tuning
tun
unin
ng fork
f rk
fo
k (TF) sensor monitored the response from
oscillation
an acoustic
the probe, recording its variations in oos
scciill
llat
a io
on am
aamplitude
plitude and resonance frequency;
frequen
sensor monitored the fluid’s response.
respons
nse.
ns
The response signals were we
w
ellll dde
esc
scriibbeed by a simple harmonic oscillator (SH
scri
well
described
(SHO) model. The
inertial mass model (tested usingg probes
pprrobbes of different diameters and at different
differ
immersion
lengths) predicted very w
ell th
el
he oob
bserved resonance frequency red-shifts. The validation
va
well
the
observed
of this
model provided a pro
ope
per fram
mewor
ewoorrrkk for the subsequent analysis of the experiment
ew
proper
framework
experimental data. On one
hand, the weak dependence
dep
ep
peen
nde
dence
nce off tthe
nc
he damping component of the probe-fluid interacti
interaction on viscosity
was attributed tto
o th
tthe
he ze
ero
ro-slip
o i hydrodynamic condition (i.e. weak role of sliding fr
zero-slip
friction). On the
other hand, a st
trro
ong
ong
ng correlation was found between the probe’s frequency shift and
a the acoustic
strong
signal generated
gen
ner
erat
ated
ed byy the
th
he fluid. Remarkably, this correlation occurred across the entire
enti 0 to 280 Pm
immersion
length
which
immers
rrssionn leng
ngth
ng
th range.
range. Further, the acoustic signal increased with the fluid’s viscosity,
v
was
molecules are forced
wa
as ex
eexplained
xplai
pllai
aine
ined
ned aalso
ne
lso in terms of the zero-slip hydrodynamic condition: water molec
to
o move
mov
o e with
wiith the solid boundary, with the viscosity helping to drag an additional
wi
additiona mass of fluid
contributing to the
((contained
coont
ntai
ain d in a ~ 5 Pm thick boundary layer surrounding the probe) and thus con
aine
acoustic
ac
coouustic signal.
We underscore the role played by the relatively new Near
field Scanning A
Near-field
Acoustic NearField Microscopy (SANM) technique in these measurements. Although the monotonic decrease
in tthe
in
h probe’s resonance amplitude and monotonic decrease in the probe’s resonance frequency
with probe immersion length was expected, the availability of the simultaneously monitored
acoustic signal (obtained with the help of the SANM apparatus) was significant. Indeed, in the
process of trying to find correlations (or lack of it) among these three signals led us to identify
the important role played by the zero-slip condition.
Placing a substrate very close to an oscillating probe (initially
(initiallly
ly interacting
inntter
te accti
ting
ng only with bulk
fluid) would certainly cause new probe-fluid-substrate (near-field)
(near-fiel
elld)
d) in
nte
teraction
rraa
me
interaction
mechanisms to be
considered. Nonetheless, the accumulated experimental
all eevidence
vviide
d nc
nce ffrom
rom pprobe/bulk-fluid
interactions about the role played by the zero-slip boundary
bouunnddar
ary condition
cco
onddit
itio
ion (being responsible for
dragging the fluid molecules contained in boundary lla
ay r su
aye
ssurrounding
urr
r ounding the pprobe and thus
layer
generating sound) suggests that a similar dynamic m
me
ech
haan
niissm could
could also be present
co
prese in near-field
mechanism
probe-fluid
- d-substrate interactions. But in the la
attteerr casee w
wee have to consider tthat those fluid
probe-fluid-substrate
latter
molecules in the boundary layer will not be as
a ccompliant
ompl
om
p iiaanntt to move along the probe as in the bulk
nearby stationary
case, because they are now also affectedd by
by aadhesion
dhes
dh
e io
io forces exerted by the ne
ion
experiencing
substrate. As a result, the net effect iss a pprobe
r be
ro
be eex
xp riencing instead a spring type restoring force
xpe
the
with the consequent increase in th
he pr
pprobe’s
obbee’’s re
rresonance
esonance frequency. This proposed hypothesis to
explain the blue-shift in the ppr
rob
obe’
e’’s resonance
ressoona
re
nance frequency in near-field probe
probe’s
probe-fluid-substrate
interactions is supported by experi
riime
ment
ntaall data accounted when the SANM was fi
experimental
first introduced.5
acoustic signal from
The reported correlation between
bet
etwe
weeen
ween
n the probe’s frequency shift and the fluid’s acous
experiments
indeed
those near-field experi
riime
m ntts ca
ca in
can
ndeed be understood by invoking the zero-slip condition that
must
fulfill
the confined fluid m
ust fu
us
fulf
ullffill at
at the
the probe’s walls and at the substrate.
REFERENCES
REFERE
EN
NC
CE
ES
S
1
K. K
Karrai
aarrra
r i and
an
nd R. D. Grober, “Piezoelectric tip-sample distance control for ne
near field optical
microscopes,”
microssccoopes,” Appl. Phys. Lett. 66, 1842-1844 (1995).
2
F.
F. JJ.. Gi
G
Giessibl,
iessibl, “Atomic resolution on Si(111)-(7x7) by noncontact atomic for
force microscopy
with
with a force sensor based on a quartz tuning fork,” Appl. Phys. Lett. 76, 1470-1472
1470-14 (2000).
3
A. Gil, J. Colchero, M. Luna, J. Gómez-Herrero and A. M. Baro, “Adsorption of Water on
Solid Surfaces Studied by Scanning Force Microscopy,” Langmuir 16, 5086-5092 (2000).
4
B. Kim, S. Kwon, H. Mun, S. An and W. Jhe, “Energy dissipation off nanocon
nanoconfined hydration
layer: Long-range hydration on the hydrophilic solid surface,” Sc
SScientific
cient
ien ific R
ie
Reports 4, 6499
(2014).
5
A. La Rosa, X. Cui, J. McCollum, N. Li and R. Nordstrom,
Nordstrom
om
m, “The
“Th
The ultrasonic/shear-force
ultraso
microscope: Integrating ultrasonic sensing into a near-field
nearr-fi
fiel
e d scanning
ssccan
a niing optica
optical microscope,”
Rev. Sci. Instrum. 76, 093707 (2005).
6
A. H. La Rosa, N. Li, and K. Asante, “The ultr
ultrasonic/shear-force
trras
asonicc/s
/sh
she
heaarr-force microscope:
microscop a metrology
tool for surface science and technology,” Invited
Invvited
iteed
it
d Pa
P
Paper,
aper, in "Nanofabrication: Technologies,
Devices, and Applications II,” Warren Y. L
Lai,
aaii, L. E.
E. Ocola,
O ola, Stanley Pau Eds., Symposium in
Oc
Optics East 2005, Boston, MA. Proc. SPIE
E 60
66002,
002
02, 16
1163-170
63-170 (2005).
7
X. Cui and A. H. La Rosa, “Investigation
“In
Inve
v sttiig
gaattion
t
of the probe-sample interaction
inter
in the
ultrasonic/shear force microscop
microscope:
The
oppe:
e: T
he phononic
he
pho
hononic friction mechanism,” Appl. Phys. Lett. 87,
231907 (2005).
8
M. Ohtsu, “Near-field Nano/Atom
Nano/Ato
om Op
O
Optics
pttiics and Technology,” Springer, Tokyo (1998).
(1
9
J. B. Segur and H. E.
E. O
Ob
Oberstar,
ber
e star
arr, “Viscosity of Glycerol and Its Aqueous Solutions,”
Soluti
Ind. Eng.
Chem 43, 2117-21
2117-2120
120
20 (1951).
(19
1199511).
10
C. S. Miner and
an
nd N.
N. N.
N. Dalton,
Dalt
Da
lton, Glycerol: American Chemical Society Monograph
Monogra Series, No.
117, Publisher:
Publissher:
hhee Literary
Literary
Li
i
y Licensing, LLC (2013).
11
A. H. L
Laa R
Rosa,
oossa,
sa N
N.. Li
L
Li,, R. Fernandez, X. Wang, R. Nordstrom and S. K. Padigi,
Padigi “Whisperinggallery
galller
ery acou
acoustic
ouust
stic
ic sensing: Characterization of mesoscopic films and sc
scanning probe
microscopy
miicr
m
cros
osco
os
scopy
coppyy applications,”
co
applications,” Rev. Sci. Instrum. 82, 093704 (2011).
12
2
J.
J. Rychen,
Rychhe
he T. Ihn, P. Studerus, A. Herrmann and K. Ensslin, “Operation ch
hen,
characteristics of
piezoelectric
temperatures,” Rev.
piez
piez
pi
ezoe
o lectric quartz tuning forks in high magnetic fields at liquid helium temp
Sci.
Sci. Instrum. 71, 1695-1697 (2000).
Sc
13
M. Lee, J. Jahng, K. Kim and W. Jhe, “Quantitative atomic force measurement with a quartz
tuning fork,” Appl. Phys. Lett. 91, 023117 (2007).
14
K. Karrai and R. D. Grober, “Near Field Optics,” in: M. A. Paeslerr and P. J.
J Moyer (Ed.),
SPIE Proceedings Series Vol. 2535, Bellingham, WA, 1995, pp. 69–81
699–81
81 ((1995).
1995).
15
M. Christen, “Air and gas damping of quartz tuning forks,” Sen
Sensors
nsoorrs
ns
r aan
and
nd Ac
Actuators
ctua
4, 555-564
(1983).
16
J. E. Sader, “Frequency response of cantilever beam
beams
ms immersed
im
mme
merrssed
mers
sed
ed in viscous
visco fluids with
applications to atomic force microscope,” J. Appl. Phys.
64-76
Phyys. 84
84, 664
4-76
76 (1998).
17
W. T. Blake, “The radiation from free-free beams
mss iin
n aai
air
ir aan
and
nd w
water,”
ater,” J. Sound V
Vib. 33, 427-450
(1974).
18
R. K. Jeyapalan and E. J. Richards, “Radiation
“Rad
dia
iati
tionn efficiencies
eff
f icciieencies of beams in flexural
flexura vibration,” J.
Sound Vib. 67, 55-67 (1979).
19
A Castellanos-Gomez, N. Agraït and
nd G Rubio-Bollinger,
nd
Rubbio-Bollinger, “Dynamics of quartz
qua tuning fork
force sensors used in scanning probe
pro
ro
robe
obbee microscopy,”
miccrro
oscopy,” Nanotechnology 20, 215502 (2009).
20
R. Fernandez, X. Wang, and
ndd A.
A. H.
H. La Rosa, “Acousto Characterization of Fluid-like
Mesoscopic Films und
under
Shear,”
Proceedings
11th
der
er S
hheear,” P
roceedings of the Nanotechnology (IEEE-NANO)
(IEEE
IEEE International C
Conference,
onfe
ferreenc
n e,
e, ppp.
p. 903-906 (2011).
21
In light of the ad
additional
ddi
ditiion
onal ine
inertial
neer ial mass model described in the text, and in orde
nert
order to isolate the
contribution only
onl
nly due
nly
due too the viscosity, we should factor out from the 25 Hz change the
du
contributi
contribution
tiioonn ddue
ue to the larger density U50% /U
ue
0%
1.13, which gives a 22 H
Hz value. This
represents
represen
een
nttss a 110%
nts
0%
% rrate
ate larger decrease in frequency shift per immersion length ccaused by a 500
% increase
inncreeaase in
in vi
vviscosity.
iscosity.
is
22
D.
D. Sch
Schaeffel,
ch
hae
aeff
ffel
el, S. Yordanov, M. Schmelzeisen, T. Yamamoto, M. Kappl, R
R. Schmitz, B.
Dunweg,
Duunw
D
n eg
g, H. Butt and K. Koynov, “Hydrodynamic boundary condition of water on
hydrophobic
hyddrrop
hy
hydr
o hobic surfaces,” Phys. Rev. E 87, 051001(R) (2013).
23
Q.
Q. Yuan, and Y. Zhao, “Multiscale dynamic wetting of a droplet on a lyophilic
lyophili pillar-arrayed
surface,” J. Fluid Mech. 716, 171-188 (2013).
24
Q. Yuan, X. Huang and Y. Zhao, “Dynamic spreading on pillar-arrayed surfaces: Viscous
resistance versus molecular friction,” Phys. of Fluids 26, 092104 (2014).
25
M. A. Drummond Roby, G. C. Wetsel Jr. and C.ǦY. Wang, “ScannedǦprobe
“Scan
nnedǦprob lateralǦforce
air,”
Appl.
determination of fluidǦdynamic effects near a solid surface in air,
,” Ap
A
pppll. Phys.
Phys Lett. 69, 130
(1996).
26
U. Raviv, P. Laurat and J. Klein, “Fluidity of water confine
confined
ed to
o ssubnanometer
ubna
ub
nannoometer films,” Nature
413, 51 (2001).
27
S. H. Khan, G. Matei, S. Patil and P. M. Hoffmann, “Dynamic
“Dy
Dynami
miic Solidification
Solidification in Nanoconfined
So
(2010).
Water Films,” Phys. Rev. Lett. 105, 106101 (2010
0).
28
K. Karrai and I. Tiemann, “Interfacial shear forc
force
rcce mi
m
microscopy,”
crros
osco
osc
copy,”
o
Physical Review B 62, 13174–
13181 (2000).
29
L. D. Landau and E. M. Lifshitz, Fluid
Fluiid Me
M
Mechanics,
ech
han
annic
ic 2nd Edition, Pergamon Press
ic
ics,
Pre (1987). See
section 24.
Sensing the
fiber’s
fiber
’s oscillation
osscillation
amplitude
am
amplitude
Z coarse
position
ner
positioner
Fiber
glass
Fraame
Frame
Lock-in #1
125 Pm
Z nanopositioner
Tuning
fork.
Ref.
Liquid
droplet
d l t
Lock-in
Lo
ock
ck-in
in #22
Interface
Water
W
SSensing
Se
ens
nsiinng the
nsi
aaccou
oussttic
ic eemission
mission
m
acoustic
f om tthe
fr
he liquid
from
Mica
disk.
Fraame
Frame
a)
b)
Fig. 1
Mica Disk
Fig. 2.
Immersion Length ((Pm)
Pm)
)LJ
)L
)LLJ
)
J Immersion Length ((Pm)
..
..
Immersion
Leng
Length
g(Pm)
th ((Pm)
Pm)
Immersion
Length
)LJ
)LJ
.
..
.
Immersion
Length
(Pm)
Immersion
Length
(Pm)
Immersion Length
Length
h ((Pm)
Pm)
Immersion Length (Pm)
(P
Fig. ϱ
Immersion L
Length
ength ((Pm)
Pm)
)LJ
)LJ
Immersion Length (Pm
(Pm)
)LJ
)LJ
32100
32
3
2
210
10
1
00
)LJ
)LJ
32110
)LJ
)LJ
Q vvss Amplitude
Amplittud
Mechanical quality factor
6000
6000
125 Pm Dia
D
1125
25 Pm
Pm D
Dia
ia
0% Q
Q= [ sqrt(3) ] * (f/width )
50% Q
40000
4000
00%
%G
Gly
ly
Q
0%
% Glyy
2000
0
0
90
50%
Gl
Gly
2000
2000
50% G
Glyy
0
180
0
270
Immersion Length ((Pm)
(Pm)
a)
0.3
0.6
0.9
1.2
Normalized
N
ormalized resonance amplitude
a
b)
F g. ϭϬ
Fi
Fig.
Q= [ sqrt(3) ] * (f/width
50% Q
50% Q
Q
4000
0%
50% Amp (n
0DVV[ .J
(VWLPDWHG
W
H
7)P
7)PDVV
PDVV
Fig 8e DATA mas
mass
,PPHUVLRQGHSWKPP
,PPHUVL
LRQGGHSWKPP
Fig.
Fig.
Fi
g PP'LD
PP'LD
PP'LD
85
-40
68
-60
A
Acoustic
cou
u i
fitting
fittin
ng
0
80
160
-80
Amp TF (nm)
Am
Probe
P
robe D
Dia.
ia. 98
8P
Pm
132
-15
88
TF 1
125 microns fiber _ pure water_FREQEUNCU and ACOUSTIC
Acoustic
Acoustti
A
Acousti
fitting
fittin
ng
ng
66
6
6
-30
-45
-60
0
80
Amplitude QTF
0
Amplitude
A
Am
mp
pllittud
ude
fitting
fiitttting
iin
ng
0
110
240
160
Freq shift QTF
Mag Freq Shift - 54.5
Acoustic fitted
TF 98 microns fiber _ 0%_
24
240
Immersion Length ( Pm)
Immersion Length ( Pm)
a)
b)
Probe
P
robe D
Dia.
ia. 81 Pm
160
16
160
Amplitude
A
m
mplitude
li d
fitt
ting
g
fitting
14
40
140
-10
-20
100
-30
Acoustic
Aco
A
ou
usticc
fitting
fitti
ing
60
0
80
160
-40
240
Immersion Length ( Pm)
c)
Fig. 1Ϯ
Freq shif
sh magnitude - 37 Hz
Acoustin )fitted)
Acousti
120
12
20
120
80
Freq shift
sh QTF
0
Freq shift (Hz)
Res.
Re
R
es.
s. aamplitude
mpli
mp
l tudee ((nm)
nm)
nm
51
Freq shift
shif QTF
Res.
Re
es.
s. Amplitude
Amp
m litude (nm)
-20
Acousto fitted
Frequency shift (Hz)
Amplitude
mp
ffitting
g
102
Mag Freq Shift munius 80 Hz
0
Frequency Shift (Hz)
Res. Amplitude (nm)
Probe Dia. 125 Pm
Amplitude QTF
Amp
TF 81 mi
microns _0% _FREQEUNCU and ACOUSTIC

 Download  Report

Paperzz.com

Your Paperzz

© Copyright 2026 Paperzz