MT-0.6081 Microfluidics and BioMEMS
Microfluidics 2
Surface tension, contact angle, capillary flow
20.1.2014
Ville Jokinen
Scaling: surface forces vs body forces
•
•
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Surface area to volume ratio scales as d-1
Microsystems often dominated by surface effects
An example:
h
Reservoir droplet
Flow channel
Case 1: The flow channel is a microchannel: 100 μm x 100 μm x 100 mm, Volume 1 μl
Volume: Hydrostatic pressure from reservoir ≈ 10 Pa
Area: Capillary pressure from channel ≈ 3000 Pa
Surface dominated!
Case 2: The flow channel is a garden hose: 1 cm x 1 cm x 10 m , Volume 1 liter
Volume: Hydrostatic pressure from reservoir ≈ 1000 Pa
Area: Capillary pressure from channel ≈ 30 Pa
Volume dominated!
Bond number: Does gravity matter?
Dimensionless number that characterizes the ratio of surface forces to body
forces
L = characteristic length scale
a = acceleration (for gravity, 9.81m/s2)
γ = surface tension
ρ = density
•
ρaL2
Bo =
γ
If Bo < 1 the system is dominated by surface forces (opposed to body forces)
For water, Bo = 1 at around 1 mm range.
Example from previous page, water in a channel with 100 µm and 1 cm dimensions:
(for 100 µm)
Bo ≈ 1.4 * 10-3
Bo ≈ 14
(for 1 cm)
Surface tension & Surface energy
Work required to create new surface =
surface energy x area created
δW = γ δA = γ Lδx
Fundamental definition of surface energy:
γ = δW / δA [ J / m2]
Hunter: Introduction to Modern
Colloid Science, p.134
Surface energy is also known as surface tension:
γ = δF / δl [ N / m]
Concept applicable to all surfaces and interfaces:
solid-solid, solid-liquid, liquid-liquid, solid-gas, liquid-gas
Molecular basis of surface energy
The surface layer lacks some of the bonds
in bulk phase
This increased potential energy compared
to the bulk is called surface energy!
Temperature dependence: water: 68 mJ/m2 at 50oC, 59 mJ/m2 at 100oC
Water has a very high surface energy because of strong intermolecular bonds.
Surface energy, cohesion, adhesion
Surface energy is linked to adhesion between materials and intra material cohesion.
Work of cohesion, W11:
Before separation: γ11=0
After separation: 2γ1
Material 1
Material 1
Material 1
γ11
Material 1
W11= 2γ1- 0 = 2γ1
γ1
γ1
Work of adhesion, W12:
Before separation: γ12
After separation: γ1 + γ2
Material 2
W12= γ1 + γ2 - γ12
Material 1
Material 2
γ12
Material 1
γ2
γ1
Laplace pressure
• There is a pressure difference across a curved liquid surface.
Young-Laplace equation
Calculating radius of curvature
For a spherical droplet or bubble:
1 μl spherical water droplet in air, ∆P ≈ 140 Pa
1 μl spherical air bubble in water, ∆P ≈ -140 Pa
Pressure is higher inside a spherical
bubble or a droplet!
Surface tension measurement:
force tensiometry
Drop weight method:
Gravity = perimeter x surface tension
mg = 2πr x γ
• Empirical correction factor needed
Wilhelmy plate method:
Force tensiometry:
The force a liquid exerts on a plate is measured
•F=2Lγ
• No correction factor needed
• Good method also in practice
Surface tension measurement:
optical tensiometry
Drop shape analysis:
• Optical tensiometry: Surface tension measured from the shape of a hanging
droplet
• Shape determined by the balance of gravity (hydrostatic pressure) and
surface tension (laplace pressure).
Image from biolin scientific.
Contact angle, experimental
• A liquid droplet makes a certain angle of contact with a solid surface
• The angle is called the apparent contact angle θ
• Property of a solid-liquid-fluid three phase system
• For a fixed liquid and fluid, contact angle is characteristic parameter of a
surface/material
Contact angle, theoretical
Young’s equation:
γLG cos(θ) = γSG - γSL
θ
γLG
γSG
γSL
Thermodynamical, or Young’s, contact angle
Liquid-vapor surface energy (“liquid surface tension”)
Solid-vapor surface energy (“solid surface energy”)
Solid-liquid surface energy (“solid-liquid interface energy”)
(often also γl, γlv)
(often also γs, γsv)
• The thermodynamical contact angle does not necessarily equal the experimental
contact angle on real surfaces because of hysteresis.
Contact angle hysteresis
On real surfaces: θrec < θeq < θadv
Hysteresis θadv – θrec
θrec = Receding contact angle
θeq = Equilibrium/static contact angle
θadv = Advancing contact angle
Reasons for contact angle hysteresis:
• Adsorption of molecules from the solution
• Desorption of molecules from the surface
• Chemical inhomogenities
• Physical surface topography
Which experimental contact angle is the one appearing in Young’s equation?
Unresolved, but some suggestions that have been made in the literature:
1. θadv
2. (θadv + θrec) /2
3. acos ((cos θadv + cosθrec)/2)
4. the most stable θ (e.g. after vibrations or other source of energy)
Contact angle measurement
Same tools and methods as for surface tension:
• Force tensiometry, often Wilhelmy plate
• Optical goniometry of a sessile droplet
Optical goniometry
Wilhelmy plate method
Hydrophilic/ Hydrophobic terminology
For water: hydrophilic/hydrophobic
For oils: oleophilic/oleophobic
For liquids in general: hygrophilic/hygrophobic, omniphilic/omniphobic
θ = 0°
Completely wetting
θ ≈ 5°
Superhydrophilic
SiO2
Clean metals
roughness+chemistry
0° < θ < 90°
90° < θ < ≈ 150°
150° ≈ < θ < 180°
Hydrophilic
Wetting
Hydrophobic
Nonwetting
Superhydrophobic
Ultrahydrophobic
SU-8, Si
PDMS, Teflon
roughness+chemistry
Measuring solid-vapor surface energies
• With some assumptions, γsv can be estimated by contact angle measurements
Zisman:
Surface energy of a solid
is the surface energy of the highest
surface tension liquid exhibiting
complete wetting.
(= critical surface tension)
Depending on the assumptions, many ways to calculate solid surface energies
from contact angles (Zisman, Owens-Wendt ,Good-vanOss etc.)
Capillary rise and depression
Capillary pressure = Laplace pressure of a meniscus inside a capillary!
Note that θ is the only material parameter of the capillary that is needed, not eg. γSG or γSL
Capillary filling of microfluidic channels
Main differences to classical capillary rise:
Horizontal vs vertical
• Capillary filling continues until the channel network is full
θt
h
Geometry usually non circular and nonuniform materials
• Hydrophilic walls contribute to filling, hydrophobic oppose it
cos θ t + cos θ b cos θ l + cos θ r
∆P = γ (
+
)
h
w
Channel architecture might be complex (wider and narrower areas)
• The capillary pressure is calculated at the filling front (and
possibly the de-wetting front), already filled areas only contribute
to flow resistance.
θl
θr
θb
w
Application example: surface immunoassay
• Immunoassays
Bernard et al. Anal. Chem. 2001
Contact angle on structured surfaces
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•
On the lowest surface energy planar surfaces, contact angles only go up to ≈ 120°
for water and ≈ 75° for oils.
Beyond that, topography can be used to enhance contact angle
Cassie state:
Possible on intrinsically
hydrophobic surfaces
Results in increased
hydrophobicity
cos(θc) = f cos(θ) -1 +f
f = air fraction
Wenzel state:
Possible on any surface
Results in enhanced
intrinsic contact angle
cos(θw) = r cos(θ)
r = roughness factor
Note!
• The contact angle is enhanced but the chemical nature of the surface remains the same
• The enhanced contact angles are relevant for fluidics, but not directly in e.g. adsorption
Superhydrophobicity
•
•
Micro/nanostructures combined to hydrophobic surface properties can result in
superhydrophobic surfaces.
Properties: θ > 150°, water repellent, water deposited on top stays as intact
droplets and moves easily → low sliding angles, self cleaning
Silicon nanopillars
(black silicon)
Jokinen, Sainiemi, Franssila: Advanced Materials 2008
Left:
oxidized silicon surface
θ ≈ 0°
Right:
fluoropolymer coating
θ ≈ 170°
Digital Microfluidics, 2-phase
• Microfluidics does not always mean continuous flow in a channel.
• Digital microfluidics increasingly common.
• Discrete droplets, either 2 immiscible liquid phases or liquid droplets and air.
• Each droplet can be viewed as a single experiment.
2-phase digital microfluidics. The surface tension keeps the droplets together.
Digital microfluidics, electrowetting
• Droplets on hydrophobic surfaces, surface tension holds the droplets together
(no spreading)
• Electrowetting used to move the droplets.
• Either one open surface or more commonly between 2 hydrophobic plates.
V = applied voltage
C = capacitance
γs =solid surface energy
γw = water surface energy
γ0ws = water solid interfacial energy with
no electric field.
CD microfluidics
• Actuating force by centrifugation. Capillary valves and hydrophobic valves to control flow.
Review
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The importance of surfaces in microfluidics/bio-MEMS
The concept of surface energy, measurement, Laplace pressure
Contact angle, theoretical and experimental aspects
Capillary rise and capillary filling of microfluidic channels
Superhydrophobicity
Surface tension effects for microfluidics
Reading material (updated)
• For lecture 2, the reading material is:
Chapter 5, surface tension, from a book “Physics of Continuous matter” by B.
Lautrup. Pages 69-83
Available from link: http://www.cns.gatech.edu/~predrag/courses/PHYS4421-13/Lautrup/surface.pdf