NORMAL FORCE CHANGE DISTRIBUTIONS ON THE CONTACT
AREA DURING THE RESONANT VIBRATIONS OF A SESSILE
DROPLET UNDER WHITE NOISE EXCITATION
Nguyen Thanh-Vinh, Kiyoshi Matsumoto and Isao Shimoyama
University of Tokyo, JAPAN
ABSTRACT
We directly measure the normal force change distributions on the contact area of a sessile droplet
during its vibration at multiple resonant modes induced simultaneously by white noise excitation. The
measurement is carried out by using an array of thirteen piezoresistive cantilevers which are highly
sensitive to detect the vibration up to the seventh mode of the droplet. We show that, for all resonant
modes, the normal force change is largest at the edge of the contact area. Moreover, for the same vibration
energy applied to the substrate, the normal force change is largest at the lowest resonant mode. We
believe these results are useful for the design of a droplet vibration detection technique based on MEMS
force sensors.
KEYWORDS: Droplet, White noise, Resonant vibration, Normal force, MEMS, Piezoresistive cantilever
INTRODUCTION
It is well-known that a liquid droplet has multiple resonant vibration modes at the frequencies:
j ( j  1)( j  2)
fj 
(1)
3m
where j=2,3,4,.. denotes the resonant modes; γ, m are surface tension and mass of the droplet, respectively.
Measuring the vibration of a droplet can provide a simple method to estimate surface tension and
viscosity using a dilute sample volume (several μL), which is very suitable for point-of-care testing.
Moreover, in MEMS2015 [1], we have shown that piezoresistive cantilever is an excellent tool to detect
the droplet vibration due to its high sensitivity and simple readout scheme in comparison with
conventional methods based on high-speed imaging [2, 3]. To obtain the instruction for the design
principle for this piezoresistive cantilever based sensing method, one has to know the force distribution
on the contact area during the vibration of the droplet since the output of a cantilever is proportional to
the force applied to its surface. In this study, we investigate the normal force change distributions on the
contact area during the vibration of a droplet at multiple resonant modes (Fig.1) using a piezoresistive
cantilever array (Fig.2a-b) reported previously[1].
Figure 1: Overview of this study. Normal force change distributions on the contact are during vibration
at multiple resonant modes of a droplet are directly measured using piezoresistive cantilevers.
978-0-9798064-8-3/µTAS 2015/$20©15CBMS-0001
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19th International Conference on Miniaturized
Systems for Chemistry and Life Sciences
October 25-29, 2015, Gyeongju, KOREA
Figure 2: (a-b) SEM images of the fabricated cantilever array.
(c) Experimental setup. (d) Vibration acceleration and its frequency spectrum of the substrate.
Figure 3: (a) Normal force changes at sensor S1 and S7 during the vibration of droplet when the white
noise vibration is applied to the substrate. S1 and S7 locate at the edge and the center of the contact
diameter, respectively. (b) Frequency spectra of the normal force changes at S1 and S7 in comparison
with that of when no vibration is applied to the substrate. (c) Amplitudes of the normal force changes at
all cantilevers during vibration modes from j=2 to j=8. The normal force change is largest at the edge of
the contact area for all modes.
(d) Ratio of the normal force changes at all cantilevers to that at S7.
EXPERIMENTS AND RESULTS
A 1.7 μL water droplet was first deposited on the cantilever array so that its contact diameter was exactly supported by the thirteen cantilevers (marked as S1 to S13). Vibration at multiple resonant modes of
the droplet was then induced by shaking the substrate using white noise vibration as shown in Fig.2c and
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Fig.2d. Fig.3a shows the normal force changes at cantilevers S1 and S7 when white noise vibration was
applied. The zoom view of the signals shows that vibration of the droplet is reflected in the outputs of the
cantilevers. Fig.3b shows the frequency spectra of the measured normal forces at S1 and S7 which clearly
indicate that multiple resonant modes occur simultaneously. Vibration up to mode j=8 can be observed
from the spectra. We then derive the amplitude of the normal force change at each sensor for each mode
from the peaks of the spectra. Fig.4a shows the amplitudes of the normal force changes plotted against the
location of the cantilevers, which indicates that the normal force change is always largest at the edge of
the contact area (S1 and S13) for all modes. The normal force change is largest at the lowest resonant
mode (j=2). We also investigate the ratio of the normal force change at a cantilever over that at S7 which
is at the center of the contact area. The result indicates that at a higher resonant mode, the ratio between
the normal force change at the edge of the contact area and that at the center of the contact area decreases
(Fig.4b).
Our results indicate that, for measurement of droplet vibration using piezoresistive cantilevers, one
should place the cantilever at the edge of the droplet and look at the lowest mode of the vibration j=2 to
obtain the maximum output of the cantilever.
CONCLUSION
We directly measured the normal force change distributions on the contact area of a sessile droplet
during its vibration at multiple resonant modes induced simultaneously by white noise excitation using an
array of thirteen piezoresistive cantilevers. It is shown that, for all resonant modes, the normal force
change is largest at the edge of the contact area and for the same vibration energy applied to the substrate,
the normal force change is the largest at the lowest resonant mode. Our results indicate that, for measurement of droplet vibration using piezoresistive cantilevers, one should place the cantilever at the edge of
the droplet and look at the lowest mode of the vibration j=2 to obtain the maximum output of the cantilever.
ACKNOWLEDGEMENTS
The photolithography masks were made using the University of Tokyo VLSI Design and Education
Center (VDEC)’s 8 inch EB writer F5112 + VD01 donated by ADVANTEST Corporation. This work
was partially supported by JSPS KAKENHI Grant Numbers 25000010. Nguyen Thanh-Vinh thanks the
Japan Society for the Promotion of Science (JSPS) for the support.
REFERENCES
[1] T.-V. Nguyen, K. Matsumoto, and I. Shimoyama, "A viscometer based on vibration of droplets on a
piezoresistive cantilever array," in Micro Electro Mechanical Systems (MEMS), 28th IEEE International Conference on, pp. 176-179, 2015.
[2] S. Mettu and M. K. Chaudhury, "Vibration Spectroscopy of a Sessile Drop and Its Contact Line,"
Langmuir, vol. 28, pp. 14100-14106, 2012.
[3] G. McHale, S. J. Elliott, M. I. Newton, D. L. Herbertson, and K. Esmer, "Levitation-Free Vibrated
Droplets: Resonant Oscillations of Liquid Marbles," Langmuir, vol. 25, pp. 529-533, 2009.
CONTACT
*Nguyen Thanh-Vinh ; phone: +81-3-5841-6318; [email protected]
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