An empirically validated model of the pressure within a droplet confined between plates at equilibrium for low Bond numbers |
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Authors: | M J Schertzer S I Gubarenko R Ben Mrad P E Sullivan |
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Institution: | (1) Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada |
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Abstract: | An analytical model is presented that describes the equilibrium pressure within a confined droplet for small Bond numbers
without prior knowledge of the interface shape. An explicit equation for the pressure was developed as a function of the gap
height, surface tension, and contact angle. This equation was verified empirically. The shape of the interface was found based
on the pressure predicted by both the proposed model and a model commonly used in electrowetting on dielectric (EWOD) investigations.
These shapes were compared against experimentally observed interfaces for aspect ratios between 3.5 and 18. The pressures
and shapes predicted by the proposed model were at least an order of magnitude more accurate than those predicted with a more
commonly used model. At an aspect ratio of 3.5, the average error in the predicted shape was almost 4%, but decreased below
the experimental error at an aspect ratio of 6. An aspect ratio of 15 is required for an EWOD device to split water droplets
in air. The error in the model pressure and its predicted interface in this case were approximately 0.3%. The analytical pressure
model proposed here can be used to increase the accuracy of models of practical EWOD devices. Better accuracy can be attained
for small aspect ratios by iteratively calculating pressure using the model proposed here. |
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