Force required to separate two plates apart

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The force required to pull two plates apart with liquid in between, at zero contact angle, depends on the speed of separation. For slow separation, the Laplace Young equation can be used to derive the force based on the curvature of the liquid bridge and the pressure difference. In contrast, for rapid separation, the situation is modeled as a squeeze film, requiring solutions from the Navier-Stokes equations and considering axi-symmetry. The capillary number plays a crucial role in determining the separation speed and the corresponding force calculations. Understanding these dynamics is essential for accurately predicting the force needed to separate the plates.
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If two plates of area A and separation d contain liquid in between with angle of contact 0 degrees, then what is the amount of force required to pull the two plates apart?

How do we derive this??
 
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Are the plates pulled apart quickly or very slowly. The "quickness" will be controlled by the capillary number.

For slow speeds the derivation will follow directly from the Laplace Young equation relating the curvature of the bridge surface to the pressure inside the bridge.

For high speeds this is a squeeze film and can be solved using the Navier Stokes solution and axi-symmetry.
 
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