Force required to separate two plates apart

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SUMMARY

The force required to separate two plates containing liquid is determined by the angle of contact, which is 0 degrees in this scenario. For slow separation speeds, the derivation utilizes the Laplace Young equation, linking the curvature of the liquid bridge to the internal pressure. Conversely, for rapid separation, the problem is modeled as a squeeze film, solvable through the Navier-Stokes equations under axi-symmetrical conditions. Understanding these principles is crucial for accurately calculating the separation force.

PREREQUISITES
  • Understanding of the Laplace Young equation
  • Familiarity with Navier-Stokes equations
  • Knowledge of capillary action and contact angles
  • Basic principles of fluid dynamics
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  • Study the derivation of the Laplace Young equation in detail
  • Explore the application of Navier-Stokes equations in fluid dynamics
  • Research the concept of capillary number and its implications
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Physicists, engineers, and researchers interested in fluid dynamics, particularly those studying capillary forces and the mechanics of liquid bridges between surfaces.

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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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