9860

Velocity Profile for Immiscible Viscous Fluids

This Demonstration shows the behavior of three immiscible fluids subjected to Couette flow. The top plate is moving to the right while the bottom plate is stationary. The velocity of each fluid is given relative to the top plate velocity. The flow is steady, incompressible, and laminar. You can vary each fluid's relative viscosity and height. The velocity distribution indicates the impact of fluid viscosity on each fluid's velocity gradient. The velocity versus height plot indicates the relative slopes (or velocity gradients) in each fluid.

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DETAILS

For unidirectional flow, the shear stress imparted on the fluid is given by:
,
where
is the shear stress (force/area)
is the viscosity of the fluid
is the velocity gradient
For shear-induced flow between two flat plates (when at least one plate is moving), the velocity profile for a Newtonian fluid is linear:
.
For three immiscible fluids, boundary conditions dictate that the shear stress and velocity at a fluid-fluid interface are the same for both fluids.
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