Page 394 - Introduction to Continuum Mechanics

378 Plane Couette Flow of Two Layers of Incompressible Fluids

Fig. 6.9

From Eqs. (6.14.1),

From Eqs. (6.14.2),

Since the bottom plate is fixed

and we have

Since the top plate is moving with v 0 to the right, therefore v' ' = v 0at *2 = +bi and we have

At the interface jc 2 = 0, we must have v^ ' = v^ ' so that there is no slipping at the fluid
interface. Therefore,

Furthermore, from Newton's third law, we have, on KI - 0, the stress vectors on the two
layers are related by