Simultaneous flow of two or more thin layers of liquid is needed to form various composite coatings. Suppose that immiscible liquids 1 and 2 flow down a surface that is inclined at an angle β relative to vertical, as shown in Fig. P7.8. The respective layer thicknesses are H₁ and H₂, the densities are ρ₁ and ρ₂, the viscosities are μ₁ and μ₂, and the fully developed velocities are

and

As usual, it may be assumed that the air pressure is constant at P₀ and that viscous stresses in the air are negligible.

(a) What is

in liquid 1?

(b) What is

in liquid 2?

(c) State the differential equations and boundary conditions and find 

and

Transcribed Image Text:

x₂