# Bingham fluid in a falling film

1. Feb 13, 2008

### slyman

2) For Bingham fluid in a falling film. $$\tau$$0.
a) Find the equation for $$\tau$$xz as a function of x using a shell balance.
b) Solve for the minimum thickness of film that will allow flow of this Bingham fluid using the equation for a Bingham fluid and the correct boundary conditions.
c) Solve this equation for vz as a function of x for a fluid whose thickness is greater than the minimum.
d) Solve for the volumetric rate of flow Q.

---

For part a, we know the shell balance is exactly the same for a Newtonian or non-Newtonian fluid so. So the equation is
τxz = ρ g x cos β

I'm having trouble with the rest of the questions. For part b we use the no slip boundary conditions but I don't know how to solve it for a bingham model. Can anyone help me out?