Acrylic latex can be described by a Bingham Plastic model where the yield stress is 11.2 N/m2, a limiting viscosity, m0, of 80 cp and a density of 0.95 g/cm3. What is the maximum thickness of this paint that can be applied to a vertical wall without running.
Shear stress = [itex]\tau[/itex]xz = -[itex]\mu[/itex]*dvz/dx
Where positive z direction is down (with gravity) and positive x direction is to the right (wall on the left, paint on the right of the wall)
Unfortunately, that is all I know of relevant to this problem. I would also say that a chart of shear rate vs shear stress depicting the Bingham Plastic model would be relevant. And perhaps the shear stress in the above equation should actually be differential (as it goes from 0 to the yield stress), but I am not entirely sure about that.
The Attempt at a Solution
I'm not quite sure where to start with this as I am not at all familiar with non-Newtonian fluids. I can only imagine that I should treat it as a Newtonian fluid at it's yield stress and solve for x in some manner and at that point it would flow.
I would try to partially solve the above equation leading to [itex]\tau[/itex]xz*∫(from x = 0 to x = x) dx = -[itex]\mu[/itex]*∫(from vz = 0 to vz = vz) dvz
I feel this is a good start but I'm a bit confused on how to deal with the velocity integral. Ideally I would think you want to integrate from the velocity is 0 to when it is infinitesimally small, which would essentially be 0 making the equation unsolvable (unless x = 0 which does not work).
I also can't help but notice that unused density number which I can only assume plays some part.
Help is much appreciated.