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ChemE_3230_PS8 - sphere with a slip velocity proportional...

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ChemE 3230 (Spring 2011) Problem Set #8 (Due by 04/29/2011) 1.0 Denn 10.2 (25 points) 2.0 A highly viscous Newtonian liquid, viscosity η and density ρ , flows isothermally with a uniform velocity U . A rigid sphere of radius R is introduced into the path of the fluid and held stationary, causing the fluid to flow around the sphere. The fluid wets the surface of the sphere marginally, which causes it to slip relative to the
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Unformatted text preview: sphere with a slip velocity proportional to the shear stress at the surface of the sphere. (a) Derive an expression for the velocity profile in the fluid. (b) Show that in the appropriate limit, this expression yields a drag force that satisfies Stokes law. (50 points) 3.0 Denn 12.5 (25 points) 4.0 Denn 12.9 (25 points)...
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