Stokes' Law Settling Velocity (Deposition)

1 Settling Velocity ( deposition ) Stokes' Law the drag on a spherical particle in a fluid is described by Stokes' Law for the following conditions: fluid is a Newtonian incompressible fluid duk/dxk=0 gravity is negligible g=0 flow is creeping flow, Re<<1 duk/dxk=0 steady-state flow duj/dt=0 Navier-Stokes Equation Bird, Stewart and Lightfoot, 1960 for j=1, 2, here we will neglect gravity so that the last term is dropped, and we will make dimensionless using characteristic Velocity u0 and length l where Re= ul/ =(inertial fluid forces)/(viscous fluid forces) l=diameter =density = =fluid viscosity u=mean speed of the undisturbed flow upstream of the body uj t+uk uj xk# $ % & ' ( = p xj+ 2uj xk xk+ gj uj* t+uk* uj* xk*# $ % & ' ( = p* xj*+1Re 2uj* xk* xk*Navier-Stokes Equation Stokes' solution with the assumptions: infinite medium rigid sphere no slip at the surface of the sphere so that in spherical coor))

1 Settling Velocity (Deposition) Stokes' Law • the drag on a spherical particle in a fluid is described by Stokes' Law for the following conditions:

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  Spherical, Deposition, Settling, Eskto, Velocity, Stokes law settling velocity

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