The dependence of particle deposition velocity on particle inertia in turbulent pipe flow

Abstract Recent measurements of particle deposition velocities on the walls of a pipe in turbulent flow (Liu and Agarwal, 1974) show a decline with increasing particle size beyond a critical particle size. A stochastic model of particle deposition is presented which explains this result. As in other models, the deposition process is composed of turbulent diffusion, together with inertial projection through the boundary layer; in this model, both processes are particle inertia dependent, in opposing ways. The observed decline is due to the increased fractional penetration of the boundary layer with increasing particle size being insufficient to compensate for the reduced rate of transport to that region. A simple expression is given for the particle deposition velocity in terms of the r.m.s. velocity at that point and the fractional penetration of the boundary layer. The inertial dependence of the particle velocity is expressed in terms of the particle's response to the turbulent velocity fluctuations of its neighbouring fluid by relating the velocity spectral densities of the particle and fluid using a linear dimensionless form of the equation of motion of the particle. The fractional penetration of the boundary layer is based on Stokes' drag with a quiescent fluid. The deposition profile shows good agreement with the experiments of Liu and Agarwal.