Translational and rotational friction in a rough sphere fluid

Abstract

A microscopic derivation of the translational and rotational friction coefficients for a Browian particle in a dilute rough sphere fluid is presented. A projection operator method is used to couple the test particle’s motion to the collective fluid fields, and the resulting generalized Langevin equations are averaged over fluctuations to yield source hydrodynamic equations. After averaging over the surface and volume of the spherical Brownian particle, these equations are algebraically manipulated to give expressions for the force and torque exerted on the tagged particle by the surrounding fluid. The Stokes’ law relations, for partial stick boundary conditions, are obtained.

Transport properties of the rough hard sphere fluid

“…The correlation functions of Eqs. (8)- (11) were calculated at fixed time intervals which were generally chosen to be approximately 10τ F , where τ F is the mean time between collisions. Correlation functions values were converged to total times of 700-2000τ f depending upon the number of particles in a simulation.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Given such importance, it is valuable to have a set of well-converged benchmark calculations against which comparisons with theory can be made. In fact, Condiff, Lu, and Dahler 2 examined in some detail the effect of different basis sets on the values of transport coefficients using the Chapman-Enskog approximation to the Boltzmann equation.…”