Drag coefficient free-molecule

Cofn, drag coefficient for free-molecule flow... 

In a free solution, the electrophoretic mobility (i.e., peiec, the particle velocity per unit applied electric field) is a function of the net charge, the hydrodynamic drag on a molecule, and the properties of the solutions (viscosity present ions—their concentration and mobility). It can be expressed as the ratio of its electric charge Z (Z = q-e, with e the charge if an electron and q the valance) to its electrophoretic friction coefficient. Different predictive models have been demonstrated involving the size, flexibility, and permeability of the molecules or particles. Henry s theoretical model of pdcc for colloids (Henry, 1931) can be combined with the Debye-Hiickel theory predicting a linear relation between mobility and the charge Z ... 

As particle size is decreased to the point where dp tp, the drag for a given velocity becomes less than predicted from Stokes law and continues to decrease with particle size. In the range dp ip, the free molecule range (Chapter 1), an expression for the friction coefficient can be derived from kinetic theory (Epstein, 1924) ... 

The accommodation coefficient or represents the fraction of the gas molecules that leave the surface in equilibrium with the surface. The fraction I — cr is specularly reflected such that the velocity normal to the surface is reversed. As in the case of Stokes law, the drag is proportional to the velocity of the spheres. However, for the free molecule range, the friction coefficient is proportional to dj whereas in the continuum regime dp ip), it is proportional to dp. The coefficient a must, in general, be evaluated experimentally but is usually near 0.9 for momentum transfer (values differ for heat and mass transfer). The friction coefficient calculated from (2.19) is only 1% of that from Stokes law for a 20-A particle. 

The rigid sphere is not an accurate picture of how a polymer molecule affects the flow of the fluid in which it is dissolved, because the fluid can penetrate within the molecule. This recognition led to the development of models in which the molecule is represented as a chain of beads, which contain all the mass of the molecule, connected by springs. In the free-draining model of Rouse [45], there is no effect of one bead on the flow pattern around other beads. This model starts from Stokes law, which gives the drag force f on a sphere in a Newtonian fluid flowing past it at the velocity U as proportional to the radius a of the sphere. In terms of the coefficient of friction f =Fj /U), Stokes law for flow past a sphere is ... 

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