Steady-state gel electrophoresis of long polymer molecules: a theoretical study

The velocity of long polymer molecules in a gel and the liquid flow profile in the vicinity of a molecule's surface were studied theoretically by combining the Navier-Stokes equation with the Poisson-Boltzmann equation. The electrophoretic mobility has been calculated in dependence of the ionic strength of the electrolyte solution, its viscosity, the gels' volume friction coefficient, the surface charge and the radius of the polymer molecule. The results are presented in a nondimensional form and depend on two dimensionless parameters only. The first parameter is the radius of the polymer molecule in units of the Debye length. The second is a parameter comprising the electrolyte's viscosity and the gel density. Thus, by similarity theory, the results apply to any given experimental arrangement.