Calculation of translational friction and intrinsic viscosity. I. General formulation for arbitrarily shaped particles

Abstract

A general method for calculating translational friction and intrinsic viscosity is developed through exploiting relations between hydrodynamics and electrostatics. An approximate relation xi = 6 pi eta 0C between the translational friction coefficient xi of a particle (eta 0: solvent viscosity) and its capacitance C was derived previously. This involved orientationally preaveraging the Oseen tensor, but the result was found to be very accurate. Based on preaveraging, we find that the intrinsic viscosity [eta] of a particle can be estimated from its polarizability alpha through [eta] = 3/4 alpha + 1/4 Vp, where Vp is the volume of the particle. Both the capacitance and the polarizability can be obtained in a single calculation using the boundary-element technique. An efficient approach is thus found for estimating [eta], a quantity that is very useful in practice because of its sensitivity to particle shape but is notoriously difficult to calculate. Illustrative calculations on ellipsoids, cylinders, and dumbbells demonstrate both the accuracy of the approximate relations and the efficiency of the present method.

Electrical fluctuations on the surfaces of proteins from hydrodynamic data

“…They arrived at this result by angular averaging of the Oseen tensor [14][15][16][17]. The connection between hydrodynamic and electrostatic properties was also recognized by Zhou [19][20][21], from the fact that the Oseen tensor, i.e., the Green function for the Navier-Stokes equation, when orientationally averaged, is proportional to the Green function for the Laplace equation. In this way Zhou obtained the same Eq.…”

“…[η] is the intrinsic viscosity, which measures the contribution of the molecule to the viscosity of the solution in which it is dissolved [19,20]. V h also represents the space occupied by a gram of solute at infinite dilution.…”

The rheology of concentrated suspensions of arbitrarily-shaped particles

“…The result is ½g ¼ 128a 3 =45. In the case of globular cylinders for which the aspect ratio L=a ranges from 1/4 to 4 the hydrodynamic properties obtained numerically are listed in Table 1 [8]. Together with the hydrodynamic properties, in the last column of Table 1, we show the critical packing which we assume to coincide with the random packing of the cylinders.…”

“…Although its calculation is difficult, there are few cases where ½g has been obtained analytically as in the case of spheres [1], ellipsoids [4,5], long cylinders [6] and dumbbells consisting of two identical spheres [6,7]. Fortunately, accurate numerical approaches have been developed to calculate the intrinsic viscosity of arbitrarily-shaped particles [8,9].…”

How thick is the layer of thermal volume surrounding the protein?

“…Here we only shortly remark that the applied method is based on the analogy between the basic equations of hydrodynamics and electrostatics. The pioneering works of Hubbard and Douglas [39] and Zhou [16,40] have been developed further.…”