The Primary Electroviscous Effect of Rigid Polyions of Arbitrary Shape and Charge Distribution

Abstract

The viscosity of a dilute suspension of charged rigid particles exceeds that of a suspension of identical, but uncharged particles, and this is called the primary electroviscous effect. This excess viscosity arises as a result of the distortion of the ion atmosphere surrounding the polyion due to the fluid shear field in which it is placed. Consequently, any theory of the primary electroviscous effect must account for this distortion. Booth (Proc. Roy. Soc. (London) 1950, 203A, 533) and later Sherwood (J. Fluid Mech. 1980, 101, 609) achieved this for a spherical polyion of uniform equilibrium surface potential by solving the coupled (low Reynold's number) Navier−Stokes, Poisson, and ion transport equations. The primary objective of the present work is to extend this approach to rigid model polyions of arbitrary shape and charge distribution. The coupled transport equations are solved by an iterative boundary element (BE) procedure applied previously to the closely related problem of electrophoresis (Allison, S. A. Macromolecules 1996, 29, 7391). In test cases on spheres containing single central charges, the BE results are found to be in very good agreement with Sherwood. The BE approach is then applied to spherical polyions containing noncentrosymmetric charge distributions as well as short (20−40 base pair) DNA models in the monovalent salt range 0.005−0.6 M. For the DNA fragments, the primary electroviscous effect ranges from about 2% to 30% (40 bp) or 45% (20bp) as the KCl concentration is reduced from 0.6 to 0.005 M, respectively. Substantially larger effects are predicted if the monovalent salt is Tris−acetate, and this is due primarily to the lower mobility of the Tris counterion relative to K+. A secondary objective is to make contact between the BE approach and “bead methods”, which have been successfully used in modeling the viscosity of rigid, but uncharged macromolecules of arbitrary shape.

Electrophoresis of Protein Charge Ladders: A Comparison of Experiment with Various Continuum Primitive Models

“…The final surface is placed at a distance b/κ from S p , where b is typically 12-16. 37 Once a plated structure and its shell array are constructed, the orientationally averaged translational diffusion constant, D t , and the electrophoretic mobility, µ, as well as other transport properties, 38 are obtained by the BE procedure. For an irregularly shaped protein model, six separate BE calculations are carried out.…”

Primary Electroviscous Effect in a Suspension of Charged Porous Spheres

“…Analytic results for a thin double layer were later obtained by Hinch and Sherwood (11). As for nonspherical particles, the primary electroviscous effect has also been studied under various assumptions (12)(13)(14).…”

Electrokinetic transport of rigid macroions in the thin double layer limit: A boundary element approach

“…In general, these equations are coupled to each other and must be solved simultaneously. Different investigators and investigations may have followed somewhat different pathways to achieve this and have employed different computational strategies, but the underlying problem has basically been the same [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For a general model particle, it has been necessary to employ BE procedures [14][15][16], which is outlined in the next subsection.…”

“…The electrophoresis [12] and electroviscosity [13] of highly charged spheres containing a porous outer "gel" layer have also been modeled. Over the last 10 years, boundary element (BE) procedures have been developed that are applicable to rigid model macroions of arbitrary size, shape, and charge distribution [14,15]. This methodology has recently been generalized to include the presence of a gel layer [16].…”

“…As developed, the procedure is applicable to large particles of uniform "zeta" potential, but no assumption needs to be made about its actual shape. The principal advantage of the new approach is that the time consuming volume integrations that must be carried out in the general BE procedure [14][15][16] are eliminated. Numerical surface integrations remain, but their computation is rapid relative to the volume integrations.…”