The bulk electroviscous effect

Abstract

Electroviscous stresses arise as hydrodynamic flows disturb the ionic (Debye) clouds that screen charged surfaces in electrolyte solutions. The contribution thereof to the effective bulk viscosity (also known as the second or volume viscosity) of two-phase suspensions is quantified here. Specifically, the bulk viscosity of two model suspensions is calculated: (1) a dilute dispersion of rigid charged spherical particles immersed in a compressible electrolyte that undergoes uniform dilatation and (2) a dilute suspension of charged gas bubbles expanding uniformly in an incompressible electrolyte. In both cases, it is assumed that the fluid flow only slightly drives the Debye cloud out of equilibrium, which formally requires that the ratio of the ion diffusion to flow time scales—a Peclet number—is small. For a suspension of rigid particles, the electroviscous contribution to the effective bulk viscosity is proportional to the particle volume fraction and decreases monotonically as the ratio of the particle radius to the Debye length increases. Similar behavior is well known for the electroviscous contribution to the effective shear viscosity of a dilute hard-sphere suspension; a quantitative comparison between the bulk and shear viscosities is made. In contrast, the electroviscous contribution to the bulk viscosity of a dilute suspension of bubbles is independent of the bubble volume fraction and attains a finite value in the limit of vanishing Debye length.