Effects of electric charge on osmotic flow across periodically arranged circular cylinders

Abstract

An electrostatic model is developed for osmotic flow across a layer consisting of identical circular cylinders with a fixed surface charge, aligned parallel to each other so as to form an ordered hexagonal arrangement. The expression of the osmotic reflection coefficient is derived for spherical solutes with a fixed surface charge suspended in an electrolyte, based on low-Reynolds-number hydrodynamics and a continuum, point-charge description of the electric double layers. The repulsive electrostatic interaction between the surface charges with the same sign on the solute and the cylinders is shown to increase the exclusion region of solute from the cylinder surface, which enhances the osmotic flow. Applying the present model to the study of osmotic flow across the endothelial surface glycocalyx of capillary walls has revealed that this electrostatic model could account well for the reflection coefficients measured for charged macromolecules, such as albumin, in the physiological range of charge density and ion concentration.Key words: biomedical flows, biological fluid dynamics, low-Reynolds-number flows IntroductionOsmotic flow is generated between solutions of different concentrations that are separated by a porous membrane. When only solvent can enter the pores and the solutes are impermeable, a net volume flux of the solvent, referred to as the osmotic flow, is realized. If the solutes are only partially excluded from the membrane, then an osmotic reflection coefficient, σ v , must be introduced so as to express the solvent flux across the leaky membrane. In this case, the thermodynamic principles yield the following expression for the solvent flux J v per unit cross-sectional area when a hydrostatic pressure difference ( p ∞ ) and osmotic pressure difference ( π ∞ ) are applied across the membranewhere L p is the hydraulic permeability and ∞ denotes the bulk solution conditions on both sides of the membrane. The accompanying expression for the solute flux J s is

Microvascular Transport and Tumor Cell Adhesion in the Microcirculation

“…Sugihara-Seki et al 82 proposed an electrostatic model to predict the effects of surface charge on the osmotic reflection coefficient of charged spherical solute across the ESG, based on the combination of low-Reynolds-number hydrodynamics and a continuum description of the electric double layers. The ESG was assumed to consist of identical circular cylinders with a fixed surface charge, aligned parallel to each other so as to form an ordered hexagonal arrangement.…”

Charge effects on the hindered transport of macromolecules across the endothelial surface glycocalyx layer

“…1(b)), and compute the values of F t , F 0 and φ for this configuration, by using appropriate periodic and symmetric boundary conditions. The procedures (i) and (ii) are described in detail elsewhere [32,33]. In procedure (i), the Stokes equation and the continuity equation were solved using a finite element method for a spherical solute, in the two cases of either the solute translating in the x-direction in an otherwise quiescent fluid or the stationary solute immersed in a pressure-driven flow in the x-direction.…”

“…Similar models for the EGL were adopted to study osmotic flow across the EGL and to estimate the osmotic reflection coefficient σ v in Eq. (1) for the neutral case [40] and for the charged case [6,33]. In Sugihara-Seki of the EGL model consisting of hexagonally arranged circular cylinders of radius r f .…”

“…Region OBDF, denoted A , is available for the fluid, and region OAEF, denoted A * , is available for the center of the solute. et al [33], the ions in the electrolyte solution were assumed to be sufficiently small, so that a continuum, point-charge description of the electrostatic double-layers was used. The electrostatic potential in the electrolyte solution around a solute was determined using a linearized form of the Poisson-Boltzmann equation, i.e., the Debye-Hückel equation, to evaluate the interaction energy between the solute and the cylinders.…”

“…The electrostatic potential in the electrolyte solution around a solute was determined using a linearized form of the Poisson-Boltzmann equation, i.e., the Debye-Hückel equation, to evaluate the interaction energy between the solute and the cylinders. In the present study, the results of the electrostatic interaction energy obtained in Sugihara-Seki et al [33] are used to estimate the diffusive and convective transport of spherical solutes across the EGL, i.e. ω and σ f in Eq.…”