Diffusiophoresis of a charged particle in a microtube

Abstract

The diffusiophoresis of a charged sphere along the axis of a circular microtube filled with an electrolyte solution is studied theoretically. The tube wall may be either nonconductive and impermeable or prescribed with a linear electrolyte concentration distribution. The electric double layers at the solid surfaces are thin, but the diffuse-layer polarization effect over the particle surface is considered. The general solutions to the electrokinetic differential equations are expressed in spherical and cylindrical coordinates, whereas the boundary conditions at the particle surface are satisfied by a collocation technique. The collocation solutions for the diffusiophoretic velocity of the particle, which are in good agreement with the asymptotic formula derived from a reflection method, are obtained for various values of the radius ratio and zeta potential ratio between the particle and the microtube and of other relevant parameters. The contributions from the diffusioosmotic flow along the tube wall and wall-corrected diffusiophoretic driving force to the particle velocity can be superimposed due to the linearity. Although the diffusiophoretic velocity in an uncharged microtube is in general a decreasing function of the particle-to-tube radius ratio and can reverse its direction, it can increase with increases in this ratio due to the competition of the wall effects of possible electrochemical enhancement and hydrodynamic retardation to the particle motion. When the zeta potentials associated with the tube and particle are equivalent, the diffusioosmotic flow induced by the tube wall dominates the diffusiophoretic motion.

Diffusiophoresis, Diffusioosmosis, and Microfluidics: Surface-Flow-Driven Phenomena in the Presence of Flow

“…The presence and influence of flow in simple geometries are relatively well understood in diffusiophoresis studies. Questions may arise for other porous structures with heterogeneity, , channels with comparable size with the particles, channels with reacting walls and/or particles, porous particles, soft surfaces, , density-driven flows, etc. In general, spatial and/or temporal heterogeneity (Figure ) in the system configuration may not behave in a linear manner, especially when both diffusiophoresis and diffusioosmosis are present.…”

Diffusiophoresis of a spherical particle in porous media

“…where g = a/l. Eqn ( 27) and ( 28) replace (23). In sum, we solve eqn ( 19) and ( 20) subject to eqn ( 25), ( 27) and ( 28) for h and C 1 i using the built-in solver NDSolve in Wolfram Mathematica.…”

“…Motivated by manufacturing colloidal coatings for vehicles, Prieve et al 5,6 pioneered a theory to predict the diffusiophoretic motion of a colloidal particle in a concentration gradient of electrolytes, the so-called log-sensing relation U = Mrlog n, where the mobility M relates the particle diffusiophoretic velocity U and gradient of the natural logarithm of the solute concentration n. Since then, much work has been done to characterize the diffusiophoretic mobility of rigid particles in various solutes, [7][8][9][10][11][12] the mobility of drops and soft particles, [13][14][15][16][17][18][19][20] and the mobility in confined environments. [21][22][23] In addition to develop fundamental theories for diffusiophoresis, progress has been made in devising new applications using diffusiophoresis, ranging from mixing and separation of colloids, 9,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] enhanced oil recovery, [41][42][43] drug delivery, 44,45 to water and surface cleaning. [46...…”

“…Since then, much work has been done to characterize the diffusiophoretic mobility of rigid particles in various solutes, 7–12 the mobility of drops and soft particles, 13–20 and the mobility in confined environments. 21–23 In addition to develop fundamental theories for diffusiophoresis, progress has been made in devising new applications using diffusiophoresis, ranging from mixing and separation of colloids, 9,24–40 enhanced oil recovery, 41–43 drug delivery, 44,45 to water and surface cleaning. 46–48 The strengths of diffusiophoresis are prominent in two aspects.…”

Diffusiophoresis of a Charged Porous Particle in a Charged Cavity

“…Colloidal particles are seldom isolated or unbounded in various applications of diffusiophoresis. , In the limit of thin electric double layer (κ a → ∞), the normalized velocity field of the fluid caused by a hard particle undergoing diffusiophoresis is identical to that for electrophoresis and the boundary effects on electrophoresis, that have been widely investigated, can be employed to construe those on diffusiophoresis. Knowing that the boundary effect in diffusiophoresis is different from that in electrophoresis when the double layer polarization is embodied, the diffusiophoretic motions of a hard sphere with a thin but polarized double layer (say, κ a ≥ 20) parallel and perpendicular to one or two plates as well as along the axis of a microtube were investigated through the use of a semianalytical boundary collocation method.…”