Abstract
The diffusiophoretic migration of a circular cylindrical particle in a nonelectrolyte solution with a solute concentration gradient normal to its axis is analytically studied for a small but finite Péclet number P e . The interfacial layer of interaction between the solute molecules and the particle is taken to be thin, but the polarization of its mobile molecules is allowed. Using a method of matched asymptotic expansions, we solve the governing equations of conservation of the system and obtain an explicit formula for the diffusiophoretic velocity of the cylinder correct to the order P e 2 . It is found that the perturbed solute concentration and fluid velocity distributions have the order P e , but the leading correction to the particle velocity has the higher order P e 2 ln P e . The correction to the particle velocity to the order P e 2 can be either positive or negative depending on the polarization parameter of the thin interfacial layer, establishing that the solute convection effect is complicated and can enhance or retard the diffusiophoretic motion. The particle velocity at P e = 0.6 can be about 17% smaller or 0.2% greater than that at P e = 0 . Under practical conditions, the solute convection effect on the diffusiophoretic velocity is much greater for a cylindrical particle than for a spherical particle, whose leading correction has the order P e 2 .
Highlights
A colloidal particle, when suspended in a fluid solution non-uniform in a solute concentration, will spontaneously move as a result of physical interaction between the solute molecules and the particle
The problem of diffusiophoresis of a long circular cylindrical particle normal to its axis at small but finite Péclet numbers is analyzed in the previous section
The diffusiophoresis of a long circular cylindrical particle surrounded by a thin polarized diffuse layer in a nonelectrolyte solution normal to its axis is analyzed for small but nonzero values of the Péclet number Pe
Summary
A colloidal particle, when suspended in a fluid solution non-uniform in a solute concentration, will spontaneously move as a result of physical interaction between the solute molecules and the particle. This motion is known as diffusiophoresis and was widely applied to particle motility and manipulations [1,2,3,4,5]. In the solution of a nonelectrolyte solute with a uniform concentration gradient. ∇ˆ C∞, the diffusiophoretic velocity of a colloidal sphere of radius a with a thin but polarized interfacial diffuse layer is [6] U 0 = kT η L∗K(1 + βa −1 ) ∇ˆ C∞, (1)
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