Diffusiophoresis of a Colloidal Cylinder at Small Finite Péclet Numbers

• Main Authors: Yu C. Chang, Huan J. Keh
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Colloids and Interfaces
• Subjects: diffusiophoresis; colloidal cylinder; thin polarized diffuse layer; solute convection effect; singular perturbation method
• Online Access: https://www.mdpi.com/2504-5377/3/2/44

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 P&#233;clet number <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>e</mi> </mrow> </semantics> </math> </inline-formula>. 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <msup> <mi>e</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula>. It is found that the perturbed solute concentration and fluid velocity distributions have the order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>e</mi> </mrow> </semantics> </math> </inline-formula>, but the leading correction to the particle velocity has the higher order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <msup> <mi>e</mi> <mn>2</mn> </msup> <mi>ln</mi> <mi>P</mi> <mi>e</mi> </mrow> </semantics> </math> </inline-formula>. The correction to the particle velocity to the order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <msup> <mi>e</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>e</mi> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics> </math> </inline-formula> can be about 17% smaller or 0.2% greater than that at <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>e</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>. 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <msup> <mi>e</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula>.