Diffusiophoresis of a charge regulated spherical polyelectrolyte nanogel (PE) due to an externally imposed ionic concentration gradient is considered. The immobile charge density of the nanogel develops through the association/dissociation reactions of their inorganic functional groups. The nanogel is ion and fluid permeable with dielectric permittivity different from that of the surrounding electrolyte medium. This difference in dielectric permittivity creates an ion partitioning due to the difference in self energy of ions. The Nernst–Planck equation for ion transport and the Poisson equation (PNP) for the electric field are modified to take into account the ion partitioning effects. The diffusiophoresis mechanism is governed by the electrophoresis generated by the induced electric field and chemiphoresis develops due to the mitigation of counterions across the double layer of the nanogel. In addition, the convection dominated double layer polarization and the counterion condensation as well as the electroosmotic flow created by the gel immobile charge play a role in the diffusiophoresis. All these effects are incorporated through the modified PNP equations coupled with the Navier–Stokes equations. The governing equations in their full form are solved numerically through a control volume approach. Present computed solutions for the limiting cases are in good agreement with the existing solutions based on the first-order perturbation analysis. In order to illustrate the diffusiophoresis mechanism we have measured the induced electric field and effective charge density of the PE and analyzed its dependence on several electrokinetic parameters. The contribution due to chemiphoresis is low for PE compared to a rigid colloid. For a highly permeable PE the diffusiophoretic velocity increases and approaches a saturation for higher range of the PE fixed charge density. The ion partitioning effect depletes counterions in PE to manifests its diffusiophoretic velocity. The diffusiophoretic velocity of PE for pH > IEP is higher than the case for which pH < IEP.

考虑由于外部施加的离子浓度梯度引起的电荷调节球形聚电解质纳米凝胶（PE）的扩散电泳。纳米凝胶的固定电荷密度通过其无机官能团的缔合/离解反应发展。纳米凝胶是离子和流体可渗透的，具有与周围电解质介质不同的介电常数。介电常数的这种差异由于离子自身能量的差异而产生了离子分配。考虑到离子分配效应，对离子迁移的能斯特-普朗克方程和电场的泊松方程（PNP）进行了修改。扩散电泳机理由感应电场产生的电泳控制，由于跨纳米凝胶双层的抗衡离子的减少，化学电泳得以发展。另外，对流主导的双层极化和抗衡离子的缩合以及由凝胶固定电荷产生的电渗流在扩散电泳中起作用。所有这些影响都通过修改后的PNP方程与Navier–Stokes方程结合在一起。完整的控制方程通过控制量法以数值方式求解。当前针对极限情况的计算解决方案与基于一阶扰动分析的现有解决方案非常吻合。为了说明扩散电泳机理，我们测量了PE的感应电场和有效电荷密度，并分析了其对几个电动参数的依赖性。与刚性胶体相比，PE的化学电泳贡献较小。对于高渗透性的PE，发散速度增加，并在PE固定电荷密度较高的范围内接近饱和。离子分配效应耗尽了PE中的抗衡离子，从而显示出其扩散电泳速度。pH> IEP时，PE的扩散电泳速度高于pH <IEP时。对于高渗透性的PE，发散速度增加，并在PE固定电荷密度较高的范围内接近饱和。离子分配效应耗尽了PE中的抗衡离子，从而显示出其扩散电泳速度。pH> IEP时，PE的扩散电泳速度高于pH <IEP时。对于高渗透性的PE，发散速度增加，并在PE固定电荷密度较高的范围内接近饱和。离子分配效应耗尽了PE中的抗衡离子，从而显示出其扩散电泳速度。pH> IEP时，PE的扩散电泳速度高于pH <IEP时。