A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions
A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions
复制标题
在强电解质溶液中，电场驱动的液滴或囊泡的流动和变形模型
DOI：
10.1017/jfm.2022.469
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发表时间：
2022-06-20
影响因子：
3.7
通讯作者：
Siegel, Michael
中科院分区：
文献类型：
--
作者：
Ma, Manman;Booty, Michael R.;Siegel, Michael
构建了一个模型来描述包含并嵌入电解质溶液中的液滴或囊泡的流场和任意变形，其中流动和变形由施加的电场引起。所施加的场产生动电流，其建立在充电时间尺度τ（*c）= λ（*）a（*）/D-* 上，其中λ（*）是德拜屏蔽长度，a（*）是夹杂物长度尺度，D-* 是离子扩散常数。该模型基于Poisson-Nernst-Planck和Stokes方程。通过形成强电解质的极限（溶解的盐在溶液中完全电离）以及薄德拜层的极限，这些都被减少或简化。相反极性的德拜层形成在液滴界面或囊泡膜的两侧，一起形成双电层。给出了该模型的两个公式。一个是利用一个积分方程的界面或膜表面上的速度场与一对积分方程的双层的外表面上的静电势。另一种是利用应力平衡边界条件的形式，将双层结构纳入层外表面上的因变量之间的关系中。这就构成了一个界面边界条件，它驱动了双层外的非受迫斯托克斯流。对于这两种制剂的关系，从每个德拜层中的离子的运输给额外的边界条件的电位和离子浓度外的双层。
A model is constructed to describe the flow field and arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the flow and deformation are caused by an applied electric field. The applied field produces an electrokinetic flow, which is set up on the charge-up time scale tau(*c) = lambda(*)a(*)/D-*, where lambda(*) is the Debye screening length, a(*) is the inclusion length scale and D-* is an ion diffusion constant. The model is based on the Poisson-Nernst-Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which dissolved salts are completely ionised in solution, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop interface or vesicle membrane, together forming an electrical double layer. Two formulations of the model are given. One utilises an integral equation for the velocity field on the interface or membrane surface together with a pair of integral equations for the electrostatic potential on the outer faces of the double layer. The other utilises a form of the stress-balance boundary condition that incorporates the double layer structure into relations between the dependent variables on the layers' outer faces. This constitutes an interfacial boundary condition that drives an otherwise unforced Stokes flow outside the double layer. For both formulations relations derived from the transport of ions in each Debye layer give additional boundary conditions for the potential and ion concentrations outside the double layer.