Casarella Angela, Gourdin-Bertin Simon, Chassagne Claire
Department of Architecture and Civil Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden.
Independent Researcher, F-75012 Paris, France.
Entropy (Basel). 2025 Mar 24;27(4):336. doi: 10.3390/e27040336.
A new analytical equation for the electrophoretic mobility of a colloidal sphere, homogeneously charged, is derived. This equation reduces to the well-known Henry's formulation for low surface potentials. For high surface potentials, the equation is compared to the full numerical result. It is found that the equation performs well up to surface potentials of 50 mV. For larger surface potentials, the equation performs well for κa>10, where κ is the inverse of Debye' s length and the radius of the particle. Differences between analytical and numerical solutions for κa<10 are studied. The case of a particle with a constant surface charge is discussed. In that case, a very simple equation relates the surface charge of the particle to the electrophoretic mobility for κa>10.
推导了一个关于均匀带电胶体球电泳迁移率的新解析方程。该方程在低表面电势时简化为著名的亨利公式。对于高表面电势，将该方程与完整的数值结果进行了比较。结果发现，该方程在表面电势高达50 mV时表现良好。对于更大的表面电势，当κa>10时该方程表现良好，其中κ是德拜长度的倒数，a是粒子半径。研究了κa<10时解析解与数值解之间的差异。讨论了具有恒定表面电荷的粒子的情况。在这种情况下，对于κa>10，一个非常简单的方程将粒子的表面电荷与电泳迁移率联系起来。
