Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, Republic of China.
J Chem Phys. 2011 Jan 28;134(4):044125. doi: 10.1063/1.3537975.
The magnetohydrodynamic (MHD) effects on the translation and rotation of a charged colloidal sphere situated at the center of a spherical cavity filled with an arbitrary electrolyte solution when a constant magnetic field is imposed are analyzed at the quasisteady state. The electric double layers adjacent to the solid surfaces may have an arbitrary thickness relative to the particle and cavity radii. Through the use of a perturbation method to the leading order, the Stokes equations modified with the electric∕Lorentz force term are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution in the fluid phase from solving the linearized Poisson-Boltzmann equation, we obtain explicit formulas for the translational and angular velocities of the colloidal sphere produced by the MHD effects valid for all values of the particle-to-cavity size ratio. For the limiting case of an infinitely large cavity with an uncharged wall, our result reduces to the relevant solution for an unbounded spherical particle available in the literature. The boundary effect on the MHD motion of the spherical particle is a qualitatively and quantitatively sensible function of the parameters a∕b and κa, where a and b are the radii of the particle and cavity, respectively, and κ is the reciprocal of the Debye screening length. In general, the proximity of the cavity wall reduces the MHD migration but intensifies the MHD rotation of the particle.
在施加恒磁场的情况下，分析了处于充满任意电解质溶液的球形腔中心的带电胶体球的平移和旋转的磁流体动力学（MHD）效应在准稳态下的情况。与固体表面相邻的双电层相对于颗粒和腔半径可能具有任意的厚度。通过对主导阶的微扰方法，使用广义互易定理处理了带有电场/洛伦兹力项的斯托克斯方程。通过求解线性化的泊松-玻尔兹曼方程，我们得到了在所有颗粒与腔尺寸比的情况下，由 MHD 效应产生的胶体球的平移和角速度的显式公式。对于具有无电荷壁的无限大腔的极限情况，我们的结果简化为文献中可用的无限大球形颗粒的相关解。球形颗粒的 MHD 运动的边界效应是参数 a∕b 和 κa 的定性和定量敏感函数，其中 a 和 b 分别是颗粒和腔的半径，κ 是德拜屏蔽长度的倒数。一般来说，腔壁的接近会降低 MHD 迁移，但会加剧颗粒的 MHD 旋转。
