Keh HJ, Liu YC
Department of Chemical Engineering, National Taiwan University, Taipei, 106-17, Taiwan, Republic of China
J Colloid Interface Sci. 1997 Nov 1;195(1):169-91. doi: 10.1006/jcis.1997.5147.
The sedimentation of a charged composite particle composed of a solid core and a surrounding porous shell in an electrolyte solution is analytically studied. In the solvent-permeable and ion-penetrable porous surface layer of the particle, idealized hydrodynamic frictional segments with fixed charges are assumed to distribute at a uniform density. The equations which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field inside and outside the surface layer of a charged composite particle migrating in an unbounded solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a composite sphere with the charge densities of the rigid core surface and of the surface layer as the small perturbation parameters. An analytical expression for the settling velocity of the composite sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. The result demonstrates that the presence of the fixed charges in the composite sphere slows down its settling velocity relative to that of an uncharged one. A closed-form formula for the sedimentation potential in a dilute suspension of identical charged composite spheres is also derived by using the requirement of zero net electric current. The Onsager reciprocal relation is found to be satisfied between sedimentation and electrophoresis. It is shown that spherically-symmetric "neutral" composite particles (bearing no net charge) can undergo electrophoresis, induce sedimentation potential, and experience a smaller settling velocity relative to corresponding uncharged particles. The direction of the electrophoretic velocity or the induced potential gradient is determined by the fixed charges in the porous surface layers of the particles. In the limiting cases, the analytical solutions describing the sedimentation velocity and sedimentation potential (or electrophoretic mobility) for charged composite spheres reduce to those for charged solid spheres and for charged porous spheres. Copyright 1997 Academic Press. Copyright 1997Academic Press
对由固体核和周围多孔壳组成的带电复合粒子在电解质溶液中的沉降进行了分析研究。在粒子的溶剂可渗透且离子可穿透的多孔表面层中，假设带有固定电荷的理想化流体动力摩擦段以均匀密度分布。假设系统仅略微偏离平衡态，对在无界溶液中迁移的带电复合粒子表面层内外的离子浓度分布、电势分布以及流体流场的控制方程进行线性化。使用微扰方法，以刚性核表面和表面层的电荷密度作为小扰动参数，求解这些线性化方程以得到复合球体的解。通过复合球体的重力、静电力和流体动力之间的平衡，得到了其沉降速度的封闭形式解析表达式。结果表明，复合球体中固定电荷的存在使其沉降速度相对于不带电球体减慢。利用净电流为零的条件，还推导了相同带电复合球体稀悬浮液中沉降电势的封闭形式公式。发现沉降和电泳之间满足昂萨格互易关系。结果表明，球形对称的“中性”复合粒子（不带净电荷）可以进行电泳，产生沉降电势，并且相对于相应的不带电粒子沉降速度更小。电泳速度或感应电势梯度的方向由粒子多孔表面层中的固定电荷决定。在极限情况下，描述带电复合球体沉降速度和沉降电势（或电泳迁移率）的解析解简化为带电固体球体和带电多孔球体的解析解。版权所有1997学术出版社。版权所有1997学术出版社
