透過您的圖書館登入
IP:18.212.87.137
  • 學位論文

帶電球型複合粒子懸浮液之沉降速度與沉降電位

Sedimentation velocity and potential in concentrated suspensions of charged composite spheres

指導教授 : 葛煥彰

摘要


本論文以理論探討帶有固定電荷的複合球型粒子在電解質溶液中形成懸浮系統所進行的沉降運動。複合粒子可分成二個部份;一為內部,即中心固體的部分,溶液中的離子與流體皆無法穿透其表面;另一為表面層,即為中心固體周圍吸附的均勻多孔性物質層或高分子層,而離子與流體皆可自由地穿透。解析的過程中,吾人使用單元小室模型以簡化粒子間的交互作用,考慮在任意電雙層厚度但低電位的條件下,求解Poisson-Boltzmann方程式和修正過的Stokes方程式。由於所考慮的系統相對於平衡狀態只受到一微小擾動,可先將原本交互聯立的非線性電動力微分方程式轉化為線性的問題,再配合正規微擾(regular perturbation)分析法以及適當的邊界條件,可求得小室內的電解質溶液中的電位分佈、流速分佈、壓力分佈以及電化學位能分佈。 求解電動力方程式後,再藉由平衡作用於粒子的重力、電力和流體阻力等三種力後,可以求得帶電複合粒子的沉降速度以及粒子懸浮液之沉降電位的解析形式表示式。結果顯示:複合粒子內部的水力摩擦環節與固定電荷密度、粒子表面的電雙層厚度、粒子在電解質溶液中的濃度、以及複合粒子表面層的內外半徑比等因素都對粒子的沉降速度以及懸浮液之沉降電位有顯著且複雜的影響。

關鍵字

球型粒子 複合粒子 沉降 懸浮液

並列摘要


The body-force-driven migration in a homogeneous suspension of charged composite spherical particles, each with the structure of a solid core surrounded by a porous shell, in an electrolyte solution is analyzed. The porous shell of a particle is treated as a solvent-permeable and ion-penetrable surface polymer layer of finite thickness, in which idealized hydrodynamic frictional segments with fixed charges are assumed to distribute at a uniform density. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the surface layer of the charged composite particle migrating in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the fixed charge densities of the rigid core surface and surface layer of the composite sphere as the small perturbation parameters. An analytical expression for the settling velocity of the composite sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged composite spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and sedimentation potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated. In the limiting cases, the analytical solutions describing the sedimentation velocity and potential for charged composite spheres reduce to those for charged solid spheres and for charged porous spheres.

並列關鍵字

composite spheres Sedimentation suspensions

參考文獻


[14]Masliyah, J. H., Neale, G. & Malysa K 1987 van de Ven TGM Chem Eng Sci 42:245-253
[57]van de Ven, T. G. M. 1989 Colloidal Hydrodynamics, Academic Press, London
[3]Masliyah J. H. 1994 Electrokinetic Transport Phenomena, AOSTRA, Edmonton, Alberta, Canada
[4]Booth, F. 1954 J. Chem. Phys. 22 ,1956.
[5]Dukhin, S. S. 1993 Adv. Colloid Interface Sci. 44, 1.

延伸閱讀