- 期刊
Mathematical Model for Biological Vesicle in Osmophoretic Migration
生物胞囊粒子滲透泳運動之數學模型
摘要
本文以一半解析半數值的數學模式探討一顆球形且外部包覆著半透膜之生物胞囊粒子垂直兩平行平板之滲透泳運動。假設外加的固定濃度梯度場的方向垂直平板且生物胞囊粒子進行滲透泳運動時仍維持球形。平板的存在對於生物胞囊粒子之滲透泳會產生兩種效應，一方面平板使得流體作用於生物胞囊粒子之黏滯力增加，另一方面濃度場受到平板的影響會加速生物胞囊粒子之泳動速度。使用圓球與圓柱兩座標系統並且利用邊界取點法可求解出主導生物胞囊內外濃度分佈與流體速度分佈之濃度與動量方程式，而生物胞囊粒子進行滲透泳運動的速度亦可以求得，並與雙球座標系統方法之計算結果互相比較，其結果相當一致。而平板之邊界效應，會增加生物胞囊粒子的運動速度。
關鍵字
無資料並列摘要
Osmophoresis indicates the motion of biological cells or small capsules in concentration gradients. This study presents a mathematical model that combined analytical- numerical study for the osmophoretic migration of a spherical biological vesicle perpendicular to two parallel plates. The imposed concentration gradient is constant and perpendicular to two parallel plates. The biological vesicle, which is a body of fluid enveloped by a continuous semipermeable membrane, may hold arbitrary solute and is assumed to maintain its spherical shape. The existence of the plane walls result in two basic effects on the biological vesicle velocity: first, the walls increase viscous retardation of the moving biological vesicle; secondly, the local concentration gradient on the biological vesicle surface is enhanced by the walls, therefore speeding up the biological vesicle. In order to solve the concentration and hydrodynamic governing equations, general solutions are constructed from the fundamental solutions in both the circular cylindrical and spherical coordinate systems. The boundary conditions are enforced first at the plane wall by the Hankel transforms and then on the biological vesicle surface by means of a boundary collocation method. For special cases of osmophoretic migration of a spherical biological vesicle normal a single plane wall, the collocation result of numerical simulations agree well with the solutions obtained by using spherical bipolar coordinates. In general, the existence of the walls always give rise to an enhancement in the osmophoretic migration.