細孔內球形囊胞之滲透泳

Osmophoresis of a Spherical Vesicle in Small Pore

許運軒(Yun-Shuan Hsu)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.01768

摘要

滲透泳是指由半透膜包覆而成的囊胞粒子，因施加溶質濃度梯度造成粒子兩端滲透壓差所引發的運動。 當一囊胞粒子於一細孔中，邊界對滲透泳之效應，其一來自囊胞粒子與邊界產生的濃度梯度交互作用，另一來自於流體之黏滯作用。 在本論文中，我們將假設粒子在低Reynolds數及低Peclet數下進行擬穩態之滲透泳動，討論兩種不同邊界之影響。
首先，在第二章中，我們分析一囊胞粒子在一圓柱形孔洞中沿其中心線之滲透泳運動。 對溶液施加一線性濃度梯度，分別考慮在孔壁上溶質不可穿透及符合外加線性濃度場之兩種邊界條件，將通解代入管壁邊界條件，利用Fourier轉換將解以無窮級數形式表現，再代入囊胞粒子球面邊界條件利用邊界取點法求出數值解，並將粒子速度與距離邊界之相對關係作圖呈現。
在第三章中，我們分析一囊胞粒子在兩無限平行平板中沿垂直平板方向運動。 沿粒子運動方向施加一外加線性濃度梯度，我們將通解代入管壁邊界條件，利用Hankel轉換將解以無窮級數形式表現出來，再代入囊胞粒子球面邊界條件利用邊界取點法求出數值解，並將粒子速度與距離邊界之相對關係作圖呈現。
由第二章及第三章兩種情況下使用邊界取點法所得到之結果和由利用反射法所得到之近似結果相比較，彼此相符。 邊界的存在將會加快囊胞粒子泳動的速度，但粒子速度和粒子與邊界的相對距離之間並非呈現一單調遞增的函數關係。 研究結果顯示，邊界存在對囊胞粒子滲透泳之影響相當顯著。

關鍵字

滲透泳

並列摘要

Osmophoresis is the motion of vesicles in liquid solution in response to an applied solute concentration gradient. The presence of a neighboring boundary causes two basic effects on the osmophoretic velocity of a vesicle: first, the local concentration gradients on the vesicle surface are altered by the wall, thereby speeding up or slowing down the vesicle; secondly, the wall enhances the viscous interaction effect on the moving vesicle. In this dissertation, the boundary effects on the osmophoresis of a spherical vesicle in small pores are studied theoretically in the quasi-steady limit of negligible Reynolds and Peclet numbers.
First, in chapter 2, we analyze the osmophoretic motion of a spherical vesicle along the centerline of a circular cylindrical pore. The imposed solute concentration gradient is uniform and parallel to the pore wall, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. To solve the equations of conservation of mass and momentum, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall by the Fourier transforms and then on the vesicle surface by a collocation technique. Numerical results for the osmophoretic velocity of the vesicle relative to that under identical conditions in an unbounded solution are presented for various values of the relevant properties of the vesicle as well as the relative separation distance between the vesicle and the pore wall.
In chapter 3, we investigate the osmophoretic motion of a spherical vesicle situated at an arbitrary position between two infinite parallel plane walls. The imposed solute concentration gradient is uniform and perpendicular to the plane walls. To solve the equations of conservation of mass and momentum, the general solutions are constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the plane walls by the Hankel transform and then on the vesicle surface by a collocation technique. Numerical results for the osmophoretic velocity of the vesicle relative to that under identical conditions in an unbounded solution are presented for various values of the relevant properties of the vesicle-solution system as well as the relative separation distances between the vesicle and the plane walls.
The collocation results of both of the cases discussed in chapters 2 and 3 agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the neighboring boundaries enhances the vesicle velocity, but its dependence on the relative vesicle-wall separation distances is not necessarily to be monotonic. In general, the boundary effect on osmophoresis is quite significant.

並列關鍵字

osmophoresis

參考文獻

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Chen, P.Y., Keh, H.J., 2003. Boundary effects on osmophoresis: motion of a spherical vesicle parallel to two plane walls. Chem. Engng. Sci. 58, 4449-4464.

Ganatos, P., Weinbaum, S., Pfeffer, R., 1980. A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion. J. Fluid Mech. 99, 739-753.