Effective Viscosity of a Suspension of Fluid Droplets

本文以理論探討均勻液滴懸浮液在穩定狀態之有效黏度值。吾人假設雷諾數很小且液滴的表面張力夠大足以使液滴於運動中仍維持球形。對於一多成份稀薄液滴懸浮液，使用整體平均方法可將懸浮液有效黏度值表示成液滴體積分率之二次維利爾展開式。以邊界取點法先計算兩顆任意球形液滴於靜止液體與線性流暢中之流體力學交互作用參數值，再使用統計力學方法計算出懸浮液之整體平均黏性應力，吾人可以獲得不含布朗運動效應與強烈布朗運動效應兩種條件下，第二維利爾係數之數值結果。對於由相同液滴組成之中高濃度懸浮液，吾人使用單元小室模型，可以解析方法求出有效黏度值隨液滴體積分率變化之關係式。對於一些液滴懸浮系統的特例，吾人在稀薄與中高濃度範圍所得到的懸浮液有效黏度值與以往文獻做比較後發現，其結果相當一致。

關鍵字

無資料

並列摘要

An analytical study of the apparent viscosity of a suspension of fluid droplets dispersed uniformly in an immiscible fluid if presented based on steady-state low-Reynolds-number hydrodynamics. It is assumed that the interfacial tension is sufficiently great to preserve the spherical shape of the droplets. For a dilute polydisperse system, the method of ensemble aver-age is used to derive the viscosity formulas to the second order of the virial expansion in the volume fractions of the droplets. Employing boundary-collocation solutions for the hydrodynamic interactions between two arbitrary spherical droplets in a quiescent fluid and in a general linear flow, we obtain numerical results of the virial coefficients for both cases that indicate negligible Brownian motion and strong Brownian motion, respectively. For a relatively concentrated suspension of identical droplets, a unit cell model is used to predict the effective viscosity. Analytical expressions in closed form are obtained as functions of the volume fraction of the droplets in a broad range. In particular cases, our results for both dilute and concentrated suspensions agree well with the available calculations in the literature.

並列關鍵字

Viscosity of Emulsion ； Droplet Interaction ； Brownian Motion ； Ensemble Average ； Unit Cell Model

國際替代計量

Effective Viscosity of a Suspension of Fluid Droplets

全文下載

主題瀏覽