Park H M, Lee W M
Department of Chemical and Biomolecular Engineering, Sogang University, Seoul, South Korea.
J Colloid Interface Sci. 2008 Jan 15;317(2):631-6. doi: 10.1016/j.jcis.2007.09.027. Epub 2007 Sep 15.
Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.
许多生物流体，如血液和DNA溶液，都是粘弹性的，表现出非凡的流动行为，这在牛顿流体中并不存在。采用适当的本构方程，这些奇特的流动行为可以通过各种数值方法进行合理建模和预测。然而，粘弹性流动的控制方程不易求解，特别是对于电渗流，其中流向速度在壁面处从零迅速变化到非常薄的电双层外部的几乎均匀速度。在本研究中，我们设计了一种简单的方法来计算通过微通道的粘弹性电渗流的体积流量。它基于牛顿流体电渗流中广泛采用的亥姆霍兹-斯莫卢霍夫斯基速度的概念。结果表明，通过求解一个简单的三次代数方程可以得到粘弹性流体的亥姆霍兹-斯莫卢霍夫斯基速度。使用该亥姆霍兹-斯莫卢霍夫斯基速度获得的体积流量与通过求解各种粘弹性流体的控制偏微分方程获得的体积流量几乎相同。
