Numerical Simulation of the Flow of Highly Viscous Drops Down a Tapered Tube

[+] Author and Article Information
R. Tran-Son-Tay, T. F. Kirk, D. V. Zhelev, R. M. Hochmuth

Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708

J Biomech Eng 116(2), 172-177 (May 01, 1994) (6 pages) doi:10.1115/1.2895716 History: Received January 18, 1993; Revised May 04, 1993; Online March 17, 2008


The flow of a highly viscous drop surrounded by an inviscid fluid inside a tapered tube is analyzed according to a Newtonian, liquid-drop model in which a variational method is used to simultaneously solve the hydrodynamic equations for low Reynolds-number flow and the equations for membrane equilibrium with a constant membrane tension. It is found that the flow in the end caps is plug and radial in the conical section of the drop. The results are compared to a simplified analytical theory that makes these assumptions. Very good agreement is found between the two approaches. Both approaches are used to analyze existing experimental results of passive neutrophils flowing down a tapered tube. The theoretical models give a good fit to published experimental data by Bagge et al. (1977) at driving pressures of 20 and 40 mm H2 O for a membrane cortical tension of 0.024 dyn/cm and an apparent cytoplasmic viscosity of about 2400 and 1400 poise, respectively.

Copyright © 1994 by The American Society of Mechanical Engineers
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