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 H2O for a membrane cortical tension of 0.024 dyn/cm and an apparent cytoplasmic viscosity of about 2400 and 1400 poise, respectively.
Numerical Simulation of the Flow of Highly Viscous Drops Down a Tapered Tube
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Tran-Son-Tay, R., Kirk, T. F., III, Zhelev, D. V., and Hochmuth, R. M. (May 1, 1994). "Numerical Simulation of the Flow of Highly Viscous Drops Down a Tapered Tube." ASME. J Biomech Eng. May 1994; 116(2): 172–177. https://doi.org/10.1115/1.2895716
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