Numerical simulation of the flow of highly viscous drops down a tapered tube.
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.
Tran-Son-Tay
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Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708.
Kirk
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Zhelev
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Hochmuth
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D005069:Evaluation Studies as Topic; D008433:Mathematics; D008962:Models, Theoretical; D009504:Neutrophils; D012212:Rheology; D013500:Surface Tension; D014783:Viscosity