Pressure of a viscous droplet squeezing through a short circular constriction: An analytical model

Zhifeng Zhang, Corina Drapaca, Dmitry Gritsenko, Jie Xu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The model of a droplet squeezed through a narrow-constricted channel has many applications in pathology, chip/filter/membrane design, drug delivery, etc. Understanding the transient physics of the squeezing process is important in the design and optimization of many micro flow systems. However, available models often ignore the influence of droplet viscosity, and they usually feature low numerical efficiency by solving Navier-Stokes equations. In the present research, we developed a low-dimension analytical model to predict the pressure of squeezing a viscous droplet through a circular constricted channel with acceptable fidelity and low computational cost. Our approach is as follows. We first adapt the Hagen-Poiseuille law to predict the viscosity effect of droplet squeezing. Next, we obtain an analytical expression for the extra pressure caused by only the curvature change obtained. Finally, the general expression of squeezing pressure taking consideration of viscosity and surface tension is expressed. The analytical model we developed is in great agreement with the numerical solutions of the Navier-Stokes equation at a low Reynolds number and low capillary number. These findings have fundamental significance for future applications in engineering and industry.

Original languageEnglish (US)
Article number102004
JournalPhysics of Fluids
Volume30
Issue number10
DOIs
StatePublished - Oct 1 2018

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compressing
constrictions
viscosity
Navier-Stokes equation
pathology
low Reynolds number
delivery
interfacial tension
drugs
industries
chips
curvature
engineering
membranes
costs
filters
physics
optimization

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

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Pressure of a viscous droplet squeezing through a short circular constriction : An analytical model. / Zhang, Zhifeng; Drapaca, Corina; Gritsenko, Dmitry; Xu, Jie.

In: Physics of Fluids, Vol. 30, No. 10, 102004, 01.10.2018.

Research output: Contribution to journalArticle

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