Abstract

Abstract

Highlights

  • The motion of an elongated bubble confined in a small geometry is typical of many biological and engineering systems

  • The goal of this paper is to study the dynamics of a confined Taylor bubble that moves in a shear-thinning fluid and to clarify the competition of the zero-shear-rate and the shear-thinning effects on bubble characteristics

  • We study the motion of a confined Taylor bubble in a shear-thinning fluid

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Summary

Introduction

The motion of an elongated bubble confined in a small geometry is typical of many biological and engineering systems. Both the local velocity field and integral variables (e.g. pressure drop and film thickness) are poorly predicted in free-surface flows due to the unrealistically and unbounded growth of the viscosity at small shear rates This is confirmed by the work of Hewson, Kapur & Gaskell (2009) that studied the motion of a Taylor bubble through both power-law and an Ellis fluids. In all the aforementioned studies, a generalized understanding of the bubble motion that embeds both the low- and high-shear-rate behaviours is still missing, including a generalization of the scaling laws for the film thickness and the bubble speed To fill this gap, the goal of this paper is to study the dynamics of a confined Taylor bubble that moves in a shear-thinning fluid and to clarify the competition of the zero-shear-rate and the shear-thinning effects on bubble characteristics. The results obtained shed light on the mechanisms that control the motion of a Taylor bubble in a realistic shear-thinning fluid

Problem formulation
Lubrication model
Film equation
Scaling of the film equation
Boundary conditions and numerical solution
Characteristics of the front meniscus
Scaling of the film thickness and generalization of the capillary number
Bubble speed
Recirculating flow patterns
Conclusions

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