Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a upmuPIV measurement

Ulrich Mießner,Jerry Westerweel,Ralph Lindken,Thorben Helmers

doi:10.1007/s00348-021-03189-5

Ulrich Mießner, Jerry Westerweel + Show 2 more

Open Access

https://doi.org/10.1007/s00348-021-03189-5

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Abstract

In this study, we reconstruct the 3D pressure field and derive the 3D contributions of the energy dissipation from a 3D3C velocity field measurement of Taylor droplets moving in a horizontal microchannel (rm Ca_c=0.0050, rm Re_c=0.0519, rm Bo=0.0043, lambda =tfrac{eta _{d}}{eta _{c}}=2.625). We divide the pressure field in a wall-proximate part and a core-flow to describe the phenomenology. At the wall, the pressure decreases expectedly in downstream direction. In contrast, we find a reversed pressure gradient in the core of the flow that drives the bypass flow of continuous phase through the corners (gutters) and causes the Taylor droplet’s relative velocity between the faster droplet flow and the slower mean flow. Based on the pressure field, we quantify the driving pressure gradient of the bypass flow and verify a simple estimation method: the geometry of the gutter entrances delivers a Laplace pressure difference. As a direct measure for the viscous dissipation, we calculate the 3D distribution of work done on the flow elements, that is necessary to maintain the stationarity of the Taylor flow. The spatial integration of this distribution provides the overall dissipated energy and allows to identify and quantify different contributions from the individual fluid phases, from the wall-proximate layer and from the flow redirection due to presence of the droplet interface. For the first time, we provide deep insight into the 3D pressure field and the distribution of the energy dissipation in the Taylor flow based on experimentally acquired 3D3C velocity data. We provide the 3D pressure field of and the 3D distribution of work as supplementary material to enable a benchmark for CFD and numerical simulations.Graphical abstract

Highlights

The applications of microscopic two-phase flow involve medical (Piao et al 2015), biological (Wolf et al 2015), chemical (Lang et al 2012) and thermal processes (Leung et al 2010). Chou et al (2015) reviewed the application of Taylor flows in various fields.Downscaled multiphase flows like Taylor flows are often realized in horizontal rectangular microchannel structures
We provide the 3D pressure field and the overall energy loss of a Taylor droplet moving in a rectangular horizontal microchannel on the basis of an experimentally acquired 3D3C velocity field
A comparison between the pressure distribution and the curvature-derived Laplace-pressure on the interface of a Taylor droplet identifies the source of the motion-related droplet deformation

Summary

Introduction

Chou et al (2015) reviewed the application of Taylor flows in various fields. Downscaled multiphase flows like Taylor flows are often realized in horizontal rectangular microchannel structures. They offer a variety of advantages for process engineering purposes: The increased specific surface area of the flow enhances heat and mass transfer (Bandara et al 2015) and allows precise handling of sample volumes (Garstecki et al 2006; Whitesides 2006). (2011) propose the application of Taylor droplets to enable high-speed processing without cross-contamination. Taylor flows in rectangular microchannels feature a bypass flow through the continuous phase-filled corners (Kreutzer et al 2005), the so-called gutters (van Steijn et al 2009)

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