Mapping the local viscosity of non-Newtonian fluids flowing through disordered porous structures

J Jiménez-Martínez,E Secchi,H J Seybold,P A Rühs,A Ofner,U Eberhard,J S Andrade,M Holzner

doi:10.1038/s41598-020-68545-7

Abstract

Flow of non-Newtonian fluids through topologically complex structures is ubiquitous in most biological, industrial and environmental settings. The interplay between local hydrodynamics and the fluid’s constitutive law determines the distribution of flow paths. Consequently the spatial heterogeneity of the viscous resistance controls mass and solute transport from the micron to the meter scale. Examples range from oil recovery and groundwater engineering to drug delivery, filters and catalysts. Here we present a new methodology to map the spatial variation of the local viscosity of a non-Newtonian fluid flowing through a complex pore geometry. We use high resolution image velocimetry to determine local shear rates. Knowing the local shear rate in combination with a separate measurement of the fluid’s constitutive law allows to quantitatively map the local viscosity at the pore scale. Our experimental results—which closely match with three-dimensional numerical simulations—demonstrate that the exponential decay of the longitudinal velocity distributions, previously observed for Newtonian fluids, is a function of the spatial heterogeneity of the local viscosity. This work sheds light on the relationship between hydraulic properties and the viscosity at the pore scale, which is of fundamental importance for predicting transport properties, mixing, and chemical reactions in many porous systems.

Highlights

Flow of non-Newtonian fluids through topologically complex structures is ubiquitous in most biological, industrial and environmental settings
By combining the rheology measurement with the shear rates calculated from the velocimetry measurements, we are able to determine the local viscosity of the fluid at the pore scale
We accomplish this task with an advanced optical velocimetry technique, called Ghost Particle Velocimetry (GPV)[32,33]

Summary

Introduction

Flow of non-Newtonian fluids through topologically complex structures is ubiquitous in most biological, industrial and environmental settings. The local viscosity of non-Newtonian fluids is spatially variable This variability in the local hydraulic resistance impacts the distribution of local flow velocities through the interstitial pore space, affecting transport, and mixing p rocesses[15]. While the measurement of the bulk viscosity of non-Newtonian fluids with rheometers and microfluidic platforms is rather common[16,17,18,19], the mapping of the local viscosity at the pore scale in a complex geometry is challenging The reason for this is that the fluid’s constitutive behavior has to be carefully matched with the experimental operating condition in order to achieve reliable measurements in the nonlinear consititutive regime. Our analysis opens a new perspective to exploit the flow of non-Newtonian fluids through disordered porous structures, by predicting local changes in viscous and hydraulic resistance and controlling mass and solute transport.

Methods

Results

Conclusion