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

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.

Localization in Flow of Non-Newtonian Fluids Through Disordered Porous Media

“…Figure 2 compares the velocimetry measurements obtained from ref. 42 in a section of the mid plane of the microfluidic chip with those obtained from numerical simulations calculated with exactly the same pore geometry, fluid properties and flow conditions. More precisely, the flow rates for the presented cases are q in 0.05 µL/min (Figure 2A) and q in 5 µL/min (Figure 2B) for the xanthan case, and q in 5 µL/min for the measurement with water (Figure 2C).…”

“…However, quantitative experiments with non-Newtonian materials which go beyond simple bulk measurements [39,40] are scarce [41] because the design of the experimental pore geometry and the operating conditions need to be adjusted in order to match the nonlinear constitutive regime of the fluid's rheology. Here we combine the results of microfluidic experiments [42] with fluid dynamics simulations to demonstrate how the nonlinear rheological properties of a fluid can be effectively exploited in order to control the macroscopic transport properties of a flow through the external operational flow conditions. These results have important consequences for the design of chemical reactors and chromatographic systems as well as for the enhancement of oil recovery and transport in porous media in general.…”

“…Our analysis is based on experimental results from the setup presented recently in Eberhard et al [42]. Their main purpose was to map the local viscosity of a non-Newtonian flow in a porous microfluidic channel by means of a high-resolution technique of image velocimetry, namely, Ghost Particle Velocimetry (GVP) [49].…”

“…4 reduces to μ C ( _ c) μ 0 , corresponding to a constant viscosity μ 0 24 Pa • s. At an intermediate range of shear rates, the fluid follows a power-law relation μ ∼ _ c n− 1 with n 0.3 in our specific case. The remaining Carreau parameter λ 50 s was determined using a nonlinear least-square fit to the experimentally measured values [42]. As shown in Figure 1, the experimental pore structure consisted of a microfluidic device containing a quasi-2D porous medium of size 30 mm × 15 mm and depth of 100 µm.…”

Heterodyne Near Field Speckles: from laser light to X-rays

“…It is worth noting how the same underlying principles are at the basis of the recently developed Ghost Particle Velocimetry technique [128]. It has been exploited to study the onset of intermittent turbulence in the flow of dense bacterial suspensions [129] and to map the spatial changes of the local viscosity and local shear rates of non-Newtonian fluids flown past disordered porous geometries [130].…”