Microfluidic systems for the analysis of the viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/ expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application

Multiphysics computational modeling in <i>C</i>Heart

From basic science to translation, modern biomedical research demands computational models which integrate several interacting physical systems. This paper describes the infrastructural framework for generic multiphysics integration implemented in the software $\boldsymbol{\mathcal{C}}\mathbf{Heart}$, a finite-element code for biomedical research. To generalize the coupling of physics systems, we introduce a framework in which the geometric and operator relationships between the constituent systems are rigorously defined. We then introduce the notion of topological interfaces and define specific operators encompassing many common model coupling requirements. These interfaces enable the evaluation of weak form integrals between mesh subregions of arbitrary finite-element bases' orders, types, and spatial dimensions. Equation maps are introduced which provide abstract representations of the individual physics systems that can be automatically combined to permit a monolithic matrix assembly. Flexible solution strategies for the resulting coupled systems are implemented, permitting fine-tuning of solution updates during fixed point iterations, and subgrouping where several problems are being solved together. Partitioning of coupled mesh domains for optimal load balancing is also supported, taking into account the per-processor cost of the entire coupled problem within the graph problem. The demonstration of the performance is illustrated through important real-world multiphysics problems relevant to cardiac physiology

Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity.

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects

Comment on Sochi's variational method for generalised Newtonian flow

A recently introduced variational method (Sochi, Rheol Acta 53:15–22, 2014) has been used to obtain flow profiles for generalised Newtonian fluids in steady rectilinear flow. This Comment examines the relationship between this variational method and the dynamical equations for such flows