No abstract

Polymeric flow through porous media is relevant in industrial applications, such as enhanced oil recovery, microbial mining, and groundwater remediation. Biological processes, such as drug delivery and the transport of cells and particles in the body, also depend on the viscoelastic flow through the porous matrix. Large elastic stresses induced due to confined geometries can lead to elastic instability for the viscoelastic fluid flow through porous media. We have numerically studied viscoelastic flow through a channel having two closely placed cylinders to investigate pore scale elastic instabilities. We have discovered three distinct flow states in the region between the cylinders. These flow states are closely coupled with the topology of the polymeric stress field. The transition between the flow states can be identified with two critical Weissenberg numbers (Wicr1 and Wicr2), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At Wi<Wicr1, the flow is stable, symmetric, and eddy free. For Wicr1<Wi<Wicr2, eddies form in the region between the cylinders. We have measured the area occupied by the eddies for different flow conditions and fluid rheological parameters. At Wi>Wicr2, the eddy disappears and the flow around the cylinders becomes asymmetric. We have quantified the flow asymmetry around the cylinders for different flow rates and fluid rheology. We have also studied the effect of the cylinders' diameter and separation on the eddies' size (Wicr1<Wi<Wicr2) and flow asymmetry (Wi>Wicr2). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers.

Complex and active fluids find broad applications in flows through porous materials. Nontrivial rheology can couple to porous microstructure leading to surprising flow patterns and associated transport properties in geophysical, biological, and industrial systems. Viscoelastic instabilities are highly sensitive to pore geometry and can give rise to chaotic velocity fluctuations. A number of recent studies have begun to untangle how the pore-scale geometry influences the sample-scale flow topology and the resulting dispersive transport properties of these complex systems. Beyond classical rheological properties, active colloids and swimming cells exhibit a range of unique properties, including reduced effective viscosity, collective motion, and random walks, that present novel challenges to understanding their mechanics and transport in porous media flows. This review article aims to provide a brief overview of essential, fundamental concepts followed by an in-depth summary of recent developments in this rapidly evolving field. The chosen topics are motivated by applications, and new opportunities for discovery are highlighted.

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as the sperm encounter background flow of different magnitude and direction on their way to the egg.

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.