Impact of osmotic pressure on the stability of Taylor vortices

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

We develop a new mathematical model for rotational sedimentation of particles for steady flows of a viscoplastic granular fluid in a concentric-cylinder Couette geometry when rotation of the Couette cell inner cylinder is prescribed. We treat the suspension as a micro-polar fluid. The model is validated by comparison with known data of measurement. Within the proposed theory, we prove that sedimentation occurs due to particles’ rotation and rotational diffusion.

Ionic strength and polyelectrolyte molecular weight effects on floc formation and growth in Taylor–Couette flows

A Taylor–Couette cell capable of radial injection was used to study the effects of varying solution ionic strength and polyelectrolyte molecular weight on the polyelectrolyte-driven flocculation of bentonite suspensions.

Evolution of shear zones in granular packings under pressure

Stress transmission in realistic granular media often occurs under external load and in the presence of boundary slip. We demonstrate how the shear strain is localized in a split-bottom Couette cell with smooth walls subject to a confining pressure.

Shearing of granular materials in a confined split-bottom Couette cell

Formation of shear bands is one of the most remarkable phenomena in the dynamics of granular matter. Several parameters have been so far identified to influence the behavior of the shear bands. We carried out experiments to investigate the evolution of the shear bands in the split-bottom Couette cell in the presence of confining pressure. We employed the Particle Image Velocimetry (PIV) to characterize the shear band both in the absence and presence of external pressure. Our results show that the location and width of the shear band are affected by both the confining pressure and the filling height. The shear zone evolves towards the middle of the cylinder and expands to a broader region with increasing applied pressure or filling height; also the angular velocity decreases relative to the rotation rate of the bottom disk. Our findings are consistent with prior empirical observations on the formation of wide shear bands at free surfaces.

A multi-component lattice Boltzmann approach to study the causality of plastic events

Using a multi-component lattice Boltzmann (LB) model, we perform fluid kinetic simulations of confined and concentrated emulsions. The system presents the phenomenology of soft-glassy materials, including a Herschel–Bulkley rheology, yield stress, ageing and long relaxation time scales. Shearing the emulsion in a Couette cell below the yield stress results in plastic topological re-arrangement events which follow established empirical seismic statistical scaling laws, making this system a good candidate to study the physics of earthquakes. One characteristic of this model is the tendency for events to occur in avalanche clusters, with larger events, triggering subsequent re-arrangements. While seismologists have developed statistical tools to study correlations between events, a process to confirm causality remains elusive. We present here, a modification to our LB model, involving small, fast vibrations applied to individual droplets, effectively a macroscopic forcing, which results in the arrest of the topological plastic re-arrangements. This technique provides an excellent tool for identifying causality in plastic event clusters by examining the evolution of the dynamics after ‘stopping’ an event, and then checking which subsequent events disappear. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Magnetic-Based Particle Tracking in a Dense Granular Shear Flow

Granular material is ubiquitous in nature and plays a significant role in industry. Researchers have paid a lot of attention to density and velocity distributions of dense granular flows. However, the motion of individual particle is hard to capture because visualizing individual particles in a dense granular flow, especially in 3D, is very difficult and could be expansive. Here we use the magnetic particle tracking (MPT) technique to capture the motion of a single particle in a sheared dense granular flow. The accuracy of MPT is quantified using experimental results. The sheared granular flow is generated in a Couette cell by rotating a plate at the bottom of a cylinder container. It is able to generate different shear stresses by controlling the speed of the plate. By tracking the magnetic particle in the cylinder, we can capture the velocity of an individual particle at different locations in the granular flow.