Session H07: Suspensions: Fluid-Particle Interactions

Single-camera 3D particle tracking and application to shear-induced migration

In the experimental investigation of suspension flows, it is important to be able to precisely track suspended particles over a wide field of view. We present a cost-effective method for single-camera 3D particle tracking using digital image correlation and demonstrate its application to studying shear-induced migration. A speckle pattern is imaged through transparent spherical particles suspended in a viscous fluid and the resulting pattern distortion is used to deduce the particles’ 3D positions. Using this method, we examine the irreversible migration of millimeter-scale particles at low Reynolds number in an oscillatory, rectangular channel flow.  We report measurements of the migration dynamics and track interparticle contacts which are generally understood to be the source of irreversibility.   

Effects of gravity-driven drainage on particle filtration during dip coating

When a solid substrate is withdrawn from a liquid bath at velocity V, a coating of thickness h is deposited according to the classical Landau Levich Derjaguin model. For a particle-laden suspension, it has been recently demonstrated by Sauret et al. (2019, 2020) that particles whose size is smaller than the resulting film thickness can be filtered. This mechanism  is both tunable and relevant to numerous industrial and medical applications.  Here, we perform an experimental study of particle filtration during dip coating using a large range of particle sizes and fluid viscosities, such that our flow is in the gravity-driven drainage regime. Low volume fraction suspensions are utilized in order to minimize changes to the rheology of the fluid and clumping of particles. The filter is tuned by altering the withdraw velocity and data is collected on the thickness of the coating using gravimetric methods while particle entrainment is measured though imaging. Our extensive data set allows us to understand this soft particle filtering process over a wide range of flow conditions.     

Shear-migration in dense suspensions from the point of view of physics-informed neural networks

Phillips et al. [Phys. Fluids A 4 (1992) 30] proposed a  phenomenological model for the shear-induced migration of particles in a low-Reynolds-number flow. Since then, the model has been the workhorse for continuum modeling of migration phenomena in suspensions. However, being phenomenological, the model has only been calibrated for certain geometries. It is not clear if the model's parameters, determined by visually matching concentration profiles, for one flow scenario are valid in others. To address this knowledge gap, we apply the physics-informed neural networks (PINNs) approach. Specifically, the NN is constrained via the Phillips et al. model, and a suitable momentum equation for the unidirectional flow of the suspension. The NN is then trained against different experiments from the literature. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. Then, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow. For the latter, there is an additional model parameter, which has not been calibrated in prior literature, that we identify using the PINN. Significantly different values for the model parameters are obtained via the PINN upon analyzing Poiseuille flow experiments, although the parameters match Phillips et al. for the classical of an annular Couette flow. The PINN results also show that the best-fit model parameters vary with the Péclet number and the particle bulk volume fraction, instead of being constant as previously assumed.   

Fluid-mediated sources to granular temperature in homogeneous fluidization

The present study considers analytical solutions for hydrodynamic sources and sinks to granular temperature in homogeneous suspensions of elastic particles at finite Reynolds numbers and solids volume fraction. We model the neighbor-induced drag disturbances with an acceleration Langevin, which allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. The quadrant conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ are derived, allowing direct computation of the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions agree with benchmark data obtained from particle-resolved direct numerical simulations. Furthermore, the theory correctly predicts saturation of steady granular temperature at small particle-fluid density ratios $\rho_p/\rho_f \ll 1$, and thus, shows promise as a general theory from gas--solid to bubbly flows.   

Fluctuating Hydrodynamics of Granular Gases Driven by Thermal Walls

At non-equilibrium, molecular gases exhibit large-scale fluctuations and long-ranged hydrodynamical correlations. Enhancement of these fluctuations and correlations have a significant effect on their transport and overall macroscopic behavior. However, in contrast to molecular gases, particle collisions in granular gases are inelastic. In this talk, I will describe the effect of such inelastic particle collisions on hydrodynamical fluctuations in driven granular gases, which are crucial in industry (fluidized beds and aerosols) and nature (aeolian transport and erosion). Using the direct simulation Monte Carlo method, non-equilibrium steady states of granular gases are established through thermal driving from isothermal walls. By systematically varying the magnitude of collision inelasticity, we study the spatial structure of hydrodynamical fluctuations in density-homogeneous and clustering granular gases.   

Fluid structure interaction simulations of arbitrary-shaped particles settling on a flat surface

Fluid structure interaction (FSI) of particles settling on a flat surface in a viscous fluid is simulated using a sharp-interface curvilinear immersed boundary (CURVIB) method. The dynamics of particles after the collision with the flat surface is governed by the conservation of angular and linear momentum, which are written with respect to the contact point (the instantaneous center of rotation) until a stable position is attained. A simple model based on the Stokes drag and damping is proposed to represent the FSI trend with varying Reynolds Numbers. The arbitrary-shaped particles tested include cube, ellipsoid, cylinder, pyramid, and irregular shape. The accuracy of the simple model and the conditions for rebound from the flat surface are discussed.     

Not Participating

We propose a fluid lubricated extension of the Hertzian contact model supported by Finite Element Method (FEM) simulations to capture the deformation features of a pair of elastic particles interacting under constant external force, which could be due to an imposed axisymmetric compressional flow. We obtain simple scaling relations that capture the lateral dimension of the deformation (film radius), maximum dynamic pressure in the narrow gap, film thickness along the line joining the centers of the particles, minimum film thickness at the edge of the film, and the particle stresslet. The characteristic length scale chosen to obtain the scaling relations in the fluid film region is time-dependent but universal, independent of the particle stiffness. A comparative study of a pair of interacting elastic particles with the droplets, capsules, and vesicles system shows that the difference in scaling relations can be attributed to the differences in the origin of the lubrication pressure that develops in the narrow gap.   

Not Participating

A suitable form of the reciprocal theorem is employed to predict the hydrodynamic forces acting on a small neutrally buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation-point flow. To this end, a simple analytical model of the undisturbed velocity field is established, reproducing the gradual transition of the actual flow from a pure linear straining flow in the bulk to a parabolic flow at the wall. The particle Reynolds number is considered small but finite and the particle is assumed to stand close enough to the wall for the latter to be in the inner region of the disturbance. Predictions including finite inertial effects are successfully compared with results provided by fully-resolved numerical simulations for the position-dependent slip velocity between the particle and the ambient fluid. Comparison with predictions based on the creeping-flow approximation reveals that finite-inertia effects due to particle–wall interactions and to the relative acceleration between the particle and fluid substantially modify the way the slip velocity varies with the distance to the wall.   

Elastic sheets in shear flows, from single sheet behavior to exfoliation process: an experimental study.

Graphene has attracted much attention of the past decade as a candidate material for applications in a variety fields such as electronics, energy generation and storage, and biomedicine. However, the fabrication of high quality graphene at industrial scale and affordable price remains a challenge. One of the most promising techniques to produce graphene from graphite is so-called liquid-phase exfoliation. In this technique, graphite is sheared in a liquid until layers of graphene detach from the bulk material.

While being poorly understood, the mechanism of exfoliation is known to rely on three physical ingredients: adhesion strength between sheets, their bending rigidity and the large scale imposed viscous shear stress. For the dynamic processes, exfoliation can be composed of different modes of deformation: peeling of two sheets, sliding between two sheets or a buckling instability, du to the compressive component of a shear flow, that leads to the formation of a blister and detach two sheets. To investigate the role of the three ingredients and the modes of deformation, here we present the first model experiment of elastic adhesive sheets in shear flows at the macroscopic scale. As a requirement one needs to understand the characteristics of viscous forces exerted on elastic sheets. To answer that question, we performed systematic studies of the dynamic of two sheets suspended in a viscous shear flow. Surprisingly, our experiments demonstrate that the critical shear rate to bend two sheets depends non-monotonically on the distance between the two sheets. The evidence of this new behavior can strongly impact the rheology a suspension composed of deformable sheets and could have many repercussions on the industrial processes of suspensions.

ERC funding (project FLEXNANOFLOW, 715475)   

Axisymmetric particle rotations in shear flow

We experimentally investigate the rotational dynamics of a neutrally-buoyant axisymmetric particle in a viscous shearing flow.

A custom-built shearing cell and a multi-view shape reconstruction method are used to obtain direct measurement of the period and the angular phase of the Jeffery orbits (Jeffery, 1922).

We report good agreement with the data available in the literature (Trevelyan and Mason, 1951; Goldsmith and Mason, 1962) and we complement these data by measuring the period and the angular phase over an extended range of particle aspect ratios. In particular, we consider aspect ratios smaller than those previously reported, which exhibit rotation periods larger than expected by Trevelyan and Mason.