Session P09: Suspensions: Fluid-Particle Interaction (3:10pm - 3:55pm CST)

The role of Reynolds number on the settling dynamics of arbitrary-shaped particles on a wall

A particle-wall collision model is implemented in a sharp-interface curvilinear immersed boundary (CURVIB) method to simulate fluid structure interaction (FSI) in a viscous fluid with irregular shaped bodies colliding and settling on a flat surface. The particle's equations of motion are modified after the collision by identifying the contact point and considering it as the instantaneous center of rotation at each time instant until the equilibrium (stable) state is reached. The rebound of particle off the wall is not considered which is a good assumption for particles with low Stokes number. A major advancement in this work is identifying the equilibrium (stable) final state for irregular shapes. Grid, domain, and boundary condition independence studies are performed. Multiple simulations are preformed to show how modifying the Reynolds number will impact the fluid dynamics of different particles and how this will affect the body-surface collision. Tested particle shapes include sphere (for validation), ellipsoid, cylinder, pyramid, and a jagged, irregular shape.   

The effect of particle shape and particle-polymer interactions on the extensional rheology of filled polymeric fluids

The addition of particles greatly alters the stresses in a polymeric fluid undergoing strong extensional flow. We investigate the extensional rheology of a suspension of prolate spheroids in such fluids using a perturbation expansion in small polymer concentration, the generalized reciprocal theorem, and ensemble-averaged equations. The method of characteristics is applied to numerically evaluate the particle-polymer interaction based on FENE-P constitutive equations. The polymers influence the particle stresslet through the surface stress and the particles influence the polymer stretch through velocity perturbations. The variation of extensional rheology with the particle shape is obtained analytically for a second-order fluid. The limiting cases of the small and large aspect ratio of the particles are understood in terms of previous results for spherical fillers and newly derived results based on slender body theory. The particle-polymer interaction stress varies non-monotonically with the extension rate. It is positive at small extension rates when the undisturbed polymers are coiled, but is negative when they are fully stretched at larger rates. The kinematics of the velocity field provide further physical insight into polymer stretching and the resulting stresses.   

Migration and conformational dynamics of von Willebrand Factor in the near wall region of a channel flow

Von Willebrand Factor, vWF, is a glycoprotein suspended in blood with central role in hemostasis. In particular, it is shown that the local concentration and conformation of vWF has significant effect on high shear thrombosis. In this study, we investigate the migration and conformation of suspended vWF in a channel flow using a coupled Langevin-Dynamics and Lattice Boltzmann method [1]. A wide range of Weissenberg numbers, Wi, changing from 60 to 1200, has been considered to reflect the high-shear condition observed in arterial thrombosis. Results indicate a correlation between trajectories of the vWF and its conformational dynamics for the Wi numbers studied. In particular, sudden ``jumps'' in vWF migration are observed under specific vWF conformation, which is quantified in terms of the polymer's end-to-end length, orientation, and tortuosity to identify the mechanisms that causes such ``jumping'' behavior. This study provides insights to the near-wall availability of vWF that is essential to the high-shear thrombus formation. [1] Liu, Zhu, Clausen, Lechman, Rao, Aidun, Int. J. Num. Methods Fluids 91 (5), 228-246, 2019.   

Fabrication of flexible micro-helices and deformation by viscous flows

The study of fluid-structure interactions between helical particles and viscous flows is of importance for both fundamental science and technological applications. The chirality of such particles indeed induces breaking of the time-reversal symmetry associated with viscous flows. This effect is exploited by microorganisms to propel themselves through viscous media by rotating helical flagella. Possible applications include swimming micro-robots or flow micro-sensors. We build on a spontaneous formation method of helical ribbons of tunable radii but vanishing pitch. We demonstrate that, by taking advantage of the visco-elasticity of the material, a non-zero pitch can be obtained, by straining the helix over extended periods of time. This two-step technique allows fabrication of flexible micro-helices with unprecedented shape control: the helical radius and pitch and the filament length can be independently tuned. These helices can serve as model systems for the study of fluid-structure interactions. Using this system, we study the deformation of helical ribbons under axial flows created in microfluidic channels. We quantify the influence of the helical radius and helical pitch on the deformation and we observe an effective stiffening as the helical pitch increases.   

Shear-induced dispersion in a dilute suspension of charged spheres

Shear-induced dispersion have been observed in suspensions in a Newtonian fluid even when thermal effects are negligible (for instance, see Leighton \& Acrivos 1987a,b; Eckstein, Bailey \& Shapiro 1977). This random walk of a particle due to hydrodynamic interactions with its neighbours in a sheared non-Brownian suspension can be characterized by a diffusivity. It is well known that in the absence of non-hydrodynamic effects, inertialess pairwise interactions being fore–aft symmetric, diffusive behaviour arises from three-particle interactions. However, for cases where pairwise interactions are asymmetric due to surface roughness (see Da Cunha \& Hinch 1996), particle inertia (see Subramanian \& Brady 2006), or short-ranged repulsive forces, the diffusivities can be obtained by averaging the transverse displacements for successive uncorrelated pairwise interactions weighted by their frequency of occurrence. In this study, we consider a repulsive electrostatic force using the Gouy–Chapman model for the electrical double layer. We determine the transverse components of the shear-induced self-diffusivity as a function of the inverse Debye length and relative strength of electrostatic to shear forces.   

Dynamics of a Flexible Fiber Suspended in High Density Foam Under Shear

Behavior of flexible fiber suspended in high density (HD) foam is of great interest in many applications. In this study, we explore the behavior and dynamics of a single fiber suspended in HD foam in simple shear flow. Rheological behavior of the HD foam varies as a function of foam density and strain rate. Experiments show that an increase in foam density leads to a decrease in shear stress. Hershel-Bulkley (HB) constitutive model provides an accurate phenomenological model to characterize the behavior of the HD foam. Fiber suspended in the HD foam is modeled as a chain of cylindrical segments interacting with the HB fluid. Linear and angular momentum equations are solved for each of the fiber segments. Thus, the evolution of the motion and orientation of the fiber is derived. HD foam flow is characterized by Reynolds number, Hedstrom number, power law index and slip velocity. Similarly, the flexible fiber is characterized by bending ratio, fiber aspect ratio and fiber volume fraction. The flow of HB fluid under shear and the dynamics of a single fiber in shear flow will be presented.   

Hydrodynamic Interactions and Friction in Sheared Colloidal Gels.

Colloidal gels, which form when attractive particles suspended in a fluid get arrested in non-equilibrium states, are ubiquitous with applications including in consumer care, agrochemical and pharmaceutical industries where engineering specific rheological properties is often a design requirement. In this work, Fast Stokesian Dynamics (FSD) simulations are employed to model the microstructural evolution of colloidal gels subject to steady, linear deformation and rheological properties are predicted. FSD is a fast method of simulating tens of thousands of Brownian spheres interacting hydrodynamically at low Reynolds numbers. Fluid-structure interactions enable formation of large scale anisotropic structures in sheared colloidal gels. We will investigate the effect of different modes of hydrodynamic interactions: far-field and near-field on the evolution of gel microstructure. In addition, the effect of finite friction between particles due to surface roughness, implemented as hydrodynamic resistance to sliding between particles at contact, will be examined.   

Designing Stress-adaptive Dense Suspensions via Dynamic Covalent Chemistry

Dense suspensions exhibiting reversible non-Newtonian flow behavior typically possess relatively weak and short-lived particle scale interactions, yet it is unclear how manipulating the strength and lifetime of microscopic contacts perturbs these macroscopic rheological properties. We utilize the catalyst-free, room temperature dynamic bonds that form between thiol-coated particles and ditopic benzalcyanoacetate-based Michael acceptors to engineer dense suspensions with well-defined and tunable contact lifetimes. Steady shear rate or stress ramps reveal pronounced negative thixotropy which relaxes upon shear cessation, which we attribute to shear-induced dynamic covalent crosslinks between particles. Constant stress measurements reveal a transition from suspensions whose viscosities diverge as a function of strain at low stresses to those which undergo continuous deformation at high stresses. The exact stress required for this transition systematically depends on the electron-donating/withdrawing nature of the Michael acceptor, which is known to control the dynamic bond strength and lifetime. We anticipate these connections between contact lifetimes and macroscopic rheology will aid in the design of smart materials which autonomously sense and adapt to applied stresses.   

Numerical study of equilibrium radial position of neutrally buoyant balls in tube flows

Segre and Silberberg (1962) observed that neutrally buoyant particles of dilute suspensions accumulate at about 0.6 of the pipe radius from the center line. This Segre-Silberberg effect has had a large influence on fluid mechanics studies of particle migration. To understand such effect at higher Reynolds numbers (Re), Matas et al. (2004) obtained that the equilibrium position moves towards the wall for higher Re as predicted by Asmolov (1999). They also found that particle migrates to an inner equilibrium position for Re > 600 in tube flows. We have studied this effect in tube flows via direct numerical simulation. For one ball case, it takes place at low Re as expected. At higher Re, the ball moves to one of two equilibrium positions. At even higher Re, the ball is pinched to an inner position. These one ball results are similar to the one obtained by Nakayama et al. (2019). For a train of two neutrally buoyant balls placed on the line parallel with the tube axis initially, the train formation is stable and its center moves to an equilibrium position at low Re like the motion of a neutrally buoyant ball. At higher Re, the averaged train position moves to the inner equilibrium position and two balls oscillate periodically with respect to such position in an alternative way.