Rheology of Confined Non-Brownian Suspensions

Cross-streamline migration and near-wall depletion of elastic fibers in micro-channel flows

The complex dynamics of elastic fibers in viscous fluids are central to many biological and industrial systems. Fluid-structure interactions underlying these dynamics govern the shape and transport of flexible fibers, and understanding these interactions can help tune flow properties in applications such as microfluidic separation, printing and clogging. In this work, we use slender-body theory to study micromechanical dynamics that arise from the coupling between the elastic backbone of a fiber and the local straining flow that contributes to filament flipping and cross-streamline migration. The resulting transverse drift is unbiased in either direction in simple shear flow. However, a non-uniform shear rate results in bias towards regions of high shear, which we connect to the shape transitions during flips. We discover a depletion layer that forms near the boundaries of pressure-driven channel flow due to the competition between such a cross-streamline drift and steric exclusion from the walls. Finally, we develop scaling laws for the curvature of filaments during flip events, demonstrating the origin of the drift bias in non-uniform flows, and confirm this behavior from our simulations. Put together, these results shed light on the role of a local and dominant coupling between elasticity and viscous resistance in dictating long-term dynamics and transport of elastic fibers in confined flows.

Flow-induced "waltzing" red blood cells: Microstructural reorganization and the corresponding rheological response

We investigate flow-induced structural organization in a dilute suspension of tumbling red blood cells (RBCs) under confined shear flow. For small Reynolds (Re = 0.1) and capillary numbers (Ca), with fully coupled hydrodynamic interaction (HI) and without interparticle adhesion, we find that HI between the biconcave discoid particles prompts the formation of layered RBC chains and synchronized rotating RBC pairs, referred here as "waltzing doublets." As the volume fraction ϕ increases, more waltzing doublets appear in RBC files. Stronger shear stress disrupts structural arrangements at higher Ca. We find that the flow-induced organization of waltzing doublets changes how the suspension viscosity varies with ϕ qualitatively. The intrinsic viscosity is particularly sensitive to microstructural rearrangement, increasing (decreasing) with ϕ at low (high) Ca that correlates with the change in the fraction of doublets. We verified flow-induced collective motion with comparison to two-cell simulations in which the cell volume fraction is controlled by varying the domain volume.

Multiscale nature of electric-field-induced structural formations in non-colloidal suspensions

Non-colloidal suspensions undergoing dipolar interactions in an electric field have been extensively studied and are also known as smart materials as they share similarities with electrorheological (ER) fluids. Although the macroscopic responses are well-documented, the multiscale nature of such suspensions is still lacking. In this study, a large-scale Stokesian dynamics simulation is used to investigate the structural formation of such suspensions in an electric field up to highly concentrated regimes across different length scales: from particle-level (microscale) to particle cluster-level (mesoscale) and stress response-level (macroscale). It is observed that at a volume fraction of ϕ ≈ 30%, the steady-state structures are the most isotropic at the microscale, but at the macroscale, their normal stress fields are the most anisotropic. Interestingly, these structures are also the most heterogeneous at both the microscale and mesoscale. Furthermore, the effects of confinement on the multiscale responses are explored, revealing that there could be a strong link between the mesoscale and macroscale. This multiscale nature can offer the potential for precisely controlling or designing ER fluids in practical applications.

Viscoelasticity of non-colloidal hydrogel particle suspensions at the liquid-solid transition

Suspensions of soft particles transition from a viscous fluid to a soft material upon increases in phase volume. The criteria defining the transition to this jammed state are difficult to define due to the porous and deformable nature of soft particles. Here, we characterise the rheology of aqueous suspensions of industrially relevant non-colloidal, polydisperse, frictional agarose microgels and evaluate shear and viscoelastic behaviour across a range of phase volumes from the dilute regime to the highly concentrated regime. In order to model the viscoelastic response of suspensions without free fitting parameters, the random close packing volume fraction (φrcp) and the particle modulus are determined, respectively, from particle size distribution measurements and direct measurements of reduced elastic modulus of individual particles (Erp) using Atomic Force Microscopy. It is found that at φrcp, previously shown to correspond to divergence of the viscosity, also corresponds to the suspension transition from a viscous to viscoelastic fluid. However, the transition to a jammed solid-like state (φj) occurs at phase volumes exceeding this value (i.e. φj > φrcp). The suspension modulus and its sudden growth at φj are well-predicted by the Evans and Lips model that incorporates the Erp of the hydrogel particles. This rheological behaviour showing a dual transition is reminiscent of two families of systems: (i) colloidal suspensions and (ii) frictional-adhesive non-colloidal suspensions. However, it does not strictly follow either case. We propose that the width of the transition region is dictated by frictional contact, particle size distribution and particle modulus, and plan to further probe this in future work.

Dynamical modes of sheared confined microscale matter

Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velocities per ring. The first one is characterized by rare slip events, where the inner rings momentarily depin from the outer ring, which is kept static by the set of optical traps. For the second state, we find a bistability of the mean angular velocities, which can be understood from the analysis of the slip events in the particle trajectories. We calculate the particle waiting- and jumping time distributions and estimate a time scale between slips, which is also reflected by a plateau in the mean squared azimuthal displacement. The dynamical transition is further reflected by the components of the stress tensor, revealing a shear-thinning behavior as well as shear stress overshoots. Finally, we briefly discuss the observed transition in the context of stochastic thermodynamics and how it may open future directions in this field.

Exact regularized point particle (ERPP) method for particle-laden wall-bounded flows in the two-way coupling regime

The Exact Regularized Point Particle (ERPP) method is extended to treat the interphase momentum coupling between particles and fluid in the presence of walls by accounting for the vorticity generation due to the particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell). The enhanced ERPP method is explained in detail and validated by considering the global impulse balance. In conditions when particles are located close to the wall, a common scenario in wall-bounded turbulent flows, the main contribution to the total impulse arises from the particle-induced vorticity at the solid boundary. The method is applied to direct numerical simulations of particle-laden turbulent pipe flow in the two-way coupling regime to address the turbulence modulation. The effects of the mass loading, the Stokes number and the particle-to-fluid density ratio are investigated. The drag is either unaltered or increased by the particles with respect to the uncoupled case. No drag reduction is found in the parameter space considered. The momentum stress budget, which includes an extra stress contribution by the particles, provides the rationale behind the drag behaviour. The extra stress produces a momentum flux towards the wall that strongly modifies the viscous stress, the culprit of drag at solid boundaries.

Viscosity Estimation of a Suspension with Rigid Spheres in Circular Microchannels Using Particle Tracking Velocimetry

Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10^-4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.

Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory

We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

Laning, thinning and thickening of sheared colloids in a two-dimensional Taylor-Couette geometry

We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.

Modeling shear-induced particle ordering and deformation in a dense soft particle suspension

We apply the lattice Boltzmann method and the bead-spring network model of deformable particles (DPs) to study shear-induced particle ordering and deformation and the corresponding rheological behavior for dense DP suspensions confined in a narrow gap under steady external shear. The particle configuration is characterized with small-angle scattering intensity, the real-space 2D local order parameter, and the particle shape factors including deformation, stretching and tilt angles. We investigate how particle ordering and deformation vary with the particle volume fraction ϕ (=0.45-0.65) and the external shear rate characterized with the capillary number Ca (=0.003-0.191). The degree of particle deformation increases mildly with ϕ but significantly with Ca. Under moderate shear rate (Ca  =  0.105), the inter-particle structure evolves from string-like ordering to layered hexagonal close packing (HCP) as ϕ increases. A long wavelength particle slithering motion emerges for sufficiently large ϕ. For ϕ  =  0.61, the structure maintains layered HCP for Ca  =  0.031-0.143 but gradually becomes disordered for larger and smaller Ca. The correlation in particle zigzag movements depends sensitively on ϕ and particle ordering. Layer-by-layer analysis reveals how the non-slippery hard walls affect particle ordering and deformation. The shear-induced reconfiguration of DPs observed in the simulation agrees qualitatively with experimental results of sheared uniform emulsions. The apparent suspension viscosity increases with ϕ but exhibits much weaker dependence compared to hard-sphere suspensions, indicating that particle deformation and unjamming under shear can significantly reduce the viscous stress. Furthermore, the suspension shear-thins, corresponding to increased inter-DP ordering and particle deformation with Ca. This work provides useful insights into the microstructure-rheology relationship of concentrated deformable particle suspensions.

Shear-induced laning transition in a confined colloidal film

Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.

Depinning and heterogeneous dynamics of colloidal crystal layers under shear flow

Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model that maps the dynamics of the shear-driven colloidal layers to the motion of a single particle driven over an effective substrate potential. This model allows us to estimate the critical shear rate of the depinning transition based on the equilibrium configuration, revealing the impact of important parameters, such as the slit-pore width and the interaction strength. We then turn to heterogeneous systems where a layer of small colloids is sheared with respect to bottom layers of large particles. For these incommensurate systems we find that the particle transport is dominated by density excitations resembling the so-called "kink" solutions of the Frenkel-Kontorova (FK) model. In contrast to the FK model, however, the corresponding "antikinks" do not move.