Bidisperse Suspensions Research Articles

Rheology of bidisperse non-Brownian suspensions.

We study the rheology of bidisperse non-Brownian suspensions using particle-based simulation, mapping the viscosity as a function of the size ratio of the species, their relative abundance, and the overall solid content. The variation of the viscosity with applied stress exhibits shear-thickening phenomenology irrespective of composition, though the stress-dependent limiting solids fraction governing the viscosity and its divergence point are nonmonotonic in the mixing ratio. Contact force data demonstrate an asymmetric exchange in the dominant stress contribution from large-large to small-small particle contacts as the mixing ratio of the species evolves. Combining a prior model for shear thickening with one for composition-dependent jamming, we obtain a full description of the rheology of bidisperse non-Brownian suspensions capable of predicting effects such as the viscosity reduction observed upon adding small particles to a suspension of large particles.

Shear-induced phase behavior of bidisperse jammed suspensions of soft particles

Particle dynamics simulations are used to determine the shear-induced microstructure and rheology of jammed suspensions of soft particles. These suspensions, known as soft particle glasses (SPGs), have an amorphous structure at rest but transform into ordered phases in strong shear flow when the particle size distribution is relatively monodisperse. Here, a series of bidisperse SPGs with different particle radii and number density ratios are considered, and their shear-induced phase diagrams are correlated with the macroscopic rheology at different shear rates and volume fractions. These shear-induced phase diagrams reveal that a combination of these parameters can lead to the emergence of various microstructures such as amorphous, layered, crystals, and in some cases, coexistence of amorphous and ordered phases. The evolution of the shear stress is correlated with the change in the microstructure and is a shear-activated process. Stress shows pseudo-steady behavior during an induction period before the final microstructural change leading to the formation of ordered structures. The outcomes provide a promising method to control the phase behavior of soft suspensions and build new self-assembled microstructures.

A High-Aspect-Ratio Deterministic Lateral Displacement Array for High-Throughput Fractionation.

Future industrial applications of microparticle fractionation with deterministic lateral displacement (DLD) devices are hindered by exceedingly low throughput rates. To enable the necessary high-volume flows, high flow velocities as well as high aspect ratios in DLD devices have to be investigated. However, no experimental studies have yet been conducted on the fractionation of bi-disperse suspensions containing particles below 10 µm with DLD at a Reynolds number (Re) above 60. Furthermore, devices with an aspect ratio of more than 4:1, which require advanced microfabrication, are not known in the DLD literature. Therefore, we developed a suitable process with deep reactive ion etching of silicon and anodic bonding of a glass lid to create pressure-resistant arrays. With a depth of 120 µm and a gap of 23 µm between posts, a high aspect ratio of 6:1 was realized, and devices were investigated using simulations and fractionation experiments. With the two-segmented array of 3° and 7° row shifts, critical diameters of 8 µm and 12 µm were calculated for low Re conditions, but it was already known that vortices behind the posts can shift these values to lower critical diameters. Suspensions with polystyrene particles in different combinations were injected with an overall flow rate of up to 15 mL/min, corresponding to Re values of up to 90. Suspensions containing particle combinations of 2 µm with 10 µm as well as 5 µm with 10 µm were successfully fractionated, even at the highest flow rate. Under these conditions, a slight widening of the displacement position was observed, but there was no further reduction in the critical size as it was for Re = 60. With an unprecedented fractionation throughput of nearly 1 L per hour, entirely new applications are being developed for chemical, pharmaceutical, and recycling technologies.

The effect of shear-induced segregation on bidisperse suspension settling

Shear is a common phenomenon in practical mineral processes, particularly in pipeline transportation. When applied to realistic polydisperse systems consisting of particles of different sizes, shear can lead to distinct interactions of each size component with the carrier fluid, resulting in segregation between sizes. This paper focuses on the effect of size segregation induced by shear on the settling process of suspension flows containing different-sized spherical particles. In this regard, the bidisperse system is considered as the simplest example of polydisperse flows, ensuring the investigation retains the essential features of the system of interest without added complexity. The Volume Penalization Immersed Boundary Method, as a resolved Eulerian–Lagrangian CFD-DEM approach, is employed to gain detailed information on individual particles. A simple cross shear is generated by the moving side walls, and its effect is initially evaluated on two simulation cases containing single spherical particles of different sizes. The results from the single particle simulation cases reveal a higher acceleration of the larger particle towards the centreline due to the higher lateral force proportional to its size. The resolved approach is then used for the bidisperse multiparticle systems with diameter ratios of l=2 and l=5, both subjected to a similar sheared field. In the suspension with l=2, the scalar dispersion function, which measures the degree of migration of each size component between the side walls, indicates segregation by size as the shear rate increases. This is evident in the motion of large particles towards the centre and the accumulation of smaller particles near the walls, which arises from higher proportional force on the larger particles observed in the single particle simulation cases. Although the increase in the diameter ratio to l=5 does not significantly change the migration behaviour of large particles, it provides a more uniform distribution of smaller ones. In this case, the small particles find it more easily to fit into the gaps between the large particles for l=5. Overall, this accumulation of each size component at specific regions in the sheared domain affects the local interaction of settling particles with the fluid flow, resulting in an increase in the settling rate of large particles up to 40% in the considered bidisperse cases. This highlights the impact of shear on the interaction of spherical particles in a multiple sized system, specifically in the practical sheared applications including mineral slurries transportation.

DNS of Marangoni effects on a suspension of droplets in microgravity using the unstructured conservative level-set method

The multi-marker unstructured conservative level-set (UCLS) method for two-phase flow with variable surface tension is used for the Direct Numerical Simulation of thermocapillary-driven motion of a bi-dispersed suspension of droplets in microgravity. The so-called Marangoni stresses induced by surface tension gradients on the interface lead to a coupling of the momentum transport equation and the thermal energy transport equation. The finite-volume method discretizes the transport equations on three-dimensional collocated unstructured meshes. The UCLS method performs interface capturing with mass conservation of the fluid phases, whereas the multiple marker approach circumvents the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters schemes discretize the convective term in transport equations. Numerical and physical findings are reported.

Wetting geometry and deposition patterns manipulation with bi-dispersed particle-laden droplets

Polygonal deposition through evaporation of the suspension droplets holds promise for printing applications. The distinctive edges present in polygonal droplets offer the potential to enhance printing resolution and enable the fabrication of diverse thin depositions. Prior investigations revolve one dimensional control with the types of wetting geometries and deposition patterns initiate from different driving factors. The current study delves into the synergistic interplay between a bi-dispersed suspension mixing ratio and particle concentration, as they collectively influence the deposition pattern of octagonal droplets formed using a micropyramid cavity patterned substrate. The investigation culminates in the development of a comprehensive phase diagram categorizing four distinct types of deposition: octagonal outer-ring deposition, octagonal ring with irregular features, octagonal uniform deposition, and central deposition. Specifically, octagonal outer-ring deposition is observed when droplets consist predominantly of 3μm particles at lower concentrations. In cases where a suspension contains 10μm particles, an intermediate concentration exceeding 50% gives a rise to the octagonal outer-ring deposition intermingled with irregular features. The octagonal uniform deposition emerges when 3μm particles, co-aggregated with 10μm particles, are compelled to settle at the deposition center within the mixture at the 3:1 ratio at 1.0 wt% and 2.6 wt%. Notably, the “curvature effect”, exhibited by the aggregates adhering to the liquid–air interface, counter-intuitively suppresses octagonal deposition despite the presence of octagonal wetting geometry and forms the central deposition. In summary, the study introduces a robust method to achieve the uniform deposition and proposes a scalable and flexible strategy for generating diverse deposition types through the judicious mixing of two suspension solutions at distinct weight ratios.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order–disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order–disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order–disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Rheology of bi-disperse dense fiber suspensions.

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

A self-cleaning micro-fluidic chip biospired by the filtering system of manta rays.

Size-based particle filtration has become indispensable in numerous biomedical and environmental applications. In this study, bioinspired by the filter-feeding mechanism (lobe filtration) of manta rays, we designed a U-shaped biomimetic gill rake filter that combined lobe filtration and Dean flow to filter monodisperse suspensions, bi-disperse suspensions and yeast cells. Compared with other equipment using the inertial focusing technology, our equipment can perform high-throughput (up to 8 mL min-1) and high-efficiency filtration of particles (maximum filtration efficiencies of 96.08% and 97.14% for 10 and 15 μm monodisperse suspensions at the optimum flow rate of 6 mL min-1). The complex velocity field of the micro-fluidic flow within the filter is numerically simulated, and in combination with experiments, a threshold for the flow rate is identified. When the inlet flow rate exceeds the threshold value, the efficiency of particle filtration is increased rapidly. Afterwards, by analysing the filtration mechanism, we develop three novel filtration processes. The equilibrium positions of the particles and yeast cells in the main channel are close to the outer wall at high flow rate, which diminishes the likelihood of particles and yeast cells entering the side channel. This configuration establishes a self-cleaning mechanism, ensuring prolonged and efficient operation of the filter with high-throughput processing. Furthermore, the influence of the filter lobe angle and channel width on the filtration efficiency and outlet flow rate ratio are explored, and an optimisation plan is prepared.

Dip coating of shear-thinning particulate suspensions.

Dip coating a planar substrate with a suspension of particles in a shear-thinning liquid will entrain particles in the liquid film, facilitating filtration and sorting of particles. Experiments were performed for both monodisperse and bidisperse particle suspensions of shear-thinning Xanthan Gum solutions. Particle entrainment occurs when the coating thickness at the stagnation point of the thin film flow is larger than the particle diameter. A model is developed to predict the entrainment criteria using lubrication theory applied to an Ostwald power-law fluid which yields a modified Landau-Levich-Derjaguin (LLD) law governing the coating film thickness that depends upon a properly defined capillary number Ca. The critical withdrawal velocity for particle entrainment depends upon the particle size and fluid rheology through a relationship between Ca and the bond number Bo, which agrees well with our model predictions and prior experimental results of A. Sauret et al. Phys. Rev. Fluids, 2019, 4, 054303 for the limiting case of Newtonian suspensions. Single particle entrainment and particle clustering is observed for monodisperse suspensions, which depends on Ca and the particle volume fraction ϕ. In bidisperse suspensions, particle sorting can occur whereby only the smaller particles are entrained in the film over an active filtration range of Ca and Bo, which also agrees well with our model predictions.

High magnetization composite magnetic fluid: structure, magnetorheology and new sealing mechanism in rotating seals.

The sealing capacity of magnetofluidic (MF) rotating seals is limited by the highest magnetization of the sealing ferrofluids (FFs) of about 1000 G (80 kA m-1). A sharp, almost an order of magnitude, increase in the supported pressure drop is possible by using a magnetorheological (MR) suspension as sealing fluid, owing to the much higher saturation magnetization of MR fluids compared to FFs. However, rotating seals with MR fluids have several shortcomings, such as a significant increase of the friction torque due to the growth of shear stress in the strong magnetic field specific to MF seals and leakage of the non-magnetic carrier liquid. At least partly, these issues can be avoided by using ferrofluid based extremely bidisperse MR suspensions of micrometer-sized iron (Fe) particles dispersed in a ferrofluid, as sealing fluid. The composite Fe3O4-Fe magnetic fluid used in this study consisted of hundreds of nanometers up to few microns size structures of interconnected (welded) Fe nanoparticles (FeMNPs) dispersed in a high colloidal stability ferrofluid with 500 G (40 kA m-1) saturation magnetization. The volume fraction of iron NPs varies from 0.5 to 15% in the ferrofluid carrier which significantly increases the magnetization and simultaneously produces important changes of flow properties in magnetic field of the resulting composite fluid, from Newtonian to strongly non-Newtonian behavior. The evaluation of the magnetic and magnetorheological behavior includes the dependence of magnetization, effective viscosity, magnetoviscous effect and dynamic yield stress on the volume fraction of Fe nanoparticles dispersed in the ferrofluid carrier. The seal gap filled with interconnected Fe nanospheres consists in randomly distributed microregions with a high intensity and high gradient magnetic field that captures the ferrofluid and provides a new sealing mechanism. Already a small amount of interconnected Fe nanospheres additive (2.5-5.0% volume fraction) produces four times increase of the rotating seal burst pressure, a much higher increase than what can be obtained from using a conventional magnetic fluid with the same magnetization. The nano-composite sealing magnetic fluid proved to be a cost-effective solution to significantly increase the performance of multi-stage rotating MF seals.

Simulation of bidisperse colloidal centrifugal sedimentation using a mixture viscosity model

Understanding the sedimentation behavior of bidisperse colloidal suspensions is critical in determining their stability and separation. While centrifugation is often used to accelerate separation, the settling of bidisperse colloids and their phase separation under these conditions is complex and difficult to predict explicitly. As an alternative, this work proposes a one-dimensional advection-diffusion model that uses an effective maximum volume fraction with a bidisperse viscosity scheme, which reflects important characteristics of bidisperse sedimentation while remaining computationally efficient. The influence of Derjaguin–Landau–Verwey–Overbeek interactions on packing fraction and dispersion viscosity is also considered. A numerical implementation is described using an adaptive finite-difference solver, which can be used for concentration profile and settling rate prediction of both species under variable acceleration. Validation experiments with silica suspensions in two size ratios (500:800 and 100:500 nm) and various total concentrations are performed using an analytical centrifuge, with results also being compared to Richardson–Zaki empirical predictions. The model is shown to be a very good fit to the data for both size ratio dispersions at three mixing ratios, with differences <10%. Slightly higher levels of variation were detected for the 500:800 nm system, owing to the smaller size ratio and resulting greater effect of uncounted secondary hydrodynamic factors, which enables the limits of the mixture viscosity model to be established. Nevertheless, this work highlights that mixture viscosity modeling combined with effective maximum volume fraction modifications can provide critical insights into the effect of bidisperse suspension dynamics on separation efficiencies.

The second shear-thinning and strain-stiffening behaviors of bidisperse non-colloidal suspensions

Experimental research is done to determine the shear-thinning behavior of a bidisperse non-colloidal suspension under steady-state shear and the strain-stiffening behavior under oscillatory shear. The second shear-thinning behavior is displayed when the volume fraction of the bidisperse particle suspension is between medium and high. It exhibits with an increase in shear rate, the viscosity drops by approximately three orders of magnitude. At low shear rates, a strong particle size dependence of viscosity is observed, while at high shear rates, the particle size dependence is almost non-existent. To further understand the behavior of the second shear thinning, three sets of oscillatory shear tests and steady-state shear tests (constant shear rate) are carried out at three stopping points in parallel using a unique experimental technique we have developed. The values of modulus and viscosity at the third position are significantly smaller than those at the first and second positions. In the oscillatory shear test, the storage and loss moduli of the bidisperse suspension first decrease and then increase as the strain amplitude increases. The particle volume fraction, not the particle size, is closely related to the bidisperse critical strain amplitude. Compared with monodisperse suspension, bidisperse suspension has low viscosity and larger modulus well under steady-state shear and oscillatory shear operations, which is beneficial to the development of new materials and processes. Moreover, by adding a surfactant of a specific concentration to the bidisperse sample, it is proved that the change in the microstructure of the suspension particle is responsible for the rheological properties of the suspension.

Dense bidisperse suspensions under non-homogeneous shear

We study the rheological behaviour of bidisperse suspensions in three dimensions under a non-uniform shear flow, made by the superimposition of a linear shear and a sinusoidal disturbance. Our results show that (i) only a streamwise disturbance in the shear-plane alters the suspension dynamics by substantially reducing the relative viscosity, (ii) with the amplitude of the disturbance determining a threshold value for the effect to kick-in and its wavenumber controlling the amount of reduction and which of the two phases is affected. We show that, (iii) the rheological changes are caused by the effective separation of the two phases, with the large or small particles layering in separate regions. We provide a physical explanation of the phase separation process and of the conditions necessary to trigger it. We test the results in the whole flow curve, and we show that the mechanism remains substantially unaltered, with the only difference being the nature of the interactions between particles modified by the phase separation.

Bifurcation of solutions through a contact manifold in bidisperse models

This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid. The dependence of solutions on the relative position of contact manifolds in the phase space is examined. The wave curve method serves as the basis for the first and second analyses. The former involves the classification of elementary waves that emerge from the origin of the phase space. Analytical solutions to prototypical Riemann problems connecting the origin with any point in the state space are provided. The latter focuses on semi-analytical solutions for Riemann problems connecting any state in the phase space with the maximum packing concentration line, as observed in standard batch sedimentation tests. When the initial condition crosses the first contact manifold, a bifurcation occurs. As the initial condition approaches the second manifold, another structure appears to undergo bifurcation, although it does not represent an actual bifurcation according to the triple shock rule. The study reveals important insights into the behavior of solutions in relation to these contact manifolds. This research sheds light on the existence of emerging quasi-umbilic points within the system, which can potentially lead to new types of bifurcations as crucial elements of the elliptic/hyperbolic boundary in the system of partial differential equations. The implications of these findings and their significance are discussed.

Dip coating of viscous granular suspensions

A solid substrate withdrawn from a liquid bath is coated with a uniform thickness given by the Landau–Levich–Derjaguin (LLD) law. If the bath is a suspension of neutrally buoyant particles, the liquid coating can entrain particles in a process known as capillary filtration that only depends on the capillary number Ca. Experiments were performed using a custom-built dip coating apparatus and gravimetry techniques. The working liquids were monodisperse and bidisperse suspensions with larger particle diameters and higher liquid viscosity than previously reported. The single particle entrainment point for monodisperse suspensions agrees well with the critical capillary number predicted in prior literature. Bidisperse suspensions exhibit active filtration regions where only the smallest particles are entrained with the range of Ca for active filtration consistent with reported models. These experimental results both validate and enhance our understanding of capillary filtration by exploring larger particle-sized granular suspensions of higher viscosity solutions, as relevant to applications in construction, medical care, personal care products, and food science.

Self-Assembly and Sorting of Graphene Nanoplatelets and Spherical Colloidal Particles via Sessile Droplet Evaporation in Saturated Alcohol Vapor

We investigated the dried deposit patterns of quasi-two-dimensional graphene nanoplatelets (GNP) on hydrophilic glass via aqueous sessile droplet evaporation in a saturated alcohol vapor atmosphere. In addition, we studied both the size- and shape-dependent self-assembly and self-sorting of colloids by employing droplets containing bidispersed suspensions comprising GNP and bulk three-dimensional colloidal particles, e.g., polystyrene microspheres (PS). We report distinct self-sorting regimes as the PS diameter Dp varies between 0.1 and 6.4 μm. Under ambient air, the droplet evaporation does not yield discernible self-sorting between GNP and PS. Under saturated alcohol vapor, a critical Dp = 1.1 μm exists, for which the self-sorting does not occur. For Dp < 1.1 μm, the PS sort out from the bidispersed suspension to form the outermost ring of the deposit. The deposit pattern reverses for Dp > 1.1 μm, and GNP deposit on the outermost edge. We corroborate experimental observations with a theoretical model based on the size- and shape-dependent interfacial forces between the colloids.

Shear-thickening of dense bidispersed suspensions

We study the rheological behaviour of a dense bidispersed suspension varying the relative size of the two dispersed phases. The main outcome of our analysis is that an enhanced flowability (reduced relative viscosity) of the suspension can be achieved by increasing the dispersion ratio of the phases. We explain the observed result by showing that the presence of large particles increases the packing efficiency of the suspension, leading to a reduction of the contribution of the contacts on the overall viscosity of the suspension in the shear-thickening regime, i.e. where the contacts are the dominating component.

Analysis of the rheology of magnetic bidisperse suspensions in the regime of discontinuous shear thickening

Analysis of the rheology of magnetic bidisperse suspensions in the regime of discontinuous shear thickening

Characterising the sedimentation of bidisperse colloidal silica using analytical centrifugation

This study investigates the settling behaviour of bidisperse colloidal silica suspensions in two different size ratios (100:500 nm and 500:800 nm) with various mixture ratios and volume fractions, using an analytical photocentrifuge. For dilute systems, translation of settling rate profiles to size distributions resulted in more accurate measurements for both monodisperse and bidisperse systems than using dynamic light scattering, in comparison to SEM. However, a critical limitation was also observed, as distinction between upper (smaller particle) and lower (larger particle) interfaces could only be measured for total volume fractions <∼0.02. For 500:800 mixtures, results were compared with Richardson-Zaki and modified Batchelor model predictions. The Batchelor model proved more accurate at predicting the lower interface rate, while both models over predicted the upper interface, likely due to increased drag that was most evident with higher fractions of smaller particles. For 100:500 cases, higher centrifugal rotation speeds were required to settle the 100 nm particles, and the influence of Brownian motion was evident. It was also found that the smaller particles obtained a lower initial settling rate than its terminal velocity, due to induced anisotropic effects or backflow from the 500 nm fraction, which was again more evident with a greater proportion of smaller particles.