Dense Particle Suspensions Research Articles

Stress overshoot, hysteresis, and the Bauschinger effect in sheared dense colloidal suspensions.

The mechanical nonlinear response of dense Brownian suspensions of polymer gel particles is studied experimentally and by means of numerical simulations. It is shown that the response to the application of a constant shear rate depends on the previous history of the suspension. When the flow starts from a suspension at rest, it exhibits an elastic response followed by a stress overshoot and then a plastic flow regime. Conversely, after flow reversal, the stress overshoot does not occur, and the apparent elastic modulus is reduced while numerical simulations reveal that the anisotropy of the local microstructure is delayed relative to the macroscopic stress.

Discontinuous shear thickening in dense suspensions: Mechanisms, force networks, and fluctuations

<h2>Abstract</h2> Dense suspensions of particles in a liquid, with industrial examples including coatings or precursors to solid ceramics and cements, can be quite difficult to process because their flow properties are very sensitive to particle surface interactions. We focus on the extreme rate dependence known as "discontinuous shear thickening" (DST) where the viscosity undergoes a finite and typically large discontinuous jump in viscosity at some shear rate. Simultaneous with DST, there is a large increase in the normal stress, including the nonequilibrium osmotic pressure, or ‘particle pressure', leading to the historical name of `dilatancy' for shear thickening. Our computational simulations inclusive of the three ingredients of i) lubrication hydrodynamics, ii) repulsive interparticle forces (e.g. due to surface charge) and iii) contact with friction have been shown to reproduce the primary features of DST found experimentally; this is called lubricated-to-frictional (LF) rheology. We describe the main features of the shear thickening transition in the LF scenario, including the observation of extreme fluctuations. Using our simulation results, we explore the microscopic basis for the LF transition in the force network developed under flow.

Scaling Analysis of Shear Thickening Suspensions

Dense suspensions of particles in viscous liquid often demonstrate the striking phenomenon of abrupt shear thickening, where their viscosity increases strongly with increase of the imposed stress or shear rate. In this work, discrete-particle simulations accounting for short-range hydrodynamic, repulsive, and contact forces are performed to simulate flow of shear thickening bidisperse suspensions, with the packing parameters of large-to-small particle radius ratio δ = 3 and large particle fraction ζ = 0.15, 0.50, and 0.85. The simulations are carried out for volume fractions 0.54 ≤ ϕ ≤ 0.60 and a wide range of shear stresses. The repulsive forces, of magnitude FR, model the effects of surface charge and electric double-layer overlap, and result in shear thinning at small stress, with shear thickening beginning at stresses σ ∼ FRa−2. A crossover scaling analysis used to describe systems with more than one thermodynamic critical point has recently been shown to successfully describe the experimentally-observed shear thickening behavior in suspensions. The scaling theory is tested here on simulated shear thickening data of the bidisperse mixtures, and also on nearly monodisperse suspensions with δ = 1.4 and ζ = 0.50. Presenting the viscosity in terms of a universal crossover scaling function between the frictionless and frictional maximum packing fractions collapses the viscosity for most of the suspensions studied. Two scaling regimes having different exponents are observed. The scaling analysis shows that the second normal stress difference N2 and the particle pressure Π also collapse on their respective curves, with the latter featuring a different exponent from the viscosity and normal stress difference. The influence of the fraction of frictional contacts, one of the parameters of the scaling analysis, and its dependence on the packing parameters are also presented.

Origin of Two Distinct Stress Relaxation Regimes in Shear Jammed Dense Suspensions.

Many dense particulate suspensions show a stress induced transformation from a liquidlike state to a solidlike shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly nonexponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and normal stress measurements confirm that such stress discontinuity originates from the localized plastic events, whereas system spanning dilation controls the slower relaxation process. We also find an intriguing correlation between the nature of transient relaxation and the steady-state shear jamming phase diagram obtained from the Wyart-Cates model.

Inter-particle adhesion induced strong mechanical memory in a dense granular suspension

Repeated/cyclic shearing can drive amorphous solids to a steady state encoding a memory of the applied strain amplitude. However, recent experiments find that the effect of such memory formation on the mechanical properties of the bulk material is rather weak. Here, we study the memory effect in a yield stress solid formed by a dense suspension of cornstarch particles in paraffin oil. Under cyclic shear, the system evolves toward a steady state showing training-induced strain stiffening and plasticity. A readout reveals that the system encodes a strong memory of the training amplitude (γT) as indicated by a large change in the differential shear modulus. We observe that memory can be encoded for a wide range of γT values both above and below the yielding albeit the strength of the memory decreases with increasing γT. In situ boundary imaging shows strain localization close to the shearing boundaries, while the bulk of the sample moves like a solid plug. In the steady state, the average particle velocity v inside the solid-like region slows down with respect to the moving plate as γ approaches γT; however, as the readout strain crosses γT, v suddenly increases. We demonstrate that inter-particle adhesive interaction is crucial for such a strong memory effect. Interestingly, our system can also remember more than one input only if the training strain with smaller amplitude is applied last.

Effect of adhesive interaction on strain stiffening and dissipation in granular gels undergoing yielding

Shear induced yielding in disordered solids, characterized by irreversibility and enhanced dissipation, is important for a wide range of industrial and geological processes. Although such phenomena in thermal systems have been extensively studied, they remain poorly understood for granular solids. Here, using oscillatory shear rheology we study energy dissipation in a disordered solid formed by dense granular suspensions of adhesive frictional particles. We find non-linear flow regimes showing intra-cycle strain stiffening and plasticity that strongly depend on both the applied strain amplitude and particle volume fraction, which can be captured by the normalized energy dissipation. Furthermore, in-situ optical imaging reveals irreversible particle rearrangements correlating with the spatio-temporal fluctuations in local velocity across the yielding transition. By directly measuring the critical jamming packing fraction using particle settling experiments, we propose a phase diagram that unravels the effect of inter-particle interactions on flow properties of the system for a large parameter space.

Fluid-mediated sources of granular temperature at finite Reynolds numbers

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modelling the neighbour-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration–velocity distribution function $P(v^{\prime },a^{\prime };t)$ . Quadrant-conditioned covariance integrals of $P(v^{\prime },a^{\prime };t)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature that can be used in Eulerian two-fluid models. Analytical predictions agree with benchmark data from particle-resolved direct numerical simulations and show promise as a general theory from gas–solid to bubbly flows.

Theoretical Analysis of a self-condensing CO2 Transcritical Power Cycle with regeneration involving DPS in a Solar Thermal Power Plant

Abstract The choice of heat transfer fluids(HTF) significantly dictates the thermal efficiency of the solar power plant. Presently, molten salt is widely used choice owing to its phase, low cost and non-toxic nature. Along with other alternatives like liquid metals, multiphase fluids, these HTFs are limited to peak operating temperatures ranging from 300-550°C. With the introduction of Dense Particle Suspensions (DPS) as an HTF, the highest operating temperatures in a Solar thermal power plant can reach up to 700°C, offering considerable scope for improving thermal efficiency. Due to the higher average specific heat as compared to the alternatives, CO2 is a promising working fluid in the considered range of moderately high operating temperatures. The cost of the components and size of the power block makes the transcritical CO2 cycle an attractive alternative. The present work analyses the theoretical efficiency of the proposed cycle, with the peak operating temperature ranging from 550°C to 700°C. The effects of the variation in the lower operating pressure and the condensation temperature have also been analysed. It is observed that thermodynamic efficiencies as high as 40% can be reached at the maximum operating temperature. The optimum combination of the lower operating pressure and the condensation temperature is also noted.

The Physics of Dense Suspensions

Dense suspensions of particles are relevant to many applications and are a key platform for developing a fundamental physics of out-of-equilibrium systems. They present challenging flow properties, apparently turning from liquid to solid upon small changes in composition or, intriguingly, in the driving forces applied to them. The emergent physics close to the ubiquitous jamming transition (and to some extent the glass and gelation transitions) provides common principles with which to achieve a consistent interpretation of a vast set of phenomena reported in the literature. In light of this, we review the current state of understanding regarding the relation between the physics at the particle scale and the rheology at the macroscopic scale. We further show how this perspective opens new avenues for the development of continuum models for dense suspensions.

Deep learning methods for predicting fluid forces in dense particle suspensions

Two deep learning methods, Multi-Layer Perceptron (MLP) network and Convolution Neural Network (CNN) are evaluated to predict drag forces in dense suspensions of ellipsoidal particles using data from Particle Resolved Simulations (PRS). The MLP is trained on the mean flow Reynolds number, solid fraction of the suspension, the aspect ratio of the particle, and orientation to flow direction. The CNN is given an additional 3D spatial map of the particle of interest and its immediate neighborhood via a distance function. The prediction capability of the trained networks is tested at different levels of complexity: on an unseen particle arrangement (Level 1), to all arrangements of an unseen numerical experiment (Level 2), and finally to all experiments of an unseen Reynolds number, solid fraction or aspect ratio (Level 3). The CNN is shown to perform better than the MLP for all testing levels except when testing on an unseen aspect ratio.

Orientational arrest in dense suspensions of elliptical particles under oscillatory shear flows

We study the rheological response of dense suspensions of elliptical particles, with an aspect ratio equal to 3, under oscillatory shear flows and imposed pressure by numerical simulations. Like for the isotropic particles, we find that the oscillatory shear flows respect the Cox-Merz rule at large oscillatory strains but differ at low strains, with a lower viscosity than the steady shear and higher shear jamming packing fractions. However, unlike the isotropic cases (i.e., discs and spheres), frictionless ellipses get dynamically arrested in their initial orientational configuration at small oscillatory strains. We illustrate this by starting at two different configurations with different nematic order parameters and the average orientation of the particles. Surprisingly, the overall orientation in the frictionless case is uncoupled to the rheological response close to jamming, and the rheology is only controlled by the average number of contacts and the oscillatory strain. Having larger oscillatory strains or adding friction does, however, help the system escape these orientational arrested states, which are evolving to a disordered state independent of the initial configuration at low strains and ordered ones at large strains.

Dense Suspension Flows: A Mathematical Model Consistent With Thermodynamics

Abstract We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of Landau and Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.

Improving axial localization of weak phase particles in digital in-line holography.

One shortcoming of digital in-line holography (DIH) is the low axial position accuracy due to the elongated particle traces in the reconstruction field. Here, we propose a method that improves the axial localization of DIH when applying it to track the motion of weak phase particles in dense suspensions. The proposed method detects particle positions based on local intensities in the reconstruction field consisting of scattering and incident waves. We perform both numerical and experimental tests and demonstrate that the proposed method has a higher axial position accuracy than the previous method based on the local intensities in the reconstructed scattered field. We show that the proposed method has an axial position error below 1.5 particle diameters for holograms with a particle concentration of 4700particles/mm3. The proposed method is further validated by tracking the Brownian motion of 1µmparticles in dense suspensions.

Exploring the roles of roughness, friction and adhesion in discontinuous shear thickening by means of thermo-responsive particles

Dense suspensions of colloidal or granular particles can display pronounced non-Newtonian behaviour, such as discontinuous shear thickening and shear jamming. The essential contribution of particle surface roughness and adhesive forces confirms that stress-activated frictional contacts can play a key role in these phenomena. Here, by employing a system of microparticles coated by responsive polymers, we report experimental evidence that the relative contributions of friction, adhesion, and surface roughness can be tuned in situ as a function of temperature. Modifying temperature during shear therefore allows contact conditions to be regulated, and discontinuous shear thickening to be switched on and off on demand. The macroscopic rheological response follows the dictates of independent single-particle characterization of adhesive and tribological properties, obtained by colloidal-probe atomic force microscopy. Our findings identify additional routes for the design of smart non-Newtonian fluids and open a way to more directly connect experiments to computational models of sheared suspensions.

Wall slip and bulk yielding in soft particle suspensions

We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, using a method that fully accounts for the fluid mechanics of the solvent between the particles, and between the particles and the walls, as well as for the solid mechanics of changes in the particle shapes. We thus capture the widely observed phenomenon of elastohydrodynamic wall slip, in which the soft particles become deformed in shear and lift away from the wall slightly, leaving behind a thin lubricating solvent layer of high shear. For imposed stresses below the material's bulk yield stress, we show the observed wall slip to be dominated by this thin solvent layer. At higher stresses, it is augmented by an additional contribution arising from a fluidisation of the first few layers of particles near the wall. By systematically varying the roughness of the walls, we quantify a suppression of slip with increasing wall roughness. For smooth walls, slip radically changes the steady state bulk flow curve of shear stress as a function of shear rate, by conferring a branch of apparent (slip-induced) flow even for $\sigma<\sigma_y$, as seen experimentally. We also elucidate the effects of slip on the dynamics of yielding following the imposition of a constant shear stress, characterising the timescales at which bulk yielding arises, and at which slip first sets in.

Design and off-design performance comparison of supercritical carbon dioxide Brayton cycles for particle-based high temperature concentrating solar power plants

Concentrated solar power (CSP) plants using dense particle suspension as heat transfer fluid and particles as the storage medium are considered as a promising solution to provide the high temperature required for the supercritical carbon dioxide (S-CO2) Brayton cycle. During plant operation, variations in the heat transfer fluid temperature and ambient temperature would significantly affect system performance. Determining the suitable S-CO2 Brayton cycle configuration for this particle-based CSP plant requires accurate prediction and comprehensive comparison on the system performance both at design and off-design conditions. This study presents a common methodology to homogeneously assess the plant performance for six 10 MW S-CO2 Brayton cycles (i.e. simple regeneration, recompression, precompression, intercooling, partial cooling and split expansion) integrated with a hot particles thermal energy storage and a dry cooling system. This methodology includes both design and off-design detailed models based on the characteristic curves of all components. The optimal design for each thermodynamic cycle has been determined under the same boundary design constrains by a genetic algorithm. Then, their off-design performances have been quantitatively compared under varying particle inlet temperature and ambient temperature, in terms of cycle efficiency, net power output and specific work. Results show that the variation in ambient temperature contributes to a greater influence on the cycle off-design performance than typical variations of the heat transfer fluid temperature. Cycles with higher complexity have larger performance deterioration when the ambient temperature increases, though they could present higher peak efficiency and specific work at design-point. In particular, the cycle with maximum efficiency or specific work presents significant changes in different ranges of ambient temperature. This means that for the selection of the best configuration, the typical off-design operation conditions should be considered as well. For integrating with high-temperature CSP plants and dry cooling systems, the simple regeneration and the recompression cycles are the most suitable S-CO2 Brayton cycle configurations due to their fewer performance degradations at ambient temperatures above 30 °C, which is a frequent environmental condition in sunny areas of the world.

Performance of drag force models for shock-accelerated flow in dense particle suspensions

Models for prediction of drag forces within a particle cloud following shock-acceleration are evaluated with the aid of results from particle-resolved simulations in order to quantify how much the disturbances introduced by the proximity of nearby particles affect the drag forces. The drag models evaluated here consist of quasi-steady forces, undisturbed flow forces, inviscid unsteady forces, and viscous unsteady forces. Two dense particle curtain correction schemes to these forces, based on volume fraction and input velocity, are also evaluated. The models are tested in two ways; first they are evaluated based on volume-averaged flow fields from particle-resolved simulations; secondly, they are applied in Eulerian-Lagrangian simulations, and the results are compared to the particle-resolved simulations.The results show that both correction schemes significantly improve the particle force predictions, but the average total impulse on the particles is still underpredicted by both correction schemes in both tests. With the volume averaged flow fields as input, the volume fraction correction gives the best results. However, in the Eulerian-Lagrangian simulations it is demonstrated that the velocity fluctuation model, associated with the velocity correction scheme, is crucial for obtaining accurate predictions of the mean flow fields.

Grid-algorithm improvements for dense suspensions of discrete element particles in finite element fluid simulations

For homogeneous systems like classical fluid dynamics and structural mechanics, finite element method (FEM) grid generation has reached a mature state. On the other hand, for multi-physics-problems like fluids with a high density of immersed particles, many researchers may not even be aware of the types of instabilities which may be triggered by unsuitable meshes. We review common types of grid generation, point out previously unrecognised types of instabilities for particles in fluids as well as remedies to obtain particle-fluid simulations with higher stability and fewer redundant degrees of freedom.

Surface-wave instability without inertia in shear-thickening suspensions

Recent simulations and experiments have shown that shear-thickening of dense particle suspensions corresponds to a frictional transition. Based on this understanding, non-monotonic rheological laws have been proposed and successfully tested in rheometers. These recent advances offer a unique opportunity for moving beyond rheometry and tackling quantitatively hydrodynamic flows of shear-thickening suspensions. Here, we investigate the flow of a shear-thickening suspension down an inclined plane and show that, at large volume fractions, surface kinematic waves can spontaneously emerge. Curiously, the instability develops at low Reynolds numbers, and therefore does not fit into the classical framework of Kapitza or ‘roll-waves’ instabilities based on inertia. We show that this instability, that we call ‘Oobleck waves’, arises from the sole coupling between the non-monotonic (S-shape) rheological laws of shear-thickening suspensions and the flow free surface.

Modelling Complex Particle–Fluid Flow with a Discrete Element Method Coupled with Lattice Boltzmann Methods (DEM-LBM)

Particle–fluid flows are ubiquitous in nature and industry. Understanding the dynamic behaviour of these complex flows becomes a rapidly developing interdisciplinary research focus. In this work, a numerical modelling approach for complex particle–fluid flows using the discrete element method coupled with the lattice Boltzmann method (DEM-LBM) is presented. The discrete element method and the lattice Boltzmann method, as well as the coupling techniques, are discussed in detail. The DEM-LBM is thoroughly validated for typical benchmark cases: the single-phase Poiseuille flow, the gravitational settling and the drag force on a fixed particle. In order to demonstrate the potential and applicability of DEM-LBM, three case studies are performed, which include the inertial migration of dense particle suspensions, the agglomeration of adhesive particle flows in channel flow and the sedimentation of particles in cavity flow. It is shown that DEM-LBM is a robust numerical approach for analysing complex particle–fluid flows.