Suspensions Of Soft Particles Research Articles

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 review on rheological models and mathematical problem formulations for blood flows

A review on constitutive equations proposed for mathematical modeling of laminar and turbulent flows of blood as a concentrated suspension of soft particles is given. The rheological models of blood as a uniform Newtonian fluid, non-Newtonian shear-thinning, viscoplastic, viscoelastic, tixotropic and micromorphic fluids are discussed. According to the experimental data presented, the adequate rheological model must describe shear-thinning tixotropic behavior with concentration-dependent viscoelastic properties which are proper to healthy human blood. Those properties can be studied on the corresponding mathematical problem formulations for the blood flows through the tudes or ducts. The corresponding systems of equations and boundary conditions for each of the proposed rheological models are discussed. Exact solutions for steady laminar flows between the parallel plates and through the circular tubes have been obtained and analyzed for the Ostwald, Hershel-Bulkley, and Bingham shear-thinning fluids. The influence of the model parameters on the velocity profiles has been studied for each model. It is shown, certain sets of fluid parameters lead to flattening of the velocity profile while others produce its sharpening around the axis of the channel. It is shown, the second-order terms in the viscoelastic models give the partial derivative differential equations with high orders in time and mixed space-time derivatives. The corresponding problem formulations for the generalized rhelogical laws are derived. Their analytical solutions in the form of a normal mode are obtained. It is shown, the dispersion equations produce an additional set for the speed of sound (so called second sound) in the fluid. It is concluded, the most general rheological model must include shear-thinning, concentration and second sound phenomena

Microscopically grounded constitutive model for dense suspensions of soft particles below jamming

Materials made up of soft elastic particles suspended in a fluid form a broad subset of complex fluids, including emulsions, suspensions of microgels, liposomes, or vesicles. Until now, no established model can describe how they flow. Here, we derive from particle-level dynamics a constitutive model describing the rheology of two-dimensional dense soft suspensions below the jamming transition, in a regime where elastic interactions dominate the stress response. Our model successfully captures many observed rheological features, such as shear thinning, normal stresses, and normal stress differences scaling respectively linearly and quadratically with deformation rate in the slow flow limit.

Integrated data-driven modeling and experimental optimization of granular hydrogel matrices

Integrated data-driven modeling and experimental optimization of granular hydrogel matrices

Shear and extensional rheological properties of whole grain rye and oat aqueous suspensions

Whole grain flours contain polysaccharides with techno-functional and nutritional properties which make them good candidates as natural texturisers in foods and beverages, thus reducing the use of highly refined ingredients. However, the use of plant components to develop complex fluids and soft materials, requires an enhanced understanding of the relationship between their physicochemical and rheological properties. Here, we systematically investigated the shear and extensional rheological properties of aqueous suspensions of whole grain rye and oat flours. Our results indicated that both types of suspensions (3.5 wt %) showed similar shear thinning behaviour (n = 0.4) however, oat suspensions presented higher viscosity and gel-like behaviour (G'>G'') compared to rye. Additionally, the oat suspensions exhibited an apparent extensional viscosity, which was not present in rye suspensions. The rheological properties of the continuous and disperse phases, separated by centrifugation, were investigated before and after starch hydrolysis and protein removal. Our results indicate that the distinct behaviour of oat suspensions is mainly due to the molecular structure of starch in the liquid phase of i.e oat starch had a higher amylose/amylopectin ratio than rye. Whilst the presence of protein and cell wall polysaccharides in the solid phase contribute to the overall rheology of the suspensions. Furthermore, our results show that the systems do not follow the Cox-Merz rule, indicating that they behaved as suspensions of soft particles rather than macromolecules in solution. Aqueous suspensions of whole grain rye and oat flours showed rheological properties that could be of interest to design low-medium viscosity food and beverage products.

Viscous resuspension of droplets

Shear-induced migration is ubiquitous in a suspension of solid and soft particles. The contribution to particle deformability and frictional contacts between particles needs to be clarified. By measuring normal forces with viscous resuspension experiments of frictionless droplets, we show droplet deformation does not play a significant role, contrary to frictional contacts, as the normal force is much weaker for droplets than for solid particles at high volume fractions.

Dynamics of microstructure anisotropy and rheology of soft jammed suspensions.

We explore the rheology predicted by a recently proposed constitutive model for jammed suspensions of soft elastic particles derived from particle-level dynamics [Cuny et al., Phys. Rev. Lett., 2021, 127, 218003]. Our model predicts that the orientation of the anisotropy of the microstructure, governed by an interplay between advection and contact elasticity, plays a key role at yielding and in flow. It generates normal stress differences contributing significantly to the yield criterion and Trouton ratio. It gives rise to non-trivial transients such as stress overshoots in step increases of shear rate, residual stresses after flow cessation and power-law decay of the shear rate in creep. Finally, it explains the collapse of storage modulus as measured in parallel superposition for a yielded suspension.

Electrophoretic Mobility and Electric Conductivity of Salt-Free Suspensions of Charged Soft Particles

A unit cell model is employed to analyze the electrophoresis and electric conduction in a concentrated suspension of spherical charged soft particles (each is a hard core coated with a porous polyelectrolyte layer) in a salt-free medium. The linearized Poisson–Boltzmann equation applicable to a unit cell is solved for the equilibrium electrostatic potential distribution in the liquid solution containing the counterions only surrounding a soft particle. The counterionic continuity equation and modified Stokes/Brinkman equations are solved for the ionic electrochemical potential energy and fluid velocity distributions, respectively. Closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension are derived, and the effect of particle interactions on these transport characteristics is interesting and significant. Same as the case in a suspension containing added electrolytes under the Debye–Hückel approximation, the scaled electrophoretic mobility in a salt-free suspension is an increasing function of the fixed charge density of the soft particles and decreases with increases in the core-to-particle radius ratio, ratio of the particle radius to the permeation length in the porous layer, and particle volume fraction, keeping the other parameters unchanged. The normalized effective electric conductivity of the salt-free suspension also increases with an increase in the fixed charge density and with a decrease in the core-to-particle radius ratio, but is not a monotonic function of the particle volume fraction.

Lattice Boltzmann simulations of drying suspensions of soft particles.

The ordering of particles in the drying process of a colloidal suspension is crucial in determining the properties of the resulting film. For example, microscopic inhomogeneities can lead to the formation of cracks and defects that can deteriorate the quality of the film considerably. This type of problem is inherently multiscale and here we study it numerically, using our recently developed method for the simulation of soft polymeric capsules in multicomponent fluids. We focus on the effect of the particle softness on the film microstructure during the drying phase and how it relates to the formation of defects. We quantify the order of the particles by measuring both the Voronoi entropy and the isotropic order parameter. Surprisingly, both observables exhibit a non-monotonic behaviour when the softness of the particles is increased. We further investigate the correlation between the interparticle interaction and the change in the microstructure during the evaporation phase. We observe that the rigid particles form chain-like structures that tend to scatter into small clusters when the particle softness is increased. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Rheological properties of artificial boluses of cereal foods enriched with legume proteins

The properties of artificial food bolus are studied by dynamic oscillatory and capillary rheometry as functions of bolus water content (WC), in the usual range of saliva hydration, for four cereal products: sponge cake, extruded flat bread and their counterpart enriched in legume proteins. All boluses followed the same rheological behavior characterized by (1) solid -like in the linear viscoelastic domain and (2) Herschel-Bulkley model for large shear strain. Hence, four characteristic rheological properties are determined: modulus at viscoelastic plateau, characteristic stress at transition to flow, yield stress and consistency in the flow regime. The decrease of these properties with WC was fitted by an exponential decay function, from which was extracted a coefficient α (5 = α ≤ 30), defined as a coefficient of interaction of the food with water. The values of α are of the same order of magnitude as the plasticization coefficient of starch by water. They were larger for the extruded pea based (EFP, α ≥ 15), and were lower for the sponge cake (SC, α ≤ 15). The variations for the different rheological properties are discussed in terms of matter state, envisioning bolus as a suspension of soft swellable particles. The comparison of these values with those encountered for real boluses from similar foods suggests that these results contribute to define a coefficient of interaction of food with saliva.

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.

Electrokinetics of Concentrated Suspension of Soft Particles with pH-Regulated Volumetric Charges.

This article presents a theoretical study on the electrokinetics of concentrated suspension of charge-regulated soft particles under a weak electric field and low potential assumptions. The inner core of the undertaken particle is "semisoft" in nature, which allows ion penetration while the fluid cannot flow within it, and the outer soft polymeric shell allows the flow of the ionized fluid. In addition, the inner core and the outer polyelectrolyte layer (PEL) bear pH-regulated basic and acidic functional groups, respectively. The Poisson-Boltzmann equation-based mathematical model was adopted here for electric potential. The fluid flow across the electrolyte medium and PEL is governed by the Stokes equation and the Darcy-Brinkman equation, respectively. The Kuwabara's unit cell model (J. Phys. Soc. Japan, 1959, 14, 522-527) was invoked to observe the effect of the interaction between the neighboring particles in a concentrated suspension. A first order perturbation technique was used to determine the mean electrophoretic mobility of the undertaken soft particles in a concentrated suspension. The effect of pH and concentration of bulk electrolyte, electrohydrodynamic properties of both the inner core and PEL, on the mean electrophoretic mobility has been studied extensively. In addition, the results have been presented for the neutralization factor that measures the fraction of fixed charges neutralized by the mobile counterions.

Thermodynamics of shear-induced phase transition of polydisperse soft particle glasses

The thermodynamics of the shear-induced phase transition of soft particle glasses is presented. Jammed suspensions of soft particles transform into a layered phase in a strong shear flow from a stable glassy phase at lower shear rates. The thermodynamics of the two phases can be computed based on the elastic energy and excess entropy of the system. At a critical shear rate, the elastic energy, the excess entropy, the free energy, the temperature, and the shear stress undergo discontinuous jumps at the phase transitions from the glassy to the layered phase. An effective temperature is defined from the derivative of the elastic energy and the excess entropy. The Helmholtz free energy is constructed using the elastic energy, excess entropy, and derived temperature. At a fixed shear rate, there is no equilibrium between the states. However, at a fixed temperature, the glassy and layered states may coexist, as indicated by the equality of their Helmholtz free energies. While this first-order phase transition is possible, it cannot be observed in simple shear because the stress is the same in both phases at the same temperature. Thus, shear banding cannot be observed in this system. Finally, an equation of state, which relates the shear stress to the excess entropy, is presented. This equation of state shows that all dynamical properties (e.g., shear-induced diffusivity and first and second normal stresses) of these jammed non-Brownian suspensions can be determined solely by measuring the shear stress.

Colloidal and polymeric contributions to the yielding of dense microgel suspensions

HypothesisSoft microgel colloids can be densely packed since particle networks can compress and interpenetrate. This evolution of the particle’s internal structure associated with packing is expected to determine the linear viscoelastic properties and the yielding behavior of dense suspensions of microgel colloids. ExperimentsWe investigated the volume fraction-dependent linear and non-linear rheological response of suspensions of soft core-shell particles formed by a poly(N-isopropylacrylamide) (PNIPAM) microgel core and a thin poly(ethylene glycol) (PEG) shell. FindingsThe linear viscoelasticity of suspensions reveals a transition from a fluid to a jammed glass state. Increasing volume fraction within the jammed state, the linear storage modulus and the yield stress show distinct regimes associated with the evolution of particle contacts, which involve progressive compression and interpenetration of the shell and core. The yielding of jammed suspensions occurs in two-steps: At small strains jammed cages are rearranged, while full disentanglement of interpenetrating networks only occurs at large deformations and results in fluidization. Yield strains and stresses increase with increasing shear rate or frequency, suggesting a progressive dominance of the timescale associated with shear over that associated with the internal dynamics of the system.

Diffusiophoresis in Suspensions of Charged Soft Particles

The diffusiophoresis in a suspension of charged soft particles in electrolyte solution is analyzed. Each soft particle is composed of a hard core of radius r0 and surface charge density σ and an adsorbed fluid-penetrable porous shell of thickness a−r0 and fixed charge density Q. The effect of particle interactions is considered by using a unit cell model. The ionic concentration, electric potential, and fluid velocity distributions in a unit cell are solved as power expansions in σ and Q, and an explicit formula for the diffusiophoretic velocity of the soft particle is derived from a balance between the hydrodynamic and electrostatic forces exerted on it. This formula is correct to the second orders of σ and Q and valid for arbitrary values of κa, λa, r0/a, and the particle volume fraction of the suspension, where κ is the Debye screening parameter and λ is the reciprocal of a length featuring the flow penetration into the porous shell. The effects of the physical characteristics and particle interactions on the diffusiophoresis (including electrophoresis and chemiphoresis) in a suspension of charged soft particles, which become those of hard particles and porous particles in the limits r0=a and r0=0, respectively, are significant and complicated.

Influence of pH on fluid gels produced from egg and whey protein isolate

Food producers are coming under increasing pressure to reduce fat content of foods. Fat forms a major structuring component in many foods responsible for the desirable texture of foods which are rich in fats. Consumers want healthier foods whilst maintaining desirable sensory properties of these foods and using ‘natural’ ingredients. In this work we present suspensions of soft gelled protein particles produced by heating induced gelation in shear of proteins. We present egg white fluid gels and compare them with previously characterized WPI fluid gels. Understanding the effects of pH on proteins is important owing to the net charge influencing gelation and gel properties. Soft tribology and rheology were used to investigate textural properties of fluid gels produced and relate these to potential mouthfeel of these systems. Fluid Gels at the IEP were shown to produce aggregated particles of less than 1 μm diameter. These systems produced at the IEP demonstrated greater friction values in the mixed and boundary regimes of lubrication.

Theoretical predictions for the rheology of dispersions of highly deformable particles under large amplitude oscillatory shear

This work is concerned with the oscillatory rheology of non-colloidal suspensions of highly deformable viscoelastic particles in Newtonian fluids under simple shear loading. To this end, use is made of the homogenization model of Avazmohammadi & Ponte Castaneda (J. Fluid Mech., vol. 763, 2015, pp. 386–432) accounting for the time evolution of the average particle shape and orientation. For small excitation amplitudes, the equations reduce to the small-strain Oldroyd model with expressions for the storage and loss moduli, and , that recover those of Roscoe (J. Fluid Mech., vol. 28 (2), 1967, pp. 273–293) for small particle concentrations. However, at sufficiently large concentrations, and may intersect, such that in a given frequency range. In the large amplitude oscillatory shear (LAOS) regime, the behaviour of and with increasing strain amplitude is consistent with type I or type III behaviour, in the terminology of Hyun et al. (J. Non-Newtonian Fluid Mech., vol. 107 (1–3), 2002, pp. 51–65), depending on the particle properties and concentration. In addition, the rheology is characterized by means of stress waveforms and Lissajous–Bowditch cycles in a Pipkin diagram. By accounting for the microstructure evolution, the model captures a number of nonlinear features commonly observed in the LAOS rheology of complex fluids, including a variety of distorted stress waveforms that manifest themselves in complex intracycle behaviour, as well as secondary loops. Furthermore, as a consequence of directional biases associated with the large deformations of the particles, the model predicts non-vanishing normal stress differences whose characteristic limit cycles are also presented in Pipkin space and reveal the formation of secondary loops for suspensions of Gent particles. However, it should be emphasized that the sources of these nonlinear rheological features for soft particle suspensions are very different from those for rigid particle colloidal systems and, in contrast to the colloidal systems, manifest themselves at dilute volume fractions of the particles.

Effect of geometrical confinement on the flow of soft microgel particle pastes

In this paper, we determine the effect of confinement on the shear flow of concentrated soft microgel particle suspensions. Utilizing a flexure-based microgap rheometer (FMR), aqueous suspensions of swollen P(NIPAM-co-AA) microgel particles of 4μ m diameter at different volume fractions larger than 64 vol% are subjected to shearing deformations between plates separated by gaps of 5–120μ m while monitoring the stress response at different rates. Describing the stress evolution from a balance of elastohydrodynamic lubrication and elastic forces following the approach of Cloitre and Bonnecaze, it could be shown that already below a critical confinement level on the order of 10 particle diameters an increase of the interparticle pressure leads to a rising shear stress at a given rate in the yielded regime. This effect is strongest for particle volume fractions close to the critical closest packing, with two orders of magnitude increase in flow resistance when approaching the single-particle confinement level, whereas this confinement effect on the flow decreases when raising the concentration. Furthermore, it could be shown that, at the onset of the yielding of the suspensions, the confinement is increasing the effective modulus, but not the yield strain.

Viscoplastic drop impact on thin films

We use high-speed imaging to study the effect of thixotropic aging in drop impact of yield-stress fluids on pre-coated substrates. Our results reveal that drop splashing is suppressed for "aged" compared to "unaged" samples, indicating that thixotropic breakdown timescales during impact are long enough to affect the dynamics. We propose and test several hypotheses for modifying the dimensionless group ${\rm IF}(D/t)$ [1,2] to account for thixotropic aging. The main challenge is that the steady flow properties (Herschel-Bulkley model parameters) used in the current dimensionless group cannot be defined or measured for thixotropically aged samples, because any deformation inherently rejuvenates and breaks down the microstructure. We find the most suitable hypothesis is to only increase the yield stress ($\sigma_{\rm y}$, plastic component) based on the storage modulus of aged samples, while keeping the viscous parameters ($K$ or $\eta_{\infty}$) constant. The work reveals fundamental insight into rarely studied short-timescale flow conditions with thixotropic effects. These results are important for applications such as fire suppression or spray coating that involve complex fluids of varying degrees of thixotropic aging.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.