Soft Particle Systems Research Articles

Self-growing biomimetic functional hydrogel particles for conformance control in tight reservoir fracture network

Hydraulic fracturing is gradually becoming a common approach for enhancing the oil production from tight reservoirs. Blocking agents such as soft particle systems are necessary as a means of conformance control to mitigate the side effect of reservoir heterogeneity due to hydraulic fracturing. In this work, a novel technique based on the mussel biomimetic concept is proposed to generate self-growing biomimetic functional hydrogel particles (SG-BFHPs). The fracture conformance control capacity of the products is evaluated, and the results show that multi-scale (0.5–3.0 mm) SG-BFHPs can cohere and grow at the reservoir condition, and the median agglomerated particle size can increase by 20–25 times. High flow resistance (Frr = 10.7–11.8), facilitated by the higher adhesion between the biomimetic particles and the pore walls, can be established by SG-BFHPs while maintaining a good injectivity. In the single-fracture model, the increased oil recovery by SG-BFHPs is about 12.2 %, and in the matrix-fracture model can be increased from 9.2 %–13.5 % to 25.8 %–28.8 %. AFM experiments show that SG-BFHPs have stronger adhesion between particles or rock surface than conventional hydrogel particles. After conformance control of SG-BFHPs, the particles are distributed in an irregular structure in the fractures and adsorbed on the fracture wall under the effect of inter-particle cohesion and adhesion, which can realize fracture channel adjustment by the particle self-growing. The SG-BFHPs studied in this paper provide valuable insights for the development of dispersed particle gel, which is of great significance in improving oil recovery in tight reservoirs.

Observation of liquid glass in molecular dynamics simulations.

Molecular anisotropy plays an important role in the glass transition of a liquid. Recently, a novel bulk glass state has been discovered by optical microscopy experiments on suspensions of ellipsoidal colloids. "Liquid glass" is a disordered analog of a nematic liquid crystal, in which rotation motion is hindered but particles diffuse freely. Global nematic order is suppressed as clusters of aligned particles intertwine. We perform Brownian dynamics simulations to test the structure and dynamics of a dense system of soft ellipsoidal particles. As seen in the experiments and in accordance with predictions from the mode coupling theory, on the time scale of our simulations, rotation motion is frozen but translation motion persists in liquid glass. Analyses of the dynamic structure functions for translation and rotation corroborates the presence of two separate glass transitions for rotation and translation, respectively. Even though the equilibrium state should be nematic, aligned structures remain small and orientational order rapidly decays with increasing size. Long-wavelength fluctuations are remnants of the isotropic-nematic transition.

Motility-induced phase separation of soft active Brownian particles

Motility-induced phase separation (MIPS) is the hallmark of non-equilibrium phase transition in active matter. Here, by means of Brownian dynamics simulations, we determine the phase behavior and the critical point for phase separation induced by motility of a two-dimensional system of soft active Brownian particles, whose interaction is modeled by the generalized purely repulsive Weeks–Chandler–Andersen potential. We refer to this model as soft active Brownian particles. We determine and analyze the influence of particle softness on the MIPS and show that the liquid–gas coexistence region is wider, the softer the interparticle interactions becomes. Moreover, the critical value of the self-propulsion velocity at which diluted and dense phases start to coexist also increases; as a consequence, the softer the particle interaction is, the bigger self-propulsion velocities are needed in order to observe a MIPS.

Stochastic methods for slip prediction in a sheared granular system.

We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.

Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium.

In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.

Predicting Defects in Soft Sphere Packings near Jamming Using the Force Network Ensemble.

Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined and can be characterized as a random instantiation within the space of the force network ensemble. In this Letter, we show that defect contacts that are not necessary for stability of the system can be uniquely identified by examining the boundaries of this space of allowed force networks. We further show that, for simulations in the near jamming limit, this identification is nearly always correct and that defect contacts are broken under decompression of the system.

Mean-field description of aging linear response in athermal amorphous solids

We study the linear response to strain in a mean-field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the ``jammed'' regime of the model, where the plastic activity exhibits a nontrivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behavior of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent $\ensuremath{\mu}$. For $\ensuremath{\mu}>1$, we find simple aging, where the stress relaxation timescale scales linearly with the age ${t}_{\mathrm{w}}$ of the material. At $\ensuremath{\mu}=1$, which corresponds to interactions mediated by the physical elastic propagator, we find instead a ${t}_{\mathrm{w}}^{1/2}$ scaling arising from the stretched exponential decay of the plastic activity. We compare these predictions with measurements of the linear response in computer simulations of a model jammed system of repulsive soft athermal particles, during its slow dissipative relaxation towards mechanical equilibrium, and find good agreement with the theory.

Multiple 2D crystal structures in bilayered lamellae from the direct self-assembly of 3D systems of soft Janus particles.

Numerous crystals and Frank-Kasper phases in two-dimensional (2D) systems of soft particles have been presented by theoretical investigations. How to realize 2D crystals or Frank-Kasper phases via the direct self-assembly of three-dimensional (3D) systems remains an important issue. Here, through numerical simulations, we report the surprising finding of multiple 2D crystal structures in bilayered lamellae from the direct self-assembly of 3D systems of soft Janus particles. With varying the patch size and particle density, soft Janus particles, which exhibit very similar self-assembly behavior to giant amphiphiles, spontaneously form ordered bilayered lamellae. Within each layer of the bilayered lamellae, we find abundant highly-ordered 2D crystals including the Frank-Kasper σ phase and open kagome lattice. The kinetic mechanisms of the formation of these 2D crystals within the layers are revealed, and include a classical one-step nucleation mechanism and a two-step nucleation mechanism. Our findings suggest a simple route towards 2D crystals via the direct self-assembly of 3D systems of amphiphilic Janus building blocks.

Soft Particles at Liquid Interfaces: From Molecular Particle Architecture to Collective Phase Behavior.

Soft particles such as microgels can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. To date, experimental efforts have predominantly provided phenomenological links between microgel structure and resulting interfacial behavior, while simulations have not been entirely successful in reproducing experiments or predicting the minimal requirements for the desired phase behavior. Here, we develop a multiscale framework to link the molecular particle architecture to the resulting interfacial morphology and, ultimately, to the collective interfacial phase behavior. To this end, we investigate interfacial morphologies of different poly(N-isopropylacrylamide) particle systems using phase-contrast atomic force microscopy and correlate the distinct interfacial morphology with their bulk molecular architecture. We subsequently introduce a new coarse-grained simulation method that uses augmented potentials to translate this interfacial morphology into the resulting phase behavior upon compression. The main novelty of this method is the possibility to efficiently encode multibody interactions, the effects of which are key to distinguishing between heterostructural (anisotropic collapse) and isostructural (isotropic collapse) phase transitions. Our approach allows us to qualitatively resolve existing discrepancies between experiments and simulations. Notably, we demonstrate the first in silico account of the two-dimensional isostructural transition, which is frequently found in experiments but elusive in simulations. In addition, we provide the first experimental demonstration of a heterostructural transition to a chain phase in a single-component system, which has been theoretically predicted decades ago. Overall, our multiscale framework provides a phenomenological bridge between physicochemical soft-particle characteristics at the molecular scale and nanoscale and the collective self-assembly phenomenology at the macroscale, serving as a stepping stone toward an ultimately more quantitative and predictive design approach.

Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function

An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood’s superposition approximation. Detailed considerations of the peaks’ shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system’s dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids’ dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid’s structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

Light scattering by densely packed optically soft particle systems, with consideration of the particle agglomeration and dependent scattering.

Light scattering and radiative transfer in optically soft particle systems are important problems in many fields of natural sciences and engineering, such as biology, ocean optics, atmospheric science, solar energy utilization, and so on. Due to the effects of particle agglomeration and dependent scattering, the radiative transfer problem will become more complex with the increase of particle volume fraction. In this study, the scattering properties and radiative transfer characteristics of densely packed optically soft particle systems, with consideration of the effects of dependent scattering and particle agglomeration, are investigated. The dependent scattering properties of densely packed silicon-dioxide spherical particles embedded in water are calculated by using the Lorenz-Mie theory and Percus-Yevick sticky hard-sphere model. The directional-hemispherical reflectance of the dispersed plane-parallel layer is obtained by using the Monte Carlo method. The results show that dependent scattering and particle agglomeration have significant influence on the scattering properties of particles. With the increase of particle agglomeration degree, the scattering coefficients and asymmetry factors of the particles increase obviously, which can be even larger than the results for independent scattering under certain circumstances. Due to the combined interaction of multiple scattering, dependent scattering, and particle agglomeration, for different size particles, the variation tendency of the hemispherical reflectance is obviously different with increasing particle agglomeration degree.

The contact detection for heart-shaped particles

The contact detection between non-spherical particles is an important issue in the discrete element method (DEM). The non-spherical particles commonly used in DEM are ellipsoids or super-ellipsoids. Such particles possess convex shape functions. The determination of contact points can be reduced to a set of nonlinear partial differential equations by the Lagrange method. Then, the Newton-Raphson method is used to solve these equations. The Lagrange method's premise is that the shape function is convex. For heart-shaped particles with concave shape functions, Lagrange method is not applicable. In this study, the contact point between heart-shaped particles is determined by grid method. This method does not need to provide the initial guess point and does not need to solve the Jacobian inverse matrix. There is no divergence in the solution process, and no limit to the concavity or convexity of the shape function. The algorithm is stable and is a general method. In the MATLAB and C compiler environment, the contact points between super-ellipsoid particles are calculated by the grid method and Newton-Raphson method, respectively. The grid method takes 60 and 0.14 ms, respectively, and its computational efficiency is better than that of the Newton-Raphson method. The time consumption for contact point of heart-shaped particles is less than that of super-ellipsoid particles. The number of contact point between two concave particles may be bigger than one; for this case, accurate results can still be obtained via the grid method. The method given in this study is applicable to the simulation of soft or hard particle systems. In addition, the method is used to simulate the evolution of the super-ellipsoid system with boundary constraints under gravity, and the stability and applicability of grid method are verified.

Parallel implicit contact algorithm for soft particle systems

This paper presents a numerical technique to model soft particle materials in which the particles can undergo large deformations. It combines an implicit finite strain formalism of the Material Point Method and the Contact Dynamics method. In this framework, the large deformations of individual particles as well as their collective interactions are treated consistently. In order to reduce the computational cost, this method is parallelised using the Message Passing Interface (MPI) strategy. Using this approach, we investigate the uniaxial compaction of 2D packings composed of particles governed by a Neo-Hookean material behaviour. We consider compressibility rates ranging from fully compressible to incompressible particles. The packing deformation mechanism is a combination of both particle rearrangements and large deformations, and leads to high packing fractions beyond the jamming state. We show that the packing strength declines when the particle compressibility decreases, and the packing can deform considerably. We also discuss the evolution of the connectivity of the particles and particle deformation distributions in the packing.

Note: Melting criterion for soft particle systems in two dimensions

A simple criterion for melting of two-dimensional crystals with soft long-ranged interactions is proposed. It states that the ratio of the transverse sound velocity of an ideal crystalline lattice to the thermal velocity is a quasi-universal number close to $4.3$ at melting. This criterion is arrived by reference to the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting, combined with the observation that the ratio of transverse-to-longitudinal sound velocities is small in the soft interaction limit. Application of this criteria allows estimating melting lines in a simple yet relatively accurate manner. Two-dimensional weakly screened Yukawa systems represent one relevant example considered.

Multiple-scale structures: from Faraday waves to soft-matter quasicrystals.

For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids. Much effort is being invested in understanding the thermodynamic properties of these soft-matter quasicrystals in order to predict and possibly control the structures that form, and hopefully to shed light on the broader yet unresolved general questions of quasicrystal formation and stability. Moreover, the ability to control the self-assembly of soft quasicrystals may contribute to the development of novel photonics or other applications based on self-assembled metamaterials. Here a path is followed, leading to quantitative stability predictions, that starts with a model developed two decades ago to treat the formation of multiple-scale quasiperiodic Faraday waves (standing wave patterns in vibrating fluid surfaces) and which was later mapped onto systems of soft particles, interacting via multiple-scale pair potentials. The article reviews, and substantially expands, the quantitative predictions of these models, while correcting a few discrepancies in earlier calculations, and presents new analytical methods for treating the models. In so doing, a number of new stable quasicrystalline structures are found with octagonal, octadecagonal and higher-order symmetries, some of which may, it is hoped, be observed in future experiments.

Continuum percolation-based tortuosity and thermal conductivity of soft superball systems: shape dependence from octahedra via spheres to cubes.

Understanding the effect of particle shape on the percolation threshold, tortuosity and thermal conductivity of soft (geometrical overlapping) particle systems is very crucial for the design and optimization of such materials, including colloids, polymers, and porous and fracture media. In this work, we first combine the excluded-volume theory with the Monte Carlo simulations to determine the percolation threshold for a family of soft superballs, the shape of which interpolates between octahedra and cubes via spheres. Then, we propose two continuum percolation-based models to respectively obtain the tortuosity and effective thermal conductivity of soft superball systems considering their percolation behavior, where monodisperse overlapping superballs are uniformly distributed in a homogeneous solid matrix. Specifically, both models cover the whole feasible range of superball volume fractions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of precisely predicting the percolation threshold, tortuosity and thermal conductivity of such systems. Furthermore, we apply the proposed models to probe the influence of particle shape on these important parameters. Our results show that the decreasing percolation threshold and tortuosity as soft particles become more anisotropic is consistent with increasing conductivity. It suggests that the anisotropic-shaped inclusion phase is more conducting than the spherical inclusion phase. The present theoretical strategies and conclusions may provide sound guidance for the synthesis of colloidal and polymer superballs.

Unjamming in models with analytic pairwise potentials.

Canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cutoff in the interaction range. The sharp cutoff renders the potential nonanalytic but makes it possible to describe many properties of the solid in terms of the coordination number z, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cutoff in the interaction range have not been studied in this context, but should in fact be considered to understand the relevance of the unjamming phenomenology in systems where such a cutoff is not present. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear-to-bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the pressure-to-bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass-forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

Interpenetration of polymeric microgels at ultrahigh densities

Soft particles such as polymeric microgels can form ultra-dense phases, where the average center-to-center distance as can be smaller than the initial unperturbed particle diameter σ0, due to their ability to interpenetrate and compress. However, despite of the effort devoted to microgels at ultrahigh densities, we know surprisingly little about their response to their environment at effective volume fractions ϕeff above close packing (ϕcp), and the existing information is often contradictory. Here we report direct measurements of the size and shape of poly(N-isopropylacrylamide) microgels at concentrations below and above ϕcp using the zero average contrast method in small-angle neutron scattering. We complement these experiments with measurements of the average interparticle distances using small-angle x-ray scattering, and a determination of the glass transition using dynamic light scattering. This allows us to unambiguously decouple interaction effects from density-dependent variations of the particle size and shape at all values of ϕeff. We demonstrate that the microgels used in this study significantly interpenetrate and thus change their size and shape only marginally even for ϕeff ≫ ϕcp, a finding that may require changes in the interpretation of a number of previously published studies on the structural and dynamic properties of dense soft particle systems.

Universal Long Ranged Correlations in Driven Binary Mixtures.

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

MPM with Frictional Contact for Application to Soft Particulate Materials

Soft particle materials are composed of discrete particles that can undergo large deformations without rupture. Most food products, many powders, colloidal pastes, vesicles and biological cells are soft particle systems. In order to model such materials, we present an efficient numerical approach combining an implicit formulation of the Material Point Method (MPM) and Contact Dynamics (CD) method. The MPM deals with bulk variables of an individual particle by discretizing it as a collection of material points, whereas the CD allows for the treatment of frictional contacts between particles. This model is applied for the simulation of the uniaxial compression of 2D soft-particle packings. The compaction is a nonlinear process in which new contacts are formed between particles and the contact areas increase. The change of particle shapes allows these materials to reach high packing fraction. We find that the contact specific surface, the orientation anisotropy and the aspect ratio of particles increase as a function of the packing fraction but at different rates. We also evidence the effect of friction, which favors strong stress chains and thus the elongation of particles, leading to larger values of the orientation anisotropy and the aspect ratio at a given level of packing fraction as compared to a frictionless particle packing.