Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method

A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions is presented. Brownian motion of the particle is investigated by direct numerical simulation of the fluctuating hydrodynamic equations. In this framework a bidirectional coupling has been introduced between the fluctuating fluid and the solid object. The force governing the motion of the solid object is solely due to the surrounding fluid particles. Since a meshfree formulation is used, the method can be extended to many real applications involving complex fluid flows. A three-dimensional implementation is presented. In particular, we observe the short and long-time behaviour of the velocity autocorrelation function (VACF) of Brownian particles and compare it with the analytical expression. Moreover, the Stokes-Einstein relation is reproduced to ensure the correct long-time behaviour of Brownian dynamics.Comment: 24 pages, 2 figure

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

Microscopic origins of shear stress in dense fluid-grain mixtures

A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere-sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique. Series of simulations in which some of the coupling terms are neglected highlight the role of the poromechanical coupling in the transient regimes. They also reveal that the shear component of the lubrication forces, though frequently neglected in the literature, has a dominant effect in the volume changes. On the other hand, the effects of lubrication torques are much less significant. The bulk shear stress is decomposed into contact stress and hydrodynamic stress terms whose dependency on a dimensionless shear rate - the so called viscous number $I_v$ - are examined. Both contributions are increasing functions of $I_v$, contacts contribution dominates at low viscous number ($I_v$ 0.15, consistently with a phenomenological law infered by other authors. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared immersed granular media in which pore pressure feedback plays a key role (triggering of avalanches, liquefaction).Comment: to appear in Granular Matte

Angle of repose and segregation in cohesive granular matter

We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid is small and it forms liquid bridges between particles, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two dimensional silo through the transparent glass side walls. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value that depends on the size of the particles. We systematically study the effect of viscosity by using water-glycerol mixtures to vary it over at least three orders of magnitude while keeping the surface tension almost constant. Besides surface tension, the viscosity of the fluid is observed to have an effect on the angle of repose and the extent of segregation. In case of bidisperse particles, segregation is observed to decrease and finally saturate depending on the size ratio of the particles and the viscosity of the fluid. The sharp initial change and the subsequent saturation in the extent of segregation and angle of repose occurs over similar volume fraction of the fluid. In the second series of experiments, particles are poured into a container filled with a fluid. Although the angle of repose is observed to be unchanged, segregation is observed to decrease with an increase in the viscosity of the fluid.Comment: 9 pages, 12 figure

Collective behavior of colloids due to critical Casimir interactions

If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. As a result effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the CCFs provide the possibility for an active control over the assembly of colloids. This has triggered a recent surge of experimental and theoretical interest in these phenomena. We present an overview of current research activities in this area. Various experiments demonstrate the occurrence of thermally reversible self-assembly or aggregation or even equilibrium phase transitions of colloids in the mixed phase below the lower consolute points of binary solvents. We discuss the status of the theoretical description of these phenomena, in particular the validity of a description in terms of effective, one-component colloidal systems and the necessity of a full treatment of a ternary solvent-colloid mixture. We suggest perspectives on the directions towards which future research in this field might develop.Comment: review, 88 pages, 19 figure

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.Comment: 16 pages, 4 figure

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.Comment: 30 pages, 17 figure

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a non-zero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.Comment: 28 pages, 8 figure