Phase separation of a two-dimensional van der Waals fluid subject to a gravitational force is studied by numerical simulations based on lattice Boltzmann methods implemented with a finite difference scheme. A growth exponent alpha = 1 is measured in the direction of the external force.

In this article a nonnegative blind source separation technique, known as nonnegative matrix factorization, is applied to microdiffraction data in order to extract characteristic patterns and to determine their spatial distribution in tissue typing problems occurring in bone-tissue engineering. In contrast to other blind source separation methods, nonnegative matrix factorization only requires nonnegative constraints on the extracted sources and corresponding weights, which makes it suitable for the analysis of data occurring in a variety of applications. In particular, here nonnegative matrix factorization is hierarchically applied to two-dimensional meshes of X-ray diffraction data measured in bone samples with implanted tissue. Such data are characterized by nonnegative profiles and their analysis provides significant information about the structure of possibly new deposited bone tissue. A simulation and real data studies show that the proposed method is able to retrieve the patterns of interest and to provide a reliable and accurate segmentation of the given X-ray diffraction data.

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle, and depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number. (C) 2015 AIP Publishing LLC.

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 x 6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca greater than or similar to 0.2.

A deep understanding of the dynamics and rheology ofsuspensions of vesicles, cells, and capsules is relevant for differentapplications, ranging from soft glasses to blood flow [1]. I willpresent the study of suspensions of fluid vesicles by acombination of molecular dynamics and mesoscalehydrodynamics simulations (multi-particle collision dynamics) intwo dimensions [2], pointing out the big potential of thenumerical method to address problems in soft matter. The flowbehavior is studied as a function of the shear rate, the volumefraction of vesicles, and the viscosity ratio between inside andoutside fluids. Results are obtained for the interactions of twovesicles, the intrinsic viscosity of the suspension, and the cell-freelayer near the walls [3-4].[1] D. Barthes-Biesel, Annu. Rev. Fluid Mech. 48, 25 (2016)[2] R. Finken, A. Lamura, U. Seifert, and G. Gompper, Eur. Phys. J. E25, 309 (2008)[3] A. Lamura and G. Gompper, EPL 102, 28004 (2013)[4] A. Lamura and G. Gompper, Procedia IUTAM 16, 3 (2015)

The dynamics and rheology of suspensions of fluid vesicles or red blood cells is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip walls, which are driven externally to generate a shear flow with shear rate (gamma) over dot. The flow behavior is studied as a function of (gamma) over dot, the volume fraction of vesicles, and the viscosity contrast between inside and outside fluids. Results are obtained for the encounter and interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

We analyze the dynamics of a two-dimensional system of interacting active dumbbells. We characterize the mean-square displacement, linear response function, and deviation from the equilibrium fluctuation-dissipation theorem as a function of activity strength, packing fraction, and temperature for parameters such that the system is in its homogeneous phase. While the diffusion constant in the last diffusive regime naturally increases with activity and decreases with packing fraction, we exhibit an intriguing nonmonotonic dependence on the activity of the ratio between the finite-density and the single-particle diffusion constants. At fixed packing fraction, the time-integrated linear response function depends nonmonotonically on activity strength. The effective temperature extracted from the ratio between the integrated linear response and the mean-square displacement in the last diffusive regime is always higher than the ambient temperature, increases with increasing activity, and, for small active force, monotonically increases with density while for sufficiently high activity it first increases and next decreases with the packing fraction. We ascribe this peculiar effect to the existence of finite-size clusters for sufficiently high activity and density at the fixed (low) temperatures at which we worked. The crossover occurs at lower activity or density the lower the external temperature. The finite-density effective temperature is higher (lower) than the single dumbbell one below (above) a crossover value of the Péclet number.

We numerically study the behavior of self-propelled liquid droplets whose motion is triggered by a Marangoni-like flow. This latter is generated by variations of surfactant concentration which affect the droplet surface tension promoting its motion. In the present paper a model for droplets with a third amphiphilic component is adopted. The dynamics is described by Navier-Stokes and convection-diffusion equations, solved by the lattice Boltzmann method coupled with finite-difference schemes. We focus on two cases. First, the study of self-propulsion of an isolated droplet is carried on and, then, the interaction of two self-propelled droplets is investigated. In both cases, when the surfactant migrates towards the interface, a quadrupolar vortex of the velocity field forms inside the droplet and causes the motion. A weaker dipolar field emerges instead when the surfactant is mainly diluted in the bulk. The dynamics of two interacting droplets is more complex and strongly depends on their reciprocal distance. If, in a head-on collision, droplets are close enough, the velocity field initially attracts them until a motionless steady state is achieved. If the droplets are vertically shifted, the hydrodynamic field leads to an initial reciprocal attraction followed by a scattering along opposite directions. This hydrodynamic interaction acts on a separation of some droplet radii otherwise it becomes negligible and droplets motion is only driven by the Marangoni effect. Finally, if one of the droplets is passive, this latter is generally advected by the fluid flow generated by the active one.

Vesicles are involved in a vast variety of transport processes in living organisms. Additionally, they serve as a model for the dynamics of cell suspensions. Predicting the rheological properties of their suspensions is still an open question, as even the interaction of pairs is yet to be fully understood. Here we analyse the effect of a single vesicle, undergoing tank-treading motion, on its surrounding shear flow by studying the induced disturbance field delta(V) over right arrow, the difference between the velocity field in its presence and absence. The comparison between experiments and numerical simulations reveals an impressive agreement. Tracking ridges in the disturbance field magnitude landscape, we identify the principal directions along which the velocity difference field is analysed in the vesicle vicinity. The disturbance magnitude is found to be significant up to about 4 vesicle radii and can be described by a power law decay with the distance d from the vesicle parallel to delta(V) over right arrow parallel to proportional to d(-3/2). This is consistent with previous experimental results on the separation distance between two interacting vesicles under similar conditions, for which their dynamics is altered. This is an indication of vesicles long-range effect via the disturbance field and calls for the proper incorporation of long-range hydrodynamic interactions when attempting to derive rheological properties of vesicle suspensions. Copyright (C) EPLA, 2016

We investigate numerically, by a hybrid lattice Boltzmann method, the morphology and the dynamics of an emulsion made of a polar active gel, contractile or extensile, and an isotropic passive fluid. We focus on the case of a highly off-symmetric ratio between the active and passive components. In absence of any activity we observe an hexatic-ordered droplets phase, with some defects in the layout. We study how the morphology of the system is affected by activity both in the contractile and extensile case. In the extensile case a small amount of activity favors the elimination of defects in the array of droplets, while at higher activities, first aster-like rotating droplets appear, and then a disordered pattern occurs. In the contractile case, at sufficiently high values of activity, elongated structures are formed. Energy and enstrophy behavior mark the transitions between the different regimes.

In this paper the phase behavior and pattern formation in a sheared nonideal fluid under a periodic potential is studied. An isothermal two-dimensional formulation of a lattice Boltzmann scheme for a liquid-vapor system with the van der Waals equation of state is presented and validated. Shear is applied by moving walls and the periodic potential varies along the flow direction. A region of the parameter space, where in the absence of flow a striped phase with oscillating density is stable, will be considered. At low shear rates the periodic patterns are preserved and slightly distorted by the flow. At high shear rates the striped phase loses its stability and traveling waves on the interface between the liquid and vapor regions are observed. These waves spread over the whole system with wavelength only depending on the length of the system. Velocity field patterns, characterized by a single vortex, will also be shown.

Purpose - The purpose of this paper is to present numerical results about phase separation of binary fluid mixtures quenched by contact with cold walls. Design/methodology/approach - The thermal phase separation is simulated by using a hybrid lattice Boltzmann method that solves the continuity and the Navier-Stokes equations. The equations for energy and concentration are solved by using a finite-difference scheme. This approach provides a complete description of the thermo-hydrodynamic effects in the mixture. Findings - A rich variety of domain patterns are found depending on the viscosity and on the heat conductivity of the mixture. Ordered lamellar structures are observed at high viscosity while domains rounded in shape dominate the phase separation at low viscosity, where two scales characterize the growth of domains. Research limitations/implications - The present approach provides a numerical method that can be extended to other systems such as liquid-vapor or lamellar systems. Moreover, a three-dimensional study can give a complete picture of thermo-hydrodynamic effects. Originality/value - This paper provides a consistent thermodynamic theoretical framework for a binary fluid mixture and a numerically stable method to simulate them.

A systems of self-propelled dumbbells interacting by a Weeks-Chandler-Anderson potential is considered. At sufficiently low temperatures the system phase separates into a dense phase and a gas-like phase. The kinetics of the cluster formation and the growth law for the average cluster size are analyzed.

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high viscosity, different morphologies are observed by varying the thermal diffusivity. In the range of thermal diffusivities with domains growing parallel to the walls, temperature and phase separation fronts propagate toward the inner of the system with power-law behavior. At low viscosity hydrodynamics favors rounded shapes, and complex patterns with different length scales appear. Off-symmetrical systems behave similarly but with more ordered configurations.

Numerical simulations of vesicle suspensions are performed in two dimensions to study their dynamical and rheological properties.An hybrid method is adopted, which combines a mesoscopic approach for the solvent with a curvature-elasticity model for themembrane. Shear flow is induced by two counter-sliding parallel walls, which generate a linear flow profile. The flow behavioris studied for various vesicle concentrations and viscosity ratios between the internal and the external fluid. Both the intrinsicviscosity and the thickness of depletion layers near the walls are found to increase with increasing viscosity ratio.

The rheology and dynamics of suspensions of fluid vesicles is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip shearing walls. The flow behavior is studied as a function of the shear rate, the volume fraction of vesicles, and the viscosity ratio between inside and outside fluids. Results are obtained for the interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

The dynamics of a quasi two-dimensional isotropic droplet in a cholesteric liquid crystal medium under symmetric shear flow is studied by lattice Boltzmann simulations. We consider a geometry in which the flow direction is along the axis of the cholesteric, as this setup exhibits a significant viscoelastic response to external stress. We find that the dynamics depends on the magnitude of the shear rate, the anchoring strength of the liquid crystal at the droplet interface and the chirality. While low shear rate and weak interface anchoring the system shows a non-Newtonian behavior, a Newtonian-like response is observed at high shear rate and strong interface anchoring. This is investigated both by estimating the secondary flow profile, namely a flow emerging along the out-of-plane direction (absent in fully-Newtonian fluids, such as water) and by monitoring defect formation and dynamics, which significantly alter the rheological response of the system.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: the force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.

Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the convection-diffusion equation for the order parameter to a generalized Navier-Stokes equation. The dynamical equations are simulated by implementing a hybrid method based on a lattice Boltzmann algorithm coupled to finite difference schemes. Simulations show that the ordering process occurs with morphologies depending on the speed of the thermal fronts or, equivalently, on the value of the thermal conductivity xi. At large values of xi, as in instantaneous quenching, the system is frozen in entangled configurations at high viscosity while it consists of grains with well-ordered lamellae at low viscosity. By decreasing the value of xi, a regime with very ordered lamellae parallel to the thermal fronts is found. At very low values of xi the preferred orientation is perpendicular to the walls in d = 2, while perpendicular order is lost moving far from the walls in d = 3.