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cond-mat.soft

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preprint2016arXiv

Viscoelastic nematodynamics

Nematic liquid crystals exhibit both crystal-like and fluid-like features. In particular, the propagation of an acoustic wave shows an unexpected occurrence of some of the solid-like features at the hydrodynamic level, namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation. The non-Newtonian behavior of nematics also emerges from the frequency-dependent viscosity coefficients. To account for these phenomena, we put forward a viscoelastic model of nematic liquid crystals, and we extend our previous theory to fully include the combined effects of compressibility, anisotropic elasticity and dynamic relaxation, at any shear rate. The low-frequency limit agrees with the compressible Ericksen-Leslie theory, while at intermediate frequencies the model correctly captures the relaxation mechanisms underlying finite shear and bulk elastic moduli. We show that there are only four relaxation times allowed by the uniaxial symmetry.

preprint2016arXiv

Elasto-buoyant heavy spheres: a unique way to test non-linear elasticity

Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius $a$ in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth ($δ$) of the bead inside the softest gels as $δ\sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean model of elastic deformation, according to which the displacement fields must diverge, it is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly non-linear materials.

preprint2017arXiv

Interplay between viscosity and elasticity in freely expanding liquid sheets

We investigate the dynamics of freely expanding liquid sheets prepared with fluids with different rheological properties, (i) viscous fluids with a zero-shear viscosity $η_0$ in the range $(1-1000) \, \mathrm{mPa.s}$ and (ii) viscoelastic Maxwell fluids whose elastic modulus, $G_0$, characteristic relaxation time, $τ$, and zero-shear viscosity, $η_0=G_0 τ$, can be tuned over several orders of magnitude. The sheets are produced by impacting a drop of fluid on a small cylindrical solid target. For viscoelastic fluids, we show that, when $τ$ is shorter than the typical lifetime of the sheet ($\sim 10$ ms), the dynamics of the sheet is similar to that of Newtonian viscous liquids with equal zero-shear viscosity. In that case, for little viscous samples ($η_0 <\sim 30$ mPa.s), the maximal expansion of the sheet, $d_{\rm{max}}$, is independent of $η_0$, whereas for more viscous samples, $d_{\rm{max}}$ decreases as $η_0$ increases. We provide a simple model to account for the dependence of the maximal expansion of the sheet with the viscosity that is based on an energy balance between inertia, surface tension and viscous shear dissipation on the solid target, and which accounts well for o

preprint2016arXiv

V-T theory for the Self-Intermediate Scattering Function in a Monatomic Liquid

In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. Comparison of V-T and mode-coupling theories for the MSD and SISF

preprint2016arXiv

Probing the shear viscosity of an active nematic

In vitro reconstituted active systems, such as the ATP-driven microtubule bundle suspension developed by the Dogic group, provide a fertile testing ground for elucidating the phenomenology of active liquid crystalline states. Controlling such novel phases of matter crucially depends on our knowledge of their material and physical properties. In this letter, we show that the rheological properties of an active nematic film can be probed by varying its hydrodynamic coupling to a bounding oil layer. Using the motion of disclinations as intrinsic tracers of the flow field and a hydrodynamic model, we obtain an estimate for the as of now unknown shear viscosity of the nematic film. Knowing this now provides us with an additional handle for robust and precision tunable control of the emergent dynamics of active fluids.

preprint2016arXiv

Order-disorder transition in repulsive self-propelled particle systems

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the systems undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.

preprint2016arXiv

Negative pressure in shear thickening band of a dilatant fluid

We perform experiments and numerical simulations to investigate spatial distribution of pressure in a sheared dilatant fluid of the Taylor-Couette flow under a constant external shear stress. In a certain range of shear stress, the flow undergoes the shear thickening oscillation around 20 Hz. We find that, during the oscillation, a localized thickened band rotates around the axis with the flow. {Based upon experiments and numerical simulations, we show that a major part of the thickened band is under negative pressure even in the case of discontinuous shear thickening}, which indicates that the thickening is caused by Reynolds dilatancy; the dilatancy causes the negative pressure in interstitial fluid, which generates contact structure in the granular medium., then frictional resistance hinders rearrangement of the structure and solidifies the medium.

preprint2016arXiv

Discontinuous Thinning in Active Microrheology of Soft Complex Matter

Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the motion of an external probe in a host medium, which we approximate as structureless. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between probe and a sufficiently dense host medium.

preprint2016arXiv

Vertical dynamics of a horizontally-oscillating active object in a 2D granular medium

We use a DEM simulation and analytical considerations to study the dynamics of a self-energised object, modelled as a disc, oscillating horizontally within a two-dimesional bed of denser and smaller particles. We find that, for given material parameters, the immersed object (IO) may rise, sink or not change depth, depending on the oscillation amplitude and frequency, as well as on the initial depth. With time, the IO settles at a specific depth that depends on the oscillation parameters. We construct a phase diagram of this behaviour in the oscillation frequency and velocity amplitude variable space. We explain the observed rich behaviour by two competing effects: climbing on particles, which fill voids opening under the disc, and sinking due to bed fluidisation. We present a cavity model that allows us to derive analytically general results, which agree very well with the observations and explain quantitatively the phase diagram. Our specific analytical results are the following. (i) Derivation of a critical frequency, $f_c$, above which the IO cannot float up against gravity. We show that this frequency depends only on the gravitational acceleration and the IO size. (ii) Derivati

preprint2016arXiv

Modified Kedem-Katchalsky equations for osmosis through nano-pore

This work presents a modified Kedem-Katchalsky equations for osmosis through nano-pore. osmotic reflection coefficient of a solute was found to be chiefly affected by the entrance of the pore while filtration reflection coefficient can be affected by both the entrance and the internal structure of the pore. Using an analytical method, we get the quantitative relationship between osmotic reflection coefficient and the molecule size. The model is verified by comparing the theoretical results with the reported experimental data of aquaporin osmosis. Our work is expected to pave the way for a better understanding of osmosis in bio-system and to give us new ideas in designing new membranes with better performance.

preprint2016arXiv

A stabilized finite element formulation for liquid shells and its application to lipid bilayers

This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using $C^1$-continuous finite elements constructed from NURBS interpolation. Both displacement-based and mixed FE formulations are proposed. The latter is needed for area-incompressible material behavior, where penalty-type regularizations can lead to misleading results. In order to obtain quasi-static solutions, several numerical stabilization schemes are proposed based on either stiffness, viscosity or projection. Several numerical examples are considered in order to illustrate the accuracy and the capabilities of the proposed formulation, and to compare the different stabilization schemes. The presented formulation is capable of simulating non-trivial surface shapes associated with tube formation and protein-induced budding of lipid bilayers. In the latter case, the presented formulation yields non-axisymmetric solutions, which have not been observed in previous simulations. It is shown that those non-axisymmetric shapes are preferred over axisymmetric ones.

preprint2016arXiv

A fast platform for simulating flexible fiber suspensions applied to cell mechanics

We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular fiber assemblies. We use the non-local slender body theory to compute the fluid-structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multiple method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by the nonlinear Euler--Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic e

preprint2016arXiv

Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the cross-over mode between the bending and the slipping to a larger value. As the vesicle parameters approach toward the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.

preprint2016arXiv

Spinodal instabilities in polydisperse lyotropic nematics

Many lyotropic liquid crystals are composed of mesogens that display a considerable spread in size or shape affecting their material properties and thermodynamics via various demixing and multi-phase coexistence scenarios. Starting from a generalized Onsager theory we formulate a generic framework that enables locating spinodal polydispersities as well as identifying the nature of incipient size fractionation for arbitrary model potentials and size distributions. We apply our theory to nematic phases of both hard rods and disks whose main particle dimension is described by a unimodal log-normal distribution. We find that both rod-based and discotic nematics become unstable at a critical polydispersity of about 20 %. We also investigate the effect of doping nematic assemblies with a small fraction of large species and highlight their effect on the stability of the uniform nematic fluid. We find that while rod-based are only weakly affected by the presence of large species, doping discotic nematics with very large platelets leads to a remarkable suppression of the spinodal instabilities. This could open up routes towards controlling the mechanical properties of nematic materials by m

preprint2016arXiv

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are sparse. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macro

preprint2016arXiv

Generalized entropy theory of glass-formation in fully flexible polymer melts

The generalized entropy theory (GET) offers many insights into how molecular parameters influence polymer glass-formation. Given the fact that chain rigidity often plays a critical role in understanding the glass-formation of polymer materials, the GET was originally developed based on models of semiflexible chains. Consequently, all previous calculations within the GET considered polymers with some degree of chain rigidity. Motivated by unexpected results from computer simulations of fully flexible polymer melts concerning the dependence of thermodynamic and dynamic properties on the cohesive interaction strength ($ε$), the present paper employs the GET to explore the influence of $ε$ on glass-formation in models of polymer melts with a vanishing bending rigidity, i.e., fully flexible polymer melts. In accord with simulations, the GET for fully flexible polymer melts predicts that basic dimensionless thermodynamic properties (such as the thermal expansion coefficient and isothermal compressibility) are universal functions of the temperature scaled by $ε$ in the regime of low pressures. Similar scaling behavior is also found for the configurational entropy density in the GET for fu

preprint2016arXiv

Pattern-induced anchoring transitions in nematic liquid crystals

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross section sculpted on a chemically homogeneous substrate which favors local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal case, we observe a homeotropic to planar anchoring transition as the substrate roughness is increased. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

preprint2016arXiv

A variational treatment of material configurations with application to interface motion and microstructural evolution

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces in polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-

preprint2016arXiv

Freezing and melting line invariants of the Lennard-Jones system

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of the isomorph theory. First the freezing/melting lines for LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phase. Structure is probed by the radial distribution function and the structure factor and dynamics is probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties by reference to the isomorph theory explains why known single-phase melting criteria holds, e.g., the Hansen-Verlet and the Lindemann criterion, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from the isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.

preprint2017arXiv

From short-range repulsion to Hele-Shaw problem in a model of tumor growth

We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is challenging in terms of computational time. To overcome this problem, we aim at deriving the associated macroscopic dynamics leading here to a porous media type equation. As we are interested in the long time behavior of the dynamics, the macroscopic equation obtained through usual derivation method fails at providing the correct qualitative behavior (e.g. stationary states differ from the microscopic dynamics). We propose a modified version of the macroscopic equation introducing a density threshold for the repulsion. We numerically validate the new formulation by comparing the solutions of the micro- and macro- dynamics. Moreover, we study the asymptotic behavior of the dynamics as the repulsion between cells becomes singular (leading to non-overlapping constraints in the microscopic model). We manage to show formally that such an asymptotic limit leads to a Hele-Shaw type problem for the macroscopic dynamics. The macroscopic model derived in

preprint2015arXiv

Continuum Nanofluidics

This paper introduces the fundamental continuum theory governing momentum transport in isotropic nanofluidic flows. The theory is an extension to the classical Navier-Stokes equation, which includes coupling between translational and rotational degrees of freedom, as well as non-local response functions that incorporates spatial correlations. The continuum theory is compared with molecular dynamics simulation data for both relaxation processes and fluid flows showing excellent agreement on the nanometer length scale. We also present practical tools to estimate when the extended theory should be used.

preprint2016arXiv

Monte Carlo Simulation of Evaporation Driven Self-Assembly in Suspension of Colloidal Rods

The vertical drying of a colloidal film containing rod-like particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice and the rods were represented as linear $k$-mers (i.e., particles occupying $k$ adjacent sites). The initial state before drying was produced using a model of random sequential adsorption (RSA) with isotropic orientations of the $k$-mers (orientation of the $k$-mers along horizontal $x$ and vertical $y$ directions are equiprobable). In the RSA model, overlapping of the $k$-mers is forbidden. During the evaporation, an upper interface falls with a linear velocity of $u$ in the vertical direction and the $k$-mers undergo translation Brownian motion. The MC simulations were run at different initial concentrations, $p_i$, ($p_i \in [0, p_j]$, where $p_j$ is the jamming concentration), lengths of $k$-mers ($k \in [1, 12]$), and solvent evaporation rates, $u$. For completely dried films, the spatial distributions of $k$-mers and their electrical conductivities in both $x$ and $y$ directions were examined. Significant evaporation-driven self-assembly and orientation stratification of the $k$-mer

preprint2016arXiv

Exactly solvable model for self-assembly of hard core - soft shell particles at interfaces

A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of vertical segments separated by plateaus. The range of order depends strongly on the strength of attraction and on the density. Our results agree with experimental observations.

preprint2014arXiv

A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.

1027 works