arXiv subjects

Serafim Kalliadasis

Publications and source records attributed to Serafim Kalliadasis.

At least 37 records · Page 2Linked to original sources

arXiv2017

Nanoscale fluid structure of liquid-solid-vapour contact lines for a wide range of contact angles

We study the nanoscale behaviour of the density of a simple fluid in the vicinity of an equilibrium contact line for a wide range of Young contact angles between 40 and 135 degrees. Cuts of the density profile at various positions along the contact line are presented, unravelling the apparent step-wise increase of the film height profile observed in contour plots of the density. The density profile is employed to compute the normal pressure acting on the substrate along the contact line. We observe that for the full range of contact angles, the maximal normal pressure cannot solely be predicted by the curvature of the adsorption film height, but is instead softened -- likely by the width of the liquid-vapour interface. Somewhat surprisingly however, the adsorption film height profile can be predicted to a very good accuracy by the Derjaguin-Frumkin disjoining pressure obtained from planar computations, as was first shown in [Nold et al., Phys. Fluids, 26, 072001, 2014] for contact angles less than 90 degrees, a result which here we show to be valid for the full range of contact angles. This suggests that while two-dimensional effects cannot be neglected for the computation of the normal pressure distribution along the substrate, one-dimensional planar computations of the Derjaguin-Frumkin disjoining pressure are sufficient to accurately predict the adsorption height profile.

physics.flu-dyn↗

arXiv2017

Pseudospectral methods for density functional theory in bounded and unbounded domains

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialized Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single- and multispecies hard-sphere and hard-disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules.

cs.CE↗

arXiv2017

Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.

cond-mat.stat-mech↗

arXiv2016

Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows

A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilizing the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent $n=3$ has been used, namely, $Π(h)\propto -1/h^{3}$, where $h$ is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent $n$. We focus on axisymmetric point-rupture solutions and show that pairs of solution branches merge as $n$ decreases, leading to a critical value $n_c \approx 1.485$ below which stable similarity solutions do not appear to exist. We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, $n_c^{\mathrm{plane}}\approx 1.5$. Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading oscillatory structures.

physics.flu-dyn↗

arXiv2016

Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions

Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig's projection-operator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary shape particles.

cond-mat.stat-mech↗

arXiv2015

A new framework for extracting coarse-grained models from time series with multiscale structure

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion.

math.ST↗

arXiv2014

A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid-gas diffuse-interface model; Navier-slip and two non-linear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of these contact angle conditions having a contact line velocity dependence); and the interface formation model is also considered. In certain parameter regimes it is shown that all of the models predict the same quasistatic droplet spreading behaviour.

physics.flu-dyn↗

arXiv2014

Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory

We examine the nanoscale behavior of an equilibrium three-phase contact line in the presence of long-ranged intermolecular forces by employing a statistical mechanics of fluids approach, namely density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. In particular, we compare the results for mean field effective Hamiltonians with disjoining pressures defined through (I) the adsorption isotherm for a planar liquid film, and (II) the normal force balance at the contact line. We find that the height profile obtained using (I) shows good agreement with the adsorption film thickness of the DFT-FMT equilibrium density profile in terms of maximal curvature and the behavior at large film heights. In contrast, we observe that while the height profile obtained by using (II) satisfies basic sum rules, it shows little agreement with the adsorption film thickness of the DFT results. The results are verified for contact angles of 20, 40 and 60 degrees.

physics.flu-dyn↗

arXiv2013

Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media

Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations [Schmuck et al., Proc. R. Soc. A 468:3705-3724, 2012.], we rigorously derive an effective macroscopic phase field formulation under the assumption of periodic flow and a sufficiently large Péclet number. As for classical convection-diffusion problems, we obtain systematically diffusion-dispersion relations (including Taylor-Aris-dispersion). Our results also provide a convenient analytical and computational framework to macroscopically track interfaces in porous media. In view of the well-known versatility of phase field models, our study proposes a promising model for many engineering and scientific applications such as multiphase flows in porous media, microfluidics, and fuel cells.

math-ph↗

arXiv2013

Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit

We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such free energies in homogeneous environments found a broad interest over the last decades and hence is now widely accepted and applied in both science and engineering. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we present a general formal derivation of upscaled phase field equations for arbitrary free energy densities and give a rigorous justification by error estimates for a broad class of polynomial free energies. The error between the effective macroscopic solution of the new upscaled formulation and the solution of the microscopic phase field problem is of order $ε^1/2$ for a material given characteristic heterogeneity $ε$. Our new, effective, and reliable macroscopic porous media formulation of general phase field equations opens new modelling directions and computational perspectives for interfacial transport in strongly heterogeneous environments.

physics.chem-ph↗

arXiv2013

The contact line behaviour of solid-liquid-gas diffuse-interface models

A solid-liquid-gas moving contact line is considered through a diffuse-interface model with the classical boundary condition of no-slip at the solid surface. Examination of the asymptotic behaviour as the contact line is approached shows that the relaxation of the classical model of a sharp liquid-gas interface, whilst retaining the no-slip condition, resolves the stress and pressure singularities associated with the moving contact line problem while the fluid velocity is well defined (not multi-valued). The moving contact line behaviour is analysed for a general problem relevant for any density dependent dynamic viscosity and volume viscosity, and for general microscopic contact angle and double well free-energy forms. Away from the contact line, analysis of the diffuse-interface model shows that the Navier--Stokes equations and classical interfacial boundary conditions are obtained at leading order in the sharp-interface limit, justifying the creeping flow problem imposed in an intermediate region in the seminal work of Seppecher [Int. J. Eng. Sci. 34, 977--992 (1996)]. Corrections to Seppecher's work are given, as an incorrect solution form was originally used.

physics.flu-dyn↗

arXiv2013

Wetting on a spherical wall: influence of liquid-gas interfacial properties

We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first reexamine the wetting properties of the model in the zero-curvature limit, i.e., for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharp-kink approximation (SKA). We obtain very good agreement with a mean-field density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the so-called soft-interface approximation (SIA) originally formulated by Napiórkowski and Dietrich [Phys. Rev. B 34, 6469 (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, it turns out that the agreement between SKA and our DFT is only qualitative. We then show that the quantitative discrepancy between the two is due to the overestimation of the liquid-gas surface tension within SKA. On the other hand, by relaxing the assumption of a sharp interface, with, e.g., a simple smoothing of the density profile there, markedly improves the predictive capability of the theory, making it quantitative and showing that the liquid-gas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected mean-field critical exponent of the liquid-gas surface tension.

cond-mat.stat-mech↗

arXiv2013

Rigorous coherent-structure theory for falling liquid films: Viscous dispersion effects on bound-state formation and self-organization

We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residuals technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a rigorous coherent-structure theory, we are able to theoretically predict the pulse-separation distances for which bound states are formed. Viscous dispersion affects the distances at which bound states are observed. We show that the theory is in very good agreement with computations of the second-order model. We also demonstrate that the presence of bound states allows the film free surface to reach a self-organized state that can be statistically described in terms of a gas of solitary waves separated by a typical mean distance and characterized by a typical density.

physics.flu-dyn↗

arXiv2013

On the moving contact line singularity: Asymptotics of a diffuse-interface model

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.

physics.flu-dyn↗

arXiv2013

New and general framework for adsorption processes on dynamic interfaces

We introduce a new and general continuum thermodynamic framework for the mathematical analysis and computation of adsorption on dynamic interfaces. To the best of our knowledge, there is no formulation available that accounts for the coupled dynamics of interfaces and densities of adsorbants. Our framework leads to analytic adsorption isotherms which also take the interfacial geometry fully into account. We demonstrate the utility and physical consistency of our framework with a new computational multi-level discretization strategy. In the computations, we recover the experimentally observed feature that the adsorption of particles minimizes the interfacial tension.

physics.flu-dyn↗

arXiv2013

Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation describing the dynamics on the longer diffusive time scale, i.e. in a homogenization framework. We examine the case where both the drift and the diffusion coefficients in the effective dynamics are space-dependent and depend on multiple unknown parameters. It is known that classical estimators, such as Maximum Likelihood and Quadratic Variation of the Path Estimators, fail to obtain reasonable estimates for parameters in the effective dynamics when based on observations of the underlying multiscale diffusion. We propose a novel algorithm for estimating both the drift and diffusion coefficients in the effective dynamics based on a semi-parametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the algorithm performs well when applied to data from a multiscale diffusion. These examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.

math.ST↗

arXiv2013

Geometry-induced phase transition in fluids: capillary prewetting

We report a new first-order phase transition preceding capillary condensation and corresponding to the discontinuous formation of a curved liquid meniscus. Using a mean-field microscopic approach based on the density functional theory we compute the complete phase diagram of a prototypical two-dimensional system exhibiting capillary condensation, namely that of a fluid with long-ranged dispersion intermolecular forces which is spatially confined by a substrate forming a semi-infinite rectangular pore exerting long-ranged dispersion forces on the fluid. In the T-mu plane the phase line of the new transition is tangential to the capillary condensation line at the capillary wetting temperature, Tcw. The surface phase behavior of the system maps to planar wetting with the phase line of the new transition, termed capillary prewetting, mapping to the planar prewetting line. If capillary condensation is approached isothermally with T>Tcw, the meniscus forms at the capping wall and unbinds continuously, making capillary condensation a second-order phenomenon. We compute the corresponding critical exponent for the divergence of adsorption.

cond-mat.soft↗

arXiv2012

Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the non-equilibrium properties of the system. We derive a general dynamical density functional theory (DDFT) which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing DDFTs and a Navier-Stokes-like equation with additional non-local terms.

cond-mat.stat-mech↗