Publications
215 results found
Durán-Olivencia MA, Goddard BD, Kalliadasis S, 2016, Dynamical Density Functional Theory for Orientable Colloids Including Inertia and Hydrodynamic Interactions, Journal of Statistical Physics, Vol: 164, Pages: 785-809, ISSN: 1572-9613
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.
Pradas M, Savva N, Benziger JB, et al., 2016, The dynamics of fattening and thinning 2D sessile droplets., Langmuir, Vol: 32, Pages: 4736-4745, ISSN: 0743-7463
We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow-outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet moves on a flat substrate with a periodic chemical pattern. We find that the droplet undergoes a stick-slip motion as the volume is increased (fattening droplet) which can be monitored by tracking the droplet contact points. If we then switch over to outflow conditions (thinning droplet) the droplet follows a different path (i.e. the distance of the droplet midpoint from the pore location evolves differently) giving rise to a hysteretic behavior. By means of geometrical arguments we are able to theoretically construct the full bifurcation diagram of the droplet equilibria (positions and droplet shapes) as the droplet volume is changed, finding excellent agreement with time-dependent computations of our diffuse-interface model.
Denner F, Pradas M, Charogiannis A, et al., 2016, Self-similarity of solitary waves on inertia-dominated falling liquid films, Physical Review E, Vol: 93, ISSN: 1539-3755
We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20–120 and surface tension coefficients σ=0.0512–0.072Nm−1 on substrates with inclination angles β=19∘–90∘. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.
Schmuck M, Kalliadasis S, 2016, General framework for adsorption processes on dynamic interfaces, Journal of Physics A-Mathematical and Theoretical, Vol: 49, ISSN: 1751-8121
We propose a novel and general variational framework modelling particleadsorption mechanisms on evolving immiscible fluid interfaces. A by-productof our thermodynamic approach is that we systematically obtain analyticadsorption isotherms for given equilibrium interfacial geometries. We validatecomputationally our mathematical methodology by demonstrating the fundamentalproperties of decreasing interfacial free energies by increasing interfacialparticle densities and of decreasing surface pressure with increasingsurface area.
Krumscheid S, Pradas M, Pavliotis GA, et al., 2015, Data-driven coarse graining in action: Modeling and prediction of complex systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 2470-0045
Gomes SN, Pradas M, Kalliadasis S, et al., 2015, Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol: 92, ISSN: 1539-3755
We present an alternative methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones or bound states), and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.
Charogiannis A, Markides CN, Denner F, et al., 2015, A simultaneous application of PLIF-PIV-PTV for the detailed experimental study of the hydrodynamic characteristics of thin film flows, 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2015)
Nold A, Sibley DN, Goddard BD, et al., 2015, Nanoscale Fluid Structure of Liquid-solid-vapour Contact Lines for a Wide Range of Contact Angles, Mathematical Modelling of Natural Phenomena, Vol: 10, Pages: 111-125, ISSN: 0973-5348
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 θY ∈ [ 40°,135° ]. 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 θY< 90°, 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.
Yatsyshin P, Savva N, Kalliadasis S, 2015, Density functional study of condensation in capped capillaries., Journal of Physics - Condensed Matter, Vol: 27, ISSN: 0953-8984
We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at [Formula: see text]) or continuous (at [Formula: see text]), where [Formula: see text] is the capillary wetting temperature. At [Formula: see text], the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.
Kalliadasis S, Krumscheid S, Pavliotis GA, 2015, A new framework for extracting coarse-grained models from time series with multiscale structure, Journal of Computational Physics, Vol: 296, Pages: 314-328, ISSN: 1090-2716
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.
Gotoda H, Pradas M, Kalliadasis S, 2015, Nonlinear Forecasting of the Generalized Kuramoto-Sivashinsky Equation, International Journal of Bifurcation and Chaos, Vol: 25, ISSN: 1793-6551
The emergence of pattern formation and chaotic dynamics is studied in the one-dimensional (1D) generalized Kuramoto–Sivashinsky (gKS) equation by means of a time-series analysis, in particular, a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases that the dynamical state of the gKS solution undergoes a transition from high-dimensional chaos to periodic pulsed oscillations through low-dimensional deterministic chaos while increasing the control parameter of the system. Our results demonstrate that the proposed nonlinear forecasting methodology allows to elucidate the dynamics of the system in terms of its predictability properties.
Schmuck M, Pradas M, Pavliotis GA, et al., 2015, A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 80, Pages: 273-301, ISSN: 0272-4960
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- Citations: 12
Lin T-S, Pradas M, Kalliadasis S, et al., 2015, Coherent structures in nonlocal dispersive active-dissipative systems, SIAM Journal on Applied Mathematics, Vol: 75, Pages: 538-563, ISSN: 1095-712X
We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto--Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto--Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103--2111]), we show that sufficiently strong dispersion regularizes the chaotic dynamics of the KS equation, and the solutions evolve into arrays of interacting pulses that can form bound states. We analyze the asymptotic characteristics of such pulses and show that their tails tend to zero algebraically but not exponentially, as for the local gKS equation. Since the Shilnikov-type approach is not applicable for analyzing bound states in nonlocal equations, we develop a weak-interaction theory and show that the standard first-neighbor approximation is no longer applicable. It is then essential to take into account long-range interactions due to the algebraic decay of the tails of the pulses. In addition, we find that the number of possible bound states for fixed parameter values is always finite, and we determine when there is long-range attractive or repulsive force between the pulses. Finally, we explain the regularizing effect of dispersion by showing that, as dispersion is increased, the pulses generally undergo a transition from absolute to convective instability. We also find that for some nonlocal operators, increasing the strength of the stabilizing/destabilizing term can have a regularizing/deregularizing effect on the dynamics.
Yatsyshin P, Savva N, Kalliadasis S, 2015, Wetting of prototypical one- and two-dimensional systems: Thermodynamics and density functional theory, JOURNAL OF CHEMICAL PHYSICS, Vol: 142, ISSN: 0021-9606
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- Citations: 30
Sibley DN, Nold A, Kalliadasis S, 2015, The asymptotics of the moving contact line: cracking an old nut, Journal of Fluid Mechanics, Vol: 764, Pages: 445-462, ISSN: 1469-7645
Vellingiri R, Tseluiko D, Kalliadasis S, 2015, Absolute and convective instabilities in counter-current gas-liquid film flows, JOURNAL OF FLUID MECHANICS, Vol: 763, Pages: 166-201, ISSN: 0022-1120
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- Citations: 24
Savva N, Kalliadasis S, 2014, Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates, JOURNAL OF FLUID MECHANICS, Vol: 754, Pages: 515-549, ISSN: 0022-1120
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- Citations: 16
Schmuck M, Pavliotis GA, Kalliadasis S, 2014, Effective macroscopic interfacial transport equations in strongly heterogeneous environments for general homogeneous free energies, APPLIED MATHEMATICS LETTERS, Vol: 35, Pages: 12-17, ISSN: 0893-9659
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- Citations: 8
Sibley DN, Nold A, Savva N, et al., 2014, A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading, Journal of Engineering Mathematics
Roydhouse MD, Pradas M, Al-Rifai N, et al., 2014, Operating ranges of gas-liquid capillary microseparators: Experiments and theory, CHEMICAL ENGINEERING SCIENCE, Vol: 114, Pages: 30-39, ISSN: 0009-2509
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- Citations: 14
Nold A, Sibley DN, Goddard BD, et al., 2014, Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory, Physics of Fluids, Vol: 26
Pradas M, Tseluiko D, Ruyer-Quil C, et al., 2014, Pulse dynamics in a power-law falling film, JOURNAL OF FLUID MECHANICS, Vol: 747, Pages: 460-480, ISSN: 0022-1120
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- Citations: 9
Tseluiko D, Kalliadasis S, 2014, Weak interaction of solitary pulses in active dispersive-dissipative nonlinear media, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 79, Pages: 274-299, ISSN: 0272-4960
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- Citations: 20
Lin T-S, Tseluiko D, Kalliadasis S, 2014, Numerical study of a non-local weakly nonlinear model for a liquid film sheared by a turbulent gas, IUTAM Symposium on Nonlinear Interfacial Wave Phenomena from the Micro- to the Macro-Scale, Publisher: ELSEVIER SCIENCE BV, Pages: 98-109, ISSN: 2210-9838
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- Citations: 3
Schmuck M, Pradas M, Pavliotis GA, et al., 2013, Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media, Nonlinearity, Vol: 26, Pages: 3259-3277, ISSN: 0951-7715
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 2012 Proc. R. Soc. A 468 3705-24), 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 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. © 2013 IOP Publishing Ltd & London Mathematical Society.
Sibley DN, Nold A, Kalliadasis S, 2013, Unifying binary fluid diffuse-interface models in the sharp-interface limit, Journal of Fluid Mechanics, Vol: 736, Pages: 5-43
Vellingiri R, Tseluiko D, Savva N, et al., 2013, Dynamics of a liquid film sheared by a co-flowing turbulent gas, International Journal of Multiphase Flow, Vol: 56, Pages: 93-104, ISSN: 0301-9322
Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model. © 2013 Elsevier Ltd.
Sibley DN, Nold A, Savva N, et al., 2013, The contact line behaviour of solid-liquid-gas diffuse-interface models, Physics of Fluids, Vol: 25
Schmuck M, Pradas M, Kalliadasis S, et al., 2013, New Stochastic Mode Reduction Strategy for Dissipative Systems, PHYSICAL REVIEW LETTERS, Vol: 110, ISSN: 0031-9007
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- Citations: 12
Savva N, Kalliadasis S, 2013, Droplet motion on inclined heterogeneous substrates, JOURNAL OF FLUID MECHANICS, Vol: 725, Pages: 462-491, ISSN: 0022-1120
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- Citations: 57
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