Publications
215 results found
Charogiannis A, Denner F, Van Wachem B, et al., 2018, Experimental investigations of liquid falling films flowing under an inclined planar substrate, Physical Review Fluids, Vol: 3, ISSN: 2469-990X
We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles (β=−15∘, −30∘, and −45∘, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of Ka=13.1 and 330), and flow Reynolds numbers covering the range Re=0.6–193. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about 40mm symmetrically on either side the centerline of the film span (80mm in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number Ka(=13.1) flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid Ka(=330) flows, rivulets were observed typically above Re≈30, depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with in
Duran-Olivencia M, Yatsyshin P, Kalliadasis S, et al., 2018, General framework for nonclassical nucleation, New Journal of Physics, Vol: 20, ISSN: 1367-2630
A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new theoretical tools to explain the occurrence and nature of these ubiquitous intermediate phases. Here we outline a unified and self-consistent theoretical framework to describe both classical and nonclassical nucleation. Our framework provides a detailed explanation of the whole multistage nucleation pathway showing in particular that the pathway involves a single energy barrier and it passes through a dense phase, starting from a low-density initial phase, before reaching the final stable state. Moreover, we demonstrate that the kinetics of matter inside subcritical clusters favors the formation of nucleation clusters with an intermediate density, i.e. nucleation precursors. Remarkably, these nucleation precursors are not associated with a local minimum of the thermodynamic potential, as commonly assumed in previous phenomenological approaches. On the contrary, we find that they emerge due to the competition between thermodynamics and kinetics of cluster formation. Thus, the mechanism uncovered for the formation of intermediate phases can be used to explain recently reported experimental findings in crystallization: up to now such phases were assumed a consequence of some complex energy landscape with multiple energy minima. Using fundamental concepts from kinetics and thermodynamics, we provide a satisfactory explanation for the so-called nonclassical nucleation pathways observed in experiments.
Braga C, Smith E, Nold A, et al., 2018, The pressure tensor across a liquid-vapour interface, Journal of Chemical Physics, Vol: 149, ISSN: 0021-9606
Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff and, later, Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17(3), 338 (1949); J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood’s argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F. P. Buff et al., Phys. Rev. Lett. 15, 621–623 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.
Yatsyshin P, Duran-Olivencia MA, Kalliadasis S, 2018, Microscopic aspects of wetting using classical density-functional theory., Journal of Physics: Condensed Matter, Vol: 30, ISSN: 0953-8984
Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions brings about an entire ``zoo" of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid-gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid-gas interface is already highly complex and non-trivial.
Yatsyshin P, Kalliadasis S, 2018, Classical density-functional theory studies of fluid adsorption on nanopatterned planar surfaces, Workshop on Coupled Mathematical Models for Physical and Nanoscale Systems and their Applications, Publisher: Springer, Pages: 171-185
This contribution is based on our talk at the BIRS Workshop on “Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications”. Our aim here is to summarize and bring together recent advances in wetting of nanostructured surfaces, using classical density-functional theory (DFT). Classical DFT is an ab initio theoretical-computational framework with a firm foundation in statistical physics allowing us to systematically account for the fluid spatial inhomogeneity, as well as for the non-localities of intermolecular fluid-fluid and fluid-substrate interactions. The cornerstone of classical DFT, is to express the grand free energy of the system as a functional of its one-body density, thus generating a hierarchy of N-body correlation functions. Unconstrained minimization of a properly approximated free-energy functional with respect to the one-body density then yields the basic DFT equation. And since most macroscopic quantities of interest can often be cast as averages over a one-body distribution, this equation provides a very useful and accessible computational tool. Indeed, there has been a rapid growth of classical DFT applications across a broad variety of fields, including phase transitions in solutions of macromolecules, interfacial phenomena, and even nucleation. Here we attempt to give a taste of what simple equilibrium DFT models look like, and what they can and cannot capture, as far as wetting on chemically heterogeneous substrates is concerned. We review recent progress in the understanding of planar prewetting and interface unbending on such substrates and compute substrate-fluid interfaces and wetting isotherms.
Radhakrishnan ANP, Pradas M, Kalliadasis S, et al., 2018, Nonlinear dynamics of gas-liquid separation in a capillary microseparator, ASME 2018 16th International Conference on Nanochannels, Microchannels, and Minichannels (ICNMM2018), Publisher: ASME, Pages: ICNMM2018-7613-ICNMM2018-7613
Copyright © 2018 ASME. Micro-engineered devices (MED) are seeing a significant growth in performing separation processes1. Such devices have been implemented in a range of applications from chemical catalytic reactors to product purification systems like microdistillation. One of the biggest advantages of these devices is the dominance of capillarity and interfacial tension forces. A field where MEDs have been used is in gas-liquid separations. These are encountered, for example, after a chemical reactor, where a gaseous component being produced needs immediate removal from the reactor, because it can affect subsequent reactions. The gaseous phase can be effectively removed using an MED with an array of microcapillaries. Phase-separation can then be brought about in a controlled manner along these capillary structures. For a device made from a hydrophilic material (e.g. Si or glass), the wetted phase (e.g. water) flows through the capillaries, while the non-wetted dispersed phase (e.g. gas) is prevented from entering the capillaries, due to capillary pressure. Separation of liquid-liquid flows can also be achieved via this approach. However, the underlying mechanism of phase separation is far from being fully understood. The pressure at which the gas phase enters the capillaries (gas-to-liquid breakthrough) can be estimated from the Young-Laplace equation, governed by the surface tension (γ) of the wetted phase, capillary width (d) and height (h), and the interface equilibrium contact angle (θeq). Similarly, the liquid-to-gas breakthrough pressure (i.e. the point at which complete liquid separation ceases and liquid exits through the gas outlet) can be estimated from the pressure drop across the capillaries via the Hagen-Poiseuille (HP) equation. Several groups reported deviations from these estimates and therefore, included various parameters to account for the deviations. These parameters usually account for (i) flow of wetted phase through 'n' ca
Yatsyshin P, Parry AO, Rascon C, et al., 2018, Wetting of a plane with a narrow solvophobic stripe, Molecular Physics, Vol: 116, Pages: 1990-1997, ISSN: 0026-8976
We present a numerical study of a simple density functional theory model of fluidadsorption occurring on a planar wall decorated with a narrow deep stripe of aweaker adsorbing (relatively solvophobic) material, where wall-fluid and fluid-fluidintermolecular forces are considered to be dispersive. Both the stripe and outersubstrate exhibit first-order wetting transitions with the wetting temperature ofthe stripe lying above that of the outer material. This geometry leads to a richphase diagram due to the interplay between the pre-wetting transition of the outersubstrate and an unbending transition corresponding to the local evaporation ofliquid near the stripe. Depending on the width of the stripe the line of unbendingtransitions merges with the pre-wetting line inducing a two-dimensional wettingtransition occurring across the substrate. In turn, this leads to the continuous pre-drying of the thick pre-wetting film as the pre-wetting line is approached from above.Interestingly we find that the merging of the unbending and pre-wetting lines occurseven for the widest stripes considered. This contrasts markedly with the scenariowhere the outer material has the higher wetting temperature, for which the mergingof the unbending and pre-wetting lines only occurs for very narrow stripes.
Nold A, González MacDowell L, Sibley DN, et al., 2018, The vicinity of an equilibrium three-phase contact line using density-functional theory: density profiles normal to the fluid interface, Molecular Physics, Vol: 116, Pages: 2239-2243, ISSN: 0026-8976
The paper by Nold et al. [Phys. Fluids 26 (7), 072001 (2014)] examined density profiles and the micro-scale structure of an equilibrium three-phase (liquid–vapour–solid) contact line in the immediate vicinity of the wall using elements from the statistical mechanics of classical fluids, namely density-functional theory. The present research note, building on the above work, further contributes to our understanding of the nanoscale structure of a contact line by quantifying the strong dependence of the liquid–vapour density profile on the normal distance to the interface, when compared to the dependence on the vertical distance to the substrate. A recent study by Benet et al. [J. Phys. Chem. C 118 (38), 22079 (2014)] has shown that this could explain the emergence of a film-height-dependent surface tension close to the wall, with implications for the Frumkin–Derjaguin theory.
Ravipati S, Aymard B, Kalliadasis S, et al., 2018, On the equilibrium contact angle of sessile liquid drops from molecular dynamics, Journal of Chemical Physics, Vol: 148, ISSN: 0021-9606
We present a new methodology to estimate the contact angles of sessile drops from molec-ular simulations, by using the Gaussian convolution method of Willard and Chandler (J.Phys. Chem. B, Vol. 114, 1954-1958, 2010) to calculate the coarse-grained density fromatomic coordinates. The iso-density contour with average coarse-grained density valueequal to half of the bulk liquid density is identified as the average liquid-vapor (LV) inter-face. Angles between the unit normal vectors to the average LV interface and unit normalvector to the solid surface, as a function of the distance normal to the solid surface, arecalculated. The cosines of these angles are extrapolated to the three-phase contact line toestimate the sessile drop contact angle. The proposed methodology, which is relativelyeasy to implement, is systematically applied to three systems: (i) a Lennard-Jones (LJ)drop on a featureless LJ9-3surface; (ii) an SPC/E water drop on a featureless LJ9-3sur-face; and (iii) an SPC/E water drop on a graphite surface. The sessile drop contact anglesestimated with our methodology for the first two systems, are shown to be in good agree-ment with the angles predicted from Young’s equation. The interfacial tensions requiredfor this equation are computed by employing the test-area perturbation method for the cor-responding planar interfaces. Our findings suggest that the widely adopted spherical-capapproximation should be used with caution, as it could take a long time for a sessile dropto relax to a spherical shape, of the order of100ns, especially for water molecules initiatedin a lattice configuration on a solid surface. But even though a water drop can take a longtime to reach the spherical shape, we find that the contact angle is well established muchfaster and the drop evolves towards the spherical shape following a constant-contact-anglerelaxation dynamics. Making use of this observation, our methodology allows a good es-timation of the sessile drop
Charogiannis A, Denner F, Van Wachem BGM, et al., 2018, Heat tranfer phenomena in falling liquid films: A synergistic experimental and computational study, International Heat Transfer Conference
We employ planar laser-induced fluorescence (PLIF), particle tracking velocimetry (PTV) and infrared thermography (IR) towards the detailed investigation of the flow and heat transfer phenomena underlying harmonically-excited, gravity-driven film flows falling over an inclined, electrically-heated substrate. PLIF is used to generate space and time-resolved film-height measurements, PTV to retrieve two-dimensional (2-D) velocity-field information, and IR to recover the temperature of the film free-surface. The experiments are complemented by direct numerical simulations (DNSs) that provide additional information on the liquid temperature, viscosity and velocity distributions between the flow inlet and the location along the axial direction of the flow where optical measurements are conducted. By adoption of this synergistic approach, we recover results on the spatiotemporal evolution of the flow and temperature fields, and link the variation of the gas-liquid interface temperature along the waves to the variation of the local film-height, flow-rate and streamwise and cross-stream velocity components. Despite the intermittent observation of localized hotspots in the experiments, which constitute precursors to the formation of thermal rivulets, the mean wall-temperature, bulk liquid-temperature and gas-liquid interface temperature display clear trends with respect to the mean film-thickness, which largely dictates the heat transfer performance of the examined film flows.
Zheng Z, Fontelos MA, Shin S, et al., 2018, Healing capillary films., Journal of Fluid Mechanics, Vol: 838, Pages: 404-434, ISSN: 0022-1120
Consider the dynamics of a healing film driven by surface tension, that is, the inward spreading process of a liquid film to fill a hole. The film is modelled using the lubrication (or thin-film) approximation, which results in a fourth-order nonlinear partial differential equation. We obtain a self-similar solution describing the early-time relaxation of an initial step-function condition and a family of self-similar solutions governing the finite-time healing. The similarity exponent of this family of solutionsis not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partialdifferential equation are also performed. We compare the self-similar profiles and exponents, obtained by matching the estimated prewetting film thickness, with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.
Denner F, Charogiannis A, Pradas M, et al., 2018, Solitary waves on falling liquid films in the inertia-dominated regime, Journal of Fluid Mechanics, Vol: 837, Pages: 491-519, ISSN: 0022-1120
We offer new insights and results on the hydrodynamics of solitary waves on inertiadominatedfalling liquid films using a combination of experimental measurements,direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNSare shown to be in very good agreement with experimental measurements in termsof the main wave characteristics and velocity profiles over the entire range ofinvestigated Reynolds numbers. And, surprisingly, the LD model is found to predictaccurately the film height even for inertia-dominated films with high Reynoldsnumbers. Based on a detailed analysis of the flow field within the liquid film, thehydrodynamic mechanism responsible for a constant, or even reducing, maximumfilm height when the Reynolds number increases above a critical value is identified,and reasons why no flow reversal is observed underneath the wave trough above acritical Reynolds number are proposed. The saturation of the maximum film heightis shown to be linked to a reduced effective inertia acting on the solitary waves asa result of flow recirculation in the main wave hump and in the moving frame ofreference. Nevertheless, the velocity profile at the crest of the solitary waves remainsparabolic and self-similar even after the onset of flow recirculation. The upper limitof the Reynolds number with respect to flow reversal is primarily the result ofsteeper solitary waves at high Reynolds numbers, which leads to larger streamwisepressure gradients that counter flow reversal. Our results should be of interest in theoptimisation of the heat and mass transport characteristics of falling liquid films andcan also serve as a benchmark for future model development.
Gotoda H, Pradas M, Kalliadasis S, 2017, Chaotic versus stochastic behavior in active-dissipative nonlinear systems, Physical Review Fluids, Vol: 2, ISSN: 2469-990X
We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise.
Charogiannis A, Denner F, van Wachem BGM, et al., 2017, Statistical characteristics of falling-film flows: A synergistic approach at the crossroads of direct numerical simulations and experiments, Physical Review Fluids, Vol: 2, ISSN: 2469-990X
We scrutinize the statistical characteristics of liquid films flowing over an inclined planar surface based on film height and velocity measurements that are recovered simultaneously by application of planar laser-induced fluorescence (PLIF) and particle tracking velocimetry (PTV), respectively. Our experiments are complemented by direct numerical simulations (DNSs) of liquid films simulated for different conditions so as to expand the parameter space of our investigation. Our statistical analysis builds upon a Reynolds-like decomposition of the time-varying flow rate that was presented in our previous research effort on falling films in [Charogiannis et al., Phys. Rev. Fluids 2, 014002 (2017)], and which reveals that the dimensionless ratio of the unsteady term to the mean flow rate increases linearly with the product of the coefficients of variation of the film height and bulk velocity, as well as with the ratio of the Nusselt height to the mean film height, both at the same upstream PLIF/PTV measurement location. Based on relations that are derived to describe these results, a methodology for predicting the mass-transfer capability (through the mean and standard deviation of the bulk flow speed) of these flows is developed in terms of the mean and standard deviation of the film thickness and the mean flow rate, which are considerably easier to obtain experimentally than velocity profiles. The errors associated with these predictions are estimated at ≈1.5% and 8% respectively in the experiments and at <1% and <2% respectively in the DNSs. Beyond the generation of these relations for the prediction of important film flow characteristics based on simple flow information, the data provided can be used to design improved heat- and mass-transfer equipment reactors or other process operation units which exploit film flows, but also to develop and validate multiphase flow models in other physical and technological settings.
Duran Olivencia MA, Yatsyshin P, Goddard B, et al., 2017, General framework for fluctuating dynamic density functional theory, New Journal of Physics, Vol: 19, ISSN: 1367-2630
We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes (NS) description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad-hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory (DFT). The resultant equation has the structure of a dynamical DFT (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating NS equations, originally derived by Landau and Lifshitz. Our framework thus provi
Schmuck M, Kalliadasis S, 2017, Rate of Convergence of General Phase Field Equations in Strongly Heterogeneous Media Toward Their Homogenized Limit, SIAM Journal on Applied Mathematics, Vol: 77, Pages: 1471-1492, ISSN: 0036-1399
Over the last few decades, phase field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g., geometric PDEs and mean curvature flow, materials science for the study of phase transitions) but also engineering ones (e.g., as a computational tool in chemical engineering for interfacial flow studies). Here, we focus on phase field equations in strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we provide the first derivation of error estimates for fourth order, homogenized, and nonlinear evolution equations. Our fourth order problem induces a slightly lower convergence rate, i.e., $\epsilon^{1/4}$, where $\epsilon$ denotes the material's specific heterogeneity, than established for second order elliptic problems (e.g., [V. Zhikov, Dokl. Math., 73 (2006), pp. 96--99, https://doi.org/10.1134/S1064562406010261.]) for the error between the effective macroscopic solution of the (new) upscaled formulation and the solution of the microscopic phase field problem. We hope that our study will motivate new modeling, analytic, and computational perspectives for interfacial transport and phase transformations in strongly heterogeneous environments.
Morciano M, Fasano M, Nold A, et al., 2017, Nonequilibrium molecular dynamics simulations of nanoconfined fluids at solid-liquid interfaces., Journal of Chemical Physics, Vol: 146, ISSN: 0021-9606
We investigate the hydrodynamic properties of a Lennard-Jones fluid confined to a nanochannel using molecular dynamics simulations. For channels of different widths and hydrophilic-hydrophobic surface wetting properties, profiles of the fluid density, stress, and viscosity across the channel are obtained and analysed. In particular, we propose a linear relationship between the density and viscosity in confined and strongly inhomogeneous nanofluidic flows. The range of validity of this relationship is explored in the context of coarse grained models such as dynamic density functional-theory.
Dallaston MC, Tseluiko D, Zheng Z, et al., 2017, Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows, Nonlinearity, Vol: 30, Pages: 2647-2666, ISSN: 0951-7715
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 utilising 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, $\Pi(h)\propto -1/h^{3}$ , 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 (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at $n_c \approx 1.485$ . 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, $n_c^{{\rm plane}}\approx 1.499$ . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.
Noronha Moreira Antunes Gomes ST, Kalliadasis S, Papageorgiou DT, et al., 2017, Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation, Physica D - Nonlinear Phenomena, Vol: 348, Pages: 33-43, ISSN: 0167-2789
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.
Yatsyshin P, Parry AO, Rascón C, et al., 2017, Classical density functional study of wetting transitions on nanopatterned surfaces., Journal of Physics: Condensed Matter, Vol: 29, ISSN: 0953-8984
Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.
Charogiannis, Denner, van Wachem, et al., 2017, Detailed Hydrodynamic Characterization of Harmonically Excited Falling-Film Flows: A Combined Experimental and Computational Study, Physical Review Fluids, Vol: 2, Pages: 014002-014002, ISSN: 2469-990X
We present results from the simultaneous application of planar laser-induced uorescence (PLIF)and particle image/tracking velocimetry, complemented by direct numerical simulations, aimed atthe detailed hydrodynamic characterization of harmonically excited liquid- lm ows falling underthe action of gravity. The experimental campaign comprises four di erent aqueous-glycerol solutionscorresponding to four Kapitza numbers (Ka= 14, 85, 350, 1800), spanning the Reynolds numberrangeRe= 2:3
Charogiannis A, Denner F, Van Wachem BGM, et al., 2017, Spatiotemporally resolved heat transfer in falling-film flows by laser-induced fluorescence, particle tracking velocimetry and infrared thermography, Second Thermal and Fluids Engineering Conference, Publisher: ASTFE Digital Library, Pages: 3043-3046, ISSN: 2379-1748
We present an experimental technique, based on the simultaneous application of planar laser-induced fluorescence (PLIF), particle tracking velocimetry (PTV) and infrared thermography (IRT), aimed at the detailed measurement of unsteady heat-transfer in harmonically-excited film flows falling under the action of gravity over an inclined, electrically-heated substrate. PLIF is employed in order to recover space- and time-resolved film-height information, PTV to obtain two-dimensional (2-D) velocity, and IRT to measure the free-surface (gas-liquid interface) temperature over a 2-D domain. Phase-lock averaged film-height, flow-field and free-surface data, we demonstrate the generation of highly localized film-height, velocity and heat-transfer along the wave topology over a range of applied heat fluxes.
Nold A, Goddard BD, Yatsyshin P, et al., 2016, Pseudospectral methods for density functional theory in bounded and unbounded domains, Journal of Computational Physics, Vol: 334, Pages: 639-664, ISSN: 1090-2716
Classical Density Functional Theory (DFT) is a statistical–mechanical framework to analyse 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 specialised 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.
Goddard BD, Nold A, Kalliadasis S, 2016, Dynamical density functional theory with hydrodynamic interactions in confined geometries, Journal of Chemical Physics, Vol: 145, ISSN: 1089-7690
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Dallaston MC, Tseluiko D, Kalliadasis S, 2016, Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity, Physical Review Fluids, Vol: 1, ISSN: 2469-990X
Consider the dynamics of a thin film flowing down a heated substrate. The substrate heating generates a temperature distribution on the free surface, which in turn induces surface-tension gradients and corresponding thermocapillary stresses that affect the free surface and therefore the fluid flow. We study here the effect of finite substrate thermal diffusivity on the film dynamics. Linear stability analysis of the full Navier-Stokes and heat transport equations indicates if the substrate diffusivity is sufficiently small, the film becomes unstable at a finite wavelength and at a Reynolds number smaller than that predicted in the long-wavelength limit. This property is captured in a reduced-order system of equations derived using a weighted-residual integral-boundary-layer method. This reduced-order model is also used to compute the bifurcation diagrams of solution branches connecting the trivial flat film to traveling waves including solitary pulses. The effect of finite diffusivity is to separate a simultaneous Hopf-transcritical bifurcation into its individual component bifurcations. The appropriate Hopf bifurcation then connects only to the solution branch of negative-hump pulses, with wave speed less than the linear wave speed, while the branch of positive-single-hump pulses merges with the branch of positive-two-hump pulses at a supercritical Reynolds number. In the regime where finite-wavelength instability occurs, there exists a Hopf-bifurcation pair connected by a branch of periodic solutions, whose period cannot be increased indefinitely. Numerical simulation of the reduced-order system shows the development of a train of coherent structures, each of which resembles a stationary positive-hump pulse, and, in the regime of finite-wavelength instability, wavelength selection and saturation to periodic traveling waves.
Dallaston MC, Fontelos MA, Tseluiko D, et al., 2016, Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures, Phys. Rev. Lett., Vol: 120
The formation of iterated structures, such as satellite and sub-satellitedrops, filaments and bubbles, is a common feature in interfacial hydrodynamics.Here we undertake a computational and theoretical study of their origin in thecase of thin films of viscous fluids that are destabilized by long-rangemolecular or other forces. We demonstrate that iterated structures appear as aconsequence of discrete self-similarity, where certain patterns repeatthemselves, subject to rescaling, periodically in a logarithmic time scale. Theresult is an infinite sequence of ridges and filaments with similarityproperties. The character of these discretely self-similar solutions as theresult of a Hopf bifurcation from ordinarily self-similar solutions is alsodescribed.
Yatsyshin P, Kalliadasis S, 2016, Mean-field phenomenology of wetting in nanogrooves, Molecular Physics, Vol: 114, Pages: 2688-2699, ISSN: 0026-8976
In this special issue article, we bring together our recent research on wetting in confinement, in particular planar walls, wedges, capillary grooves and slit pores, with emphasis on phase transitions and competition between wetting, filling and condensation, and highlight their similarities and disparities. The results presented are obtained with the classical density functional theory (DFT) for fluids, which is a mean-field statistical mechanical framework for including the spatial variations of the fluid density into the thermodynamic equation of state. For wetting in sculpted substrates, we solve numerically the DFT equations to obtain the fluid density profiles, wetting isotherms and phase diagrams. This allows us to contrast the wetting phenomenology of grooves, planar walls, slit and wedge-shaped pores. Of particular interest are the transitions associated with capillary condensation, planar pre-wetting and mean-field wedge pre-filling lines.
Duncan AB, Kalliadasis S, Pavliotis GA, et al., 2016, Noise-induced transitions in rugged energy landscapes, Physical Review E, Vol: 94, ISSN: 1539-3755
We consider the problem of an overdamped Brownian particle moving in multiscale potential with N+1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space-dependent diffusion tensor, the calculation of which requires the solution of N fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems, and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential, and we investigate the limit of infinitely many small scales.
Charogiannis A, Pradas M, Denner F, et al., 2016, Hydrodynamic characteristics of harmonically excited thin-film flows: Experiments and computations, 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
Parry AO, Kalliadasis S, Yatsyshin P, 2016, Complete prewetting, Journal of Physics: Condensed Matter, Vol: 28, Pages: 1-12, ISSN: 0953-8984
We study continuous interfacial transitions, analagous to two-dimensional complete wetting, associated with the first-order prewetting line, which can occur on steps, patterned walls, grooves and wedges, and which are sensitive to both the range of the intermolecular forces and interfacial fluctuation effects. These transitions compete with wetting, filling and condensation producing very rich phase diagrams even for relatively simple prototypical geometries. Using microscopic classical density functional theory to model systems with realistic Lennard-Jones fluid–fluid and fluid–substrate intermolecular potentials, we compute mean-field fluid density profiles, adsorption isotherms and phase diagrams for a variety of confining geometries.
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