Publications
152 results found
Anderson TG, Cimpeanu R, Papageorgiou DT, et al., 2017, Electric field stabilization of viscous liquid layers coating the underside of a surface, PHYSICAL REVIEW FLUIDS, Vol: 2, ISSN: 2469-990X
We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a horizontal surface in the presence of an electric field applied parallel to the surface. The model includes the effect of bounding solid dielectric regions above and below the liquid-air system that are typically found in experiments. The competition between gravitational forces, surface tension, and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semispectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations using the volume-of-fluid methodology and assess the accuracy of the obtained solutions in the long-wave (thin-film) regime when varying the electric field strength from zero up to the point when complete stabilization occurs. We employ DNS to examine the limitations of the asymptotically derived behavior as the liquid layer thickness increases and find excellent agreement even beyond the regime of strict applicability of the asymptotic solution. Finally, the asymptotic and computational approaches are utilized to identify robust and efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.
Moore MR, Mughal MS, Papageorgiou DT, 2017, Ice formation within a thin film flowing over a flat plate, Journal of Fluid Mechanics, Vol: 817, Pages: 455-489, ISSN: 0022-1120
We present a model for ice formation in a thin, viscous liquid film driven by aBlasius boundary layer after heating is switched off along part of the flat plate. Theflow is assumed to initially be in the Nelson et al. (J. Fluid Mech., vol. 284, 1995,pp. 159–169) steady-state configuration with a constant flux of liquid supplied atthe tip of the plate, so that the film thickness grows like x1/4in distance alongthe plate. Plate cooling is applied downstream of a point, Lx0, an O(L)-distancefrom the tip of the plate, where L is much larger than the film thickness. Thecooling is assumed to be slow enough that the flow is quasi-steady. We present athorough asymptotic derivation of the governing equations from the incompressibleNavier–Stokes equations in each fluid and the corresponding Stefan problem for icegrowth. The problem breaks down into two temporal regimes corresponding to therelative size of the temperature difference across the ice, which are analysed in detailasymptotically and numerically. In each regime, two distinct spatial regions arise, anouter region of the length scale of the plate, and an inner region close to x0 in whichthe film and air are driven over the growing ice layer. Moreover, in the early timeregime, there is an additional intermediate region in which the air–water interfacepropagates a slope discontinuity downstream due to the sudden onset of the ice atthe switch-off point. For each regime, we present ice profiles and growth rates, andshow that for large times, the film is predicted to rupture in the outer region whenthe slope discontinuity becomes sufficiently enhanced.
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.
Dubrovina E, Craster RV, Papageorgiou DT, 2017, Two-layer electrified pressure-driven flow in topographically structured channels, Journal of Fluid Mechanics, Vol: 814, Pages: 222-248, ISSN: 0022-1120
The flow of two stratified viscous immiscible perfect dielectric fluids in a channel withtopographically structured walls is investigated. The flow is driven by a streamwisepressure gradient and an electric field across the channel gap. This problem isexplored in detail by deriving and studying a nonlinear evolution equation for theinterface valid for large-amplitude long waves in the Stokes flow regime. For flatwalls, the electrified flow is long-wave unstable with a critical cutoff wavenumberthat increases linearly with the magnitude of the applied voltage. In the nonlinearregime, it is found that the presence of pressure-driven flow prevents electrostaticallyinduced interface touchdown that has been observed previously – time-modulatednonlinear travelling waves emerge instead. When topography is present, linearly stableuniform flows become non-uniform spatially periodic steady states; a small-amplitudeasymptotic theory is carried out and compared with computations. In the linearlyunstable regime, intricate nonlinear structures emerge that depend, among otherthings, on the magnitude of the wall corrugations. For a low-amplitude sinusoidalboundary, time-modulated travelling waves are observed that are similar to thosefound for flat walls but are influenced by the geometry of the wall and slide over itwithout touching. The flow over a high-amplitude sinusoidal pattern is also examinedin detail and it is found that for sufficiently large voltages the interface evolves tolarge-amplitude waves that span the channel and are subharmonic relative to the wall.A type of ‘walking’ motion emerges that causes the lower fluid to wash through thetroughs and create strong vortices over the peaks of the lower boundary. Non-uniformsteady states induced by the topography are calculated numerically for moderate andlarge values of the flow rate, and their stability is analysed using Floquet theory.The effect of large flow rates is also considered asymptotically to fi
Kirk TL, Hodes M, Papageorgiou DT, 2016, Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature, Journal of Fluid Mechanics, Vol: 811, Pages: 315-349, ISSN: 1469-7645
We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.
Kalogirou A, Cîmpeanu R, Keaveny EE, et al., 2016, Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models, Journal of Fluid Mechanics, Vol: 806, Pages: R1-R13, ISSN: 1469-7645
The nonlinear stability of two-fluid Couette flows is studied using a novel evolution equation whose dynamics is validated by direct numerical simulation (DNS). The evolution equation incorporates inertial effects at arbitrary Reynolds numbers through a non-local term arising from the coupling between the two fluid regions, and is valid when one of the layers is thin. The equation predicts asymmetric solutions and exhibits bistability, features that are essential observations in the experiments of Barthelet et al. (J. Fluid Mech., vol. 303, 1995, pp. 23–53). Related low-inertia models have been used in qualitative predictions rather than the direct comparisons carried out here, and ad hoc modifications appear to be necessary in order to predict asymmetry and bistability. Comparisons between model solutions and DNS show excellent agreement at Reynolds numbers of O(103)O(103) found in the experiments. Direct comparisons are also made with the available experimental results of Barthelet et al. (J. Fluid Mech., vol. 303, 1995, pp. 23–53) when the thin layer occupies 1/51/5 of the channel height. Pointwise comparisons of the travelling wave shapes are carried out, and once again the agreement is very good.
Kalogirou A, Papageorgiou DT, 2016, Nonlinear dynamics of surfactant-laden two-fluid Couette flows in the presence of inertia, Journal of Fluid Mechanics, Vol: 802, Pages: 5-36, ISSN: 1469-7645
The nonlinear stability of immiscible two-fluid Couette flows in the presence of inertia is considered. The interface between the two viscous fluids can support insoluble surfactants and the interplay between the underlying hydrodynamic instabilities and Marangoni effects is explored analytically and computationally in both two and three dimensions. Asymptotic analysis when one of the layers is thin relative to the other yields a coupled system of nonlinear equations describing the spatio-temporal evolution of the interface and its local surfactant concentration. The system is non-local and arises by appropriately matching solutions of the linearised Navier–Stokes equations in the thicker layer to the solution in the thin layer. The scaled models are used to study different physical mechanisms by varying the Reynolds number, the viscosity ratio between the two layers, the total amount of surfactant present initially and a scaled Péclet number measuring diffusion of surfactant along the interface. The linear stability of the underlying flow to two- and three-dimensional disturbances is investigated and a Squire’s type theorem is found to hold when inertia is absent. When inertia is present, three-dimensional disturbances can be more unstable than two-dimensional ones and so Squire’s theorem does not hold. The linear instabilities are followed into the nonlinear regime by solving the evolution equations numerically; this is achieved by implementing highly accurate linearly implicit schemes in time with spectral discretisations in space. Numerical experiments for finite Reynolds numbers indicate that for two-dimensional flows the solutions are mostly nonlinear travelling waves of permanent form, even though these can lose stability via Hopf bifurcations to time-periodic travelling waves. As the length of the system (that is the wavelength of periodic waves) increases, the dynamics becomes more complex and includes time-periodic, quasi-periodic
Papageorgiou DT, Wang Q, 2016, Using electric fields to induce patterning in leaky dielectric fluids in a rod-annular geometry, IMA Journal of Applied Mathematics, ISSN: 0272-4960
The stability and axisymmetric deformation of two immiscible, viscous, perfect or leaky dielectric fluids confined in the annulus between two concentric cylinders are studied in the presence of radial electricfields. The fields are set up by imposing a constant voltage potential difference between the inner andouter cylinders. We derive a set of equations for the interface in the long-wavelength approximation which retains the essential physics of the system and allows for interfacial deformations to be as large as the annular gap hence accounting for possible touchdown at the inner or outer electrode. The effects of the electric parameters are evaluated initially by performing a linear stability analysis which shows excellent agreement with the linear theory of the full axisymmetric problem in the appropriate long wavelengthregime. The nonlinear interfacial dynamics are investigated by carrying out direct numerical simulations of the derived long wave models, both in the absence and presence of electric fields. For non-electrified thin layer flows (i.e. one of the layers thin relative to the other) the long-time dynamics agree with thelubrication approximation results found in literature. When the liquid layers have comparable thickness our results demonstrate the existence of both finite time and infinite time singularities (asymptotic touching solutions) in the system. It is shown that a two-side touching solution is possible for both the non-electrified and perfect dielectric cases, while only one-side touching is found in the case of leaky dielectric liquids, where the flattened interface shape resembles the pattern solutions found in literature.Meanwhile the finite-time singular solution agrees qualitatively with the experiments of Reynolds (196
Gomes SN, Papageorgiou DT, Pavliotis GA, 2016, Stabilizing non-trivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 82, Pages: 158-194, ISSN: 0272-4960
Thompson AB, Gomes SN, Pavliotis, et al., 2016, Stabilising falling liquid film flows using feedback control, Physics of Fluids, Vol: 28, ISSN: 1089-7666
Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slopesufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating andheat transfer, which benefit from smooth and wavy interfaces, respectively. Here we discuss how the dynamicsof the system are altered by feedback controls based on observations of the interface height, and supplied tothe system via the perpendicular injection and suction of fluid through the wall. In this study, we modelthe system using both Benney and weighted-residual models that account for the fluid injection throughthe wall. We find that feedback using injection and suction is a remarkably effective control mechanism:the controls can be used to drive the system towards arbitrary steady states and travelling waves, and thequalitative effects are independent of the details of the flow modelling. Furthermore, we show that the systemcan still be successfully controlled when the feedback is applied via a set of localised actuators and only asmall number of system observations are available, and that this is possible using both static (where thecontrols are based on only the most recent set of observations) and dynamic (where the controls are based onan approximation of the system which evolves over time) control schemes. This study thus provides a solidtheoretical foundation for future experimental realisations of the active feedback control of falling liquid films.
Karamanis G, Hodes M, Kirk T, et al., 2016, Nusselt Numbers for Fully-Developed Flow Between Parallel Plates with One Plate Textured with Isothermal Parallel Ridges, ASME Summer Heat Transfer Conference, Publisher: AMER SOC MECHANICAL ENGINEERS
Papageorgiou DT, Thompson AB, Tseluiko D, 2015, Falling liquid films with blowing and suction, Journal of Fluid Mechanics, Vol: 787, Pages: 292-330, ISSN: 1469-7645
Flow of a thin viscous film down a flat inclined plane becomes unstable to long-wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle of inclination to the horizontal increases, and in particular becomes zero when the plate is vertical). Control of these interfacial instabilities is relevant to a wide range of industrial applications including coating processes and heat or mass transfer systems. This study considers the effect of blowing and suction through the substrate in order to construct from first principles physically realistic models that can be used for detailed passive and active control studies of direct relevance to possible experiments. Two different long-wave, thin-film equations are derived to describe this system; these include the imposed blowing/suction as well as inertia, surface tension, gravity and viscosity. The case of spatially periodic blowing and suction is considered in detail and the bifurcation structure of forced steady states is explored numerically to predict that steady states cease to exist for sufficiently large suction speeds since the film locally thins to zero thickness, giving way to dry patches on the substrate. The linear stability of the resulting non-uniform steady states is investigated for perturbations of arbitrary wavelength, and any instabilities are followed into the fully nonlinear regime using time-dependent computations. The case of small amplitude blowing/suction is studied analytically both for steady states and their stability. Finally, the transition between travelling waves and non-uniform steady states is explored as the amplitude of blowing and suction is increased.
Ruban A, Cimpeanu R, Papageorgiou DT, et al., 2015, How to make a splash: droplet impact and liquid film applications in aerodynamics, 68th Annual Meeting of the APS Division of Fluid Dynamics doi: 10.1103/APS.DFD.2015.GFM.P0032
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.
Kalogirou A, Keaveny EE, Papageorgiou DT, 2015, An in-depth numerical study of the two-dimensional Kuramoto-Sivashinsky equation, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 471, ISSN: 1364-5021
The Kuramoto–Sivashinsky equation in one spatial dimension (1D KSE) is one of the most well-known and well-studied partial differential equations. It exhibits spatio-temporal chaos that emerges through various bifurcations as the domain length increases. There have been several notable analytical studies aimed at understanding how this property extends to the case of two spatial dimensions. In this study, we perform an extensive numerical study of the Kuramoto–Sivashinsky equation (2D KSE) to complement this analytical work. We explore in detail the statistics of chaotic solutions and classify the solutions that arise for domain sizes where the trivial solution is unstable and the long-time dynamics are completely two-dimensional. While we find that many of the features of the 1D KSE, including how the energy scales with system size, carry over to the 2D case, we also note several differences including the various paths to chaos that are not through period doubling.
Wang Q, Papageorgiou DT, Vanden-Broeck J-M, 2015, Korteweg–de Vries solitons on electrified liquid jets, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 91, Pages: 063012-1-063012-7, ISSN: 1063-651X
The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric fieldis considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jetconcentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivialinteraction arises between the hydrodynamics and the electric field in the annulus, resulting in the formationof electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of suchaxisymmetric waves in the weakly nonlinear regime, which is valid for long waves relative to the undisturbedjet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and theapplied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and aweakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical systemthat arises is the Kortweg–de Vries equation with coefficients that vary as the electric field and the electroderadius are varied. Interestingly, the coefficient of the highest-order third derivative term does not change sign andremains strictly positive, whereas the coefficient α of the nonlinear term can change sign for certain values of theparameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevationfor α > 0 and of depression for α < 0. Regions in parameter space are identified where such waves are found.
Cimpeanu R, Papageorgiou DT, 2015, Electrostatically induced mixing in confined stratified multi-fluid systems, International Journal of Multiphase Flow, Vol: 75, Pages: 194-204, ISSN: 1879-3533
Electrostatic control mechanisms underpin a wide range of modern industrial processes, from lab-on-a-chip devices to microfluidic sensors for security applications. During the last decades, the striking impact of fluid interface manipulation in contexts such as polymer self-assembly, micromanufacturing and mixing in viscous media has established the field of electrically driven interfacial flows as invaluable. This work investigates electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in channels with plane walls. The present study demonstrates theoretically that interfacial instabilities can be utilized to achieve efficient mixing in different immiscible fluid regions. This is accomplished by electrostatically driving stable flows far from their equilibrium states to attain time-oscillatory and highly nonlinear flows producing mixing. The nonlinear electrohydrodynamic instabilities play the role of imposed background velocity fields or moving device parts in more traditional mixing protocols. Initially, simple yet efficient on–off voltage protocols are investigated and subsequently symmetry-breaking voltage distributions are considered and shown to considerably enhance the achieved level of mixing. Both two- and three-dimensional flows, containing realistic fluid configurations (water and oils), are computed using direct numerical simulations based on the Navier–Stokes equations. Such numerical investigations facilitate the quantitative study of the flow into the fully nonlinear regime and constitute the basis of optimization methods in the context of microfluidic mixing applications in two- and three-dimensional geometries.
Wray AW, Matar OK, Craster, et al., 2015, Electrostatic Suppression of the "Coffee-stain Effect", Procedia IUTAM, Vol: 15, Pages: 172-177, ISSN: 2210-9838
The dynamics of a slender, nano-particle laden droplet are examined when it is subjected to an electric field. Under a long-waveassumption, the governing equations are reduced to a coupled pair of nonlinear evolution equations prescribing the dynamics of theinterface and the depth-averaged particle concentration. This incorporates the effects of viscous stress, capillarity, electrostaticallyinducedMaxwell stress, van der Waals forces, evaporation and concentration-dependent rheology. It has previously been shown27that electric fields can be used to suppress the ring effect typically exhibited when such a droplet undergoes evaporation. Wedemonstrate here that the use of electric fields affords many diverse ways of controlling the droplets.
Papaefthymiou ES, Papageorgiou DT, 2015, Vanishing viscosity limits of mixed hyperbolic–elliptic systems arising in multilayer channel flows, Nonlinearity, Vol: 28, Pages: 1607-1631, ISSN: 0951-7715
This study considers the spatially periodic initial value problem of 2 × 2 quasilinearparabolic systems in one space dimension having quadratic polynomialflux functions. These systems arise physically in the interfacial dynamicsof viscous immiscible multilayer channel flows. The equations describethe spatiotemporal evolution of phase-separating interfaces with dissipationarising from surface tension (fourth-order) and/or stable stratification effects(second-order). A crucial mathematical aspect of these systems is the presenceof mixed hyperbolic–elliptic flux functions that provide the only source ofinstability. The study concentrates on scaled spatially 2π-periodic solutionsas the dissipation vanishes, and in particular the behaviour of such limitswhen generalized dissipation operators (spanning second to fourth-order) areconsidered. Extensive numerical computations and asymptotic analysis suggestthat the existence (or not) of bounded vanishing viscosity solutions dependscrucially on the structure of the flux function. In the absence of linearterms (i.e. homogeneous flux functions) the vanishing viscosity limit doesnot exist in the L∞-norm. On the other hand, if linear terms in the fluxfunction are present the computations strongly suggest that the solutions existand are bounded in the L∞-norm as the dissipation vanishes. It is foundthat the key mechanism that provides such boundedness centres on persistentspatiotemporal hyperbolic–elliptic transitions. Strikingly, as the dissipationdecreases, the flux function becomes almost everywhere hyperbolic except ona fractal set of elliptic regions, whose dimension depends on the order of theregularized operator. Furthermore, the spatial structures of the emerging weaksolutions are found to support an increasing number of discontinuities (measurevaluedsolutions) located in the vicinity of the fractally distributed ellipticregions. For the unscaled problem, such spatially oscillatory solution
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.
Cimpeanu R, Papageorgiou DT, 2014, On the generation of nonlinear travelling waves in confined geometries using electric fields, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 372, Pages: 1-14, ISSN: 1364-503X
We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid–surface–structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid–fluid interface and study the characteristics of the generated velocity field inside the channel.
Wray AW, Papageorgiou DT, Craster RV, et al., 2014, Electrostatic Suppression of the "Coffee Stain Effect", LANGMUIR, Vol: 30, Pages: 5849-5858, ISSN: 0743-7463
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- Citations: 49
Cimpeanu R, Papageorgiou DT, Petropoulos PG, 2014, On the control and suppression of the Rayleigh-Taylor instability using electric fields, PHYSICS OF FLUIDS, Vol: 26, ISSN: 1070-6631
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- Citations: 53
Wray AW, Papageorgiou DT, Matar OK, 2013, Electrostatically controlled large-amplitude, non-axisymmetric waves in thin film flows down a cylinder, Journal of Fluid Mechanics, Vol: 736, ISSN: 1469-7645
We examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.
Papageorgiou DT, Pavliotis GA, Papaefthymiou ES, 2013, Nonlinear interfacial dynamics in stratified multilayer channel flows, Journal of Fluid Mechanics, Vol: 734, Pages: 114-143, ISSN: 0022-1120
Wray AW, Papageorgiou DT, Matar OK, 2013, Electrified coating flows on vertical fibres: enhancement or suppression of interfacial dynamics, JOURNAL OF FLUID MECHANICS, Vol: 735, Pages: 427-456, ISSN: 0022-1120
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- Citations: 13
Cimpeanu R, Papageorgiou DT, 2013, Electrohydrodynamically induced mixing in immiscible multilayer flows, Publisher: Elsevier
In the present study we investigate electrostatic stabilization mechanismsacting on stratified fluids. Electric fields have been shown to control andeven suppress the Rayleigh-Taylor instability when a heavy fluid lies abovelighter fluid. From a different perspective, similar techniques can also beused to generate interfacial dynamics in otherwise stable systems. We aim toidentify active control protocols in confined geometries that induce timedependent flows in small scale devices without having moving parts. This effecthas numerous applications, ranging from mixing phenomena to electriclithography. Two-dimensional computations are carried out and several suchprotocols are described. We present computational fluid dynamics videos withdifferent underlying mixing strategies, which show promising results.
Booty MR, Papageorgiou DT, Siegel M, et al., 2013, Long-wave equations and direct simulations for the breakup of a viscous fluid thread surrounded by an immiscible viscous fluid, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 78, Pages: 851-867, ISSN: 0272-4960
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- Citations: 6
Tseluiko D, Blyth MG, Papageorgiou DT, 2013, Stability of film flow over inclined topography based on a long-wave nonlinear model, JOURNAL OF FLUID MECHANICS, Vol: 729, Pages: 638-671, ISSN: 0022-1120
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- Citations: 41
Akrivis G, Papageorgiou DT, Smyrlis Y-S, 2013, On the analyticity of certain dissipative-dispersive systems, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 45, Pages: 52-60, ISSN: 0024-6093
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- Citations: 11
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