Demetrios Papageorgiou | Imperial College London (original) (raw)
Papers by Demetrios Papageorgiou
Physics of Fluids, Jul 1, 1995
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Ima Journal of Applied Mathematics, 1994
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Journal of Fluid Mechanics, Jun 1, 2005
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Bulletin of the American Physical Society, Nov 22, 2016
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ICASE/LaRC interdisciplinary series in science and engineering, 1994
We use asymptotic methods to derive a system of nonlinear evolution equations that govern the flo... more We use asymptotic methods to derive a system of nonlinear evolution equations that govern the flow of a viscous jet, at order one Reynolds numbers, when the surface of the jet supports interfacial tension and is allowed to deform to arbitrary amplitudes. The reduced set of equations are valid in the regime where a characteristic axial lengthscale of the deformations is large compared to the unperturbed jet radius. It is shown analytically that leading order solutions form shocks after a finite time and the theory must be carried out to second order in order to obtain physically meaningful pinching solutions. We use the model equations to construct similarity solutions which describe the flow as the jet radius tends to zero, the solutions being consistent with the slender jet ansatz.
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Siam Journal on Applied Mathematics, 2000
ABSTRACT
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Zeitschrift für Angewandte Mathematik und Physik, Nov 24, 2011
ABSTRACT We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a seco... more ABSTRACT We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions.
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Physical review fluids, Jun 24, 2019
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Journal of Engineering Mathematics, Sep 12, 2007
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Journal of Heat Transfer, 2018
We consider convective heat transfer for laminar flow of liquid between parallel plates. The conf... more We consider convective heat transfer for laminar flow of liquid between parallel plates. The configurations analyzed are both plates textured with symmetrically aligned isothermal ridges oriented parallel to the flow, and one plate textured as such and the other one smooth and adiabatic. The liquid is assumed to be in the Cassie state on the textured surface(s) to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). We solve for the developing three-dimensional temperature profile resulting from a step change of the ridge temperature in the streamwise direction assuming a hydrodynamically developed flow. Axial conduction is accounted for, i.e., we consider the extended Graetz–Nusselt problem; therefore, the domain is of infinite length. The effects of viscous dissipation and (uniform) volumetric heat ...
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We study large amplitude three-dimensional waves at the interface of two laminar immiscible fluid... more We study large amplitude three-dimensional waves at the interface of two laminar immiscible fluids of different densities and velocities which are bounded between two infinite horizontal plates. Both surface tension and gravity are present. We derive a set of three coupled PDEs which govern the evolution of the interface and velocity jumps across the interface in the in-plane directions. We
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Journal of Fluid Mechanics, Jun 10, 2019
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Ima Journal of Applied Mathematics, Jun 1, 2016
Written to coincide with the anniversary of the launch of our journal, this survey reviews some o... more Written to coincide with the anniversary of the launch of our journal, this survey reviews some of the highlights from the first fifty years of the IMA Journal of Applied Mathematics and its predecessor the Journal of the IMA. Rather than an exhaustive survey, we have chosen some of our personal favourite articles from the last fifty years. For each, we have given only the briefest of summaries—readers can download each of these papers for themselves, as they have each been put on open access to coincide with this Issue. We also attempt to put the work in context. More importantly, these papers were chosen as they have had, and continue to have, a considerable influence. For each, we try to spell out the impact of the work, and by implication, the impact of our journal.
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Journal of Fluid Mechanics, Aug 11, 2023
Analytical solutions are derived showing that a stagnant cap of surfactant at the interface betwe... more Analytical solutions are derived showing that a stagnant cap of surfactant at the interface between two viscous fluids caused by a linear extensional flow can be remobilized by fast kinetic exchange of surfactant with one of the fluids. Using a complex variable formulation of this multiphysics problem at zero capillary number, zero Reynolds number and zero bulk Péclet number, and assuming a linear equation of state, it is shown that the system is governed by a forced complex Burgers equation at arbitrary surface Péclet number. Consequently, this nonlinear system is shown to be linearizable using a complex analogue of the Cole–Hopf transformation. Steady equilibria of the system at any finite value of the surface Péclet number are found explicitly in terms of parabolic cylinder functions. While surface diffusion is naturally expected to mollify sharp gradients associated with stagnant caps and to remobilize the interface, this work gives an analytical demonstration of the less intuitive result that fast kinetic exchange has a similar effect. Indeed, the analytical approach here imposes no limit on the surface Péclet number, which can be taken to be infinitely large so that surface diffusion is completely absent. Mathematically, the solution structure is then very rich allowing a theoretical investigation of this extreme case where it is seen that fast surfactant exchange with the bulk can alone remobilize a stagnant cap. Remarkably, it is also possible to track explicitly the time evolution of the system to these remobilized equilibria by finding time-evolving exact solutions.
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arXiv (Cornell University), Jan 12, 2015
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Ima Journal of Applied Mathematics, Oct 14, 2022
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Physical Review Fluids, 2022
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Advances in Soil Science, 1990
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Bulletin of the American Physical Society, 2014
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Physics of Fluids, Jul 1, 1995
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Ima Journal of Applied Mathematics, 1994
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Journal of Fluid Mechanics, Jun 1, 2005
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Bulletin of the American Physical Society, Nov 22, 2016
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ICASE/LaRC interdisciplinary series in science and engineering, 1994
We use asymptotic methods to derive a system of nonlinear evolution equations that govern the flo... more We use asymptotic methods to derive a system of nonlinear evolution equations that govern the flow of a viscous jet, at order one Reynolds numbers, when the surface of the jet supports interfacial tension and is allowed to deform to arbitrary amplitudes. The reduced set of equations are valid in the regime where a characteristic axial lengthscale of the deformations is large compared to the unperturbed jet radius. It is shown analytically that leading order solutions form shocks after a finite time and the theory must be carried out to second order in order to obtain physically meaningful pinching solutions. We use the model equations to construct similarity solutions which describe the flow as the jet radius tends to zero, the solutions being consistent with the slender jet ansatz.
Bookmarks Related papers MentionsView impact
Siam Journal on Applied Mathematics, 2000
ABSTRACT
Bookmarks Related papers MentionsView impact
Zeitschrift für Angewandte Mathematik und Physik, Nov 24, 2011
ABSTRACT We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a seco... more ABSTRACT We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions.
Bookmarks Related papers MentionsView impact
Physical review fluids, Jun 24, 2019
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Journal of Engineering Mathematics, Sep 12, 2007
Bookmarks Related papers MentionsView impact
Journal of Heat Transfer, 2018
We consider convective heat transfer for laminar flow of liquid between parallel plates. The conf... more We consider convective heat transfer for laminar flow of liquid between parallel plates. The configurations analyzed are both plates textured with symmetrically aligned isothermal ridges oriented parallel to the flow, and one plate textured as such and the other one smooth and adiabatic. The liquid is assumed to be in the Cassie state on the textured surface(s) to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). We solve for the developing three-dimensional temperature profile resulting from a step change of the ridge temperature in the streamwise direction assuming a hydrodynamically developed flow. Axial conduction is accounted for, i.e., we consider the extended Graetz–Nusselt problem; therefore, the domain is of infinite length. The effects of viscous dissipation and (uniform) volumetric heat ...
Bookmarks Related papers MentionsView impact
We study large amplitude three-dimensional waves at the interface of two laminar immiscible fluid... more We study large amplitude three-dimensional waves at the interface of two laminar immiscible fluids of different densities and velocities which are bounded between two infinite horizontal plates. Both surface tension and gravity are present. We derive a set of three coupled PDEs which govern the evolution of the interface and velocity jumps across the interface in the in-plane directions. We
Bookmarks Related papers MentionsView impact
Journal of Fluid Mechanics, Jun 10, 2019
Bookmarks Related papers MentionsView impact
Ima Journal of Applied Mathematics, Jun 1, 2016
Written to coincide with the anniversary of the launch of our journal, this survey reviews some o... more Written to coincide with the anniversary of the launch of our journal, this survey reviews some of the highlights from the first fifty years of the IMA Journal of Applied Mathematics and its predecessor the Journal of the IMA. Rather than an exhaustive survey, we have chosen some of our personal favourite articles from the last fifty years. For each, we have given only the briefest of summaries—readers can download each of these papers for themselves, as they have each been put on open access to coincide with this Issue. We also attempt to put the work in context. More importantly, these papers were chosen as they have had, and continue to have, a considerable influence. For each, we try to spell out the impact of the work, and by implication, the impact of our journal.
Bookmarks Related papers MentionsView impact
Journal of Fluid Mechanics, Aug 11, 2023
Analytical solutions are derived showing that a stagnant cap of surfactant at the interface betwe... more Analytical solutions are derived showing that a stagnant cap of surfactant at the interface between two viscous fluids caused by a linear extensional flow can be remobilized by fast kinetic exchange of surfactant with one of the fluids. Using a complex variable formulation of this multiphysics problem at zero capillary number, zero Reynolds number and zero bulk Péclet number, and assuming a linear equation of state, it is shown that the system is governed by a forced complex Burgers equation at arbitrary surface Péclet number. Consequently, this nonlinear system is shown to be linearizable using a complex analogue of the Cole–Hopf transformation. Steady equilibria of the system at any finite value of the surface Péclet number are found explicitly in terms of parabolic cylinder functions. While surface diffusion is naturally expected to mollify sharp gradients associated with stagnant caps and to remobilize the interface, this work gives an analytical demonstration of the less intuitive result that fast kinetic exchange has a similar effect. Indeed, the analytical approach here imposes no limit on the surface Péclet number, which can be taken to be infinitely large so that surface diffusion is completely absent. Mathematically, the solution structure is then very rich allowing a theoretical investigation of this extreme case where it is seen that fast surfactant exchange with the bulk can alone remobilize a stagnant cap. Remarkably, it is also possible to track explicitly the time evolution of the system to these remobilized equilibria by finding time-evolving exact solutions.
Bookmarks Related papers MentionsView impact
arXiv (Cornell University), Jan 12, 2015
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Ima Journal of Applied Mathematics, Oct 14, 2022
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Physical Review Fluids, 2022
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Advances in Soil Science, 1990
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Bulletin of the American Physical Society, 2014
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