This version is available at https://strathprints.strath.ac.uk/52305/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. A systematic investigation of unstable steady-state solutions of the Darcy-OberbeckBoussinesq equations at large values of the Rayleigh number Ra is performed to gain insight into two-dimensional porous medium convection in domains of varying aspectratio L. The steady convective states are shown to transport less heat than the statistically steady 'turbulent' flow realised at the same parameter values: the Nusselt number N u ∼ Ra for turbulent porous medium convection, while N u ∼ Ra 0.6 for the maximum heat-transporting steady solutions. A key finding is that the lateral scale of the heat-fluxmaximising solutions shrinks roughly as L ∼ Ra −0.5 , reminiscent of the decrease of the mean inter-plume spacing observed in turbulent porous medium convection as the thermal forcing is increased. A spatial Floquet analysis is performed to investigate the linear stability of the fully nonlinear steady convective states, extending a recent study by Hewitt et al. (J. Fluid Mech. 737, 2013) by treating a base convective state -and secondary stability modes -that satisfy appropriate boundary conditions along plane parallel walls. As in that study, a bulk instability mode is found for sufficiently small aspect-ratio base states. However, the growth rate of this bulk mode is shown to be significantly reduced by the presence of the walls. Beyond a certain critical Ra-dependent aspect-ratio, the base state is most strongly unstable to a secondary mode that is localised near the heated and cooled walls. Direct numerical simulations, strategically initialised to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically-steady porous medium convection results from a balance between the competing effects of these two types of inst...

We consider, both theoretically and experimentally, the deformation due to an electric field of a pinned nearly hemispherical static sessile drop of an ionic fluid with a high conductivity resting on the lower substrate of a parallel-plate capacitor. Using both numerical and asymptotic approaches, we find solutions to the coupled electrostatic and augmented Young–Laplace equations which agree very well with the experimental results. Our asymptotic solution for the drop interface extends previous work in two ways, namely, to drops that have zero-field contact angles that are not exactly π/2 and to higher order in the applied electric field, and provides useful predictive equations for the changes in the height, contact angle, and pressure as functions of the zero-field contact angle, drop radius, surface tension, and applied electric field. The asymptotic solution requires some numerical computations, and so a surprisingly accurate approximate analytical asymptotic solution is also obtained.

This version is available at https://strathprints.strath.ac.uk/50366/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. For small field induced deformations of the droplet shape the change in maximum droplet height, ∆h = h(E) -h(0), was found to be virtually independent of the plate separation provided that w > 3h(0). In this regime a scaling law obtains ∆h α E 2 r 2 , where r is the constant droplet radius, in agreement with the asymptotic predictions Basaran and Scriven (J. Short Communication

We consider, both theoretically and experimentally, a thin sessile drop of conductive liquid that rests on the lower plate of a parallel-plate capacitor. We derive analytical expressions for both the initial deformation and the relaxation dynamics of the drop as the electric field is either abruptly applied or abruptly removed, as functions of the geometrical, electrical, and material parameters, and investigate the ranges of validity of these expressions by comparison with full numerical simulations. These expressions provide a reasonable description of the experimentally measured dynamic response of a drop of conductive ionic liquid 1-butyl-3-methyl imidazolium tetrafluoroborate.

No abstract