Evolution of convection in a layered porous medium

The effect of a series of thin, horizontal, low-permeability layers on convective motion from a distributed dense source along an upper boundary in an otherwise homogeneous, two-dimensional porous medium is considered. This set-up provides an idealised version of a relatively common form of heterogeneity in geological formations. The thickness and permeability of the thin layers are assumed to be small relative to the distance between them and the bulk permeability, respectively. As such, the layers can be parameterised by their impedance Ω – a dimensionless ratio of the effective layer thickness and permeability – while the strength of convection is controlled by the dimensionless distance H≫1 between layers, which can also be interpreted as an effective Rayleigh number for the flow. The role of Ω is explored with the aid of high-resolution numerical simulations, and simple analytical models are developed for the evolution of the mean concentration and the flux in the limits of small and large Ω . For intermediate values of Ω , the flow undergoes a transition from predominantly diffusive transfer across the layers to predominantly advective transfer, and the lateral scale of the flow can become very large. This transition is characterised and a simple model is developed

Mud swimming: Locomotion through a viscoplastic fluid

Different classical models of small, slow (inertialess) swimming are considered when the ambient fluid has a yield stress. A variety of organisms inhabit and have to move through mud, mucus and other biological media, or more generally, soil and sand, all of which can exhibit viscoplastic behaviour. Basic mechanisms for inertialess swimming in ‘simple’ viscoplastic (Bingham) fluids are considered from a theoretical and numerical standpoint, with a particular focus on the role of the yield stress, the location of plugged-up regions around the swimmer's body, and the speed and efficiency of locomotion. Taylor's canonical ‘swimming sheet’, idealised versions of squirming organisms, and long, thin worm-like motions are all discussed, the latter of which involves a generalisation of classical slender-body theory for viscoplastic fluids

The development of a professional: reinterpretation of the professionalization problem from the perspective of cognitive/moral development

Unprofessionalism is not so much a problem of competence or morals as it is an indication that students and some of their mentors require more profound cognitive and moral development. An analysis of student intellectual complexity using a social, educationally oriented developmental model provides evidence that some students who are more adolescent than adult might be overly challenged by a truly "professional" curriculum. Literature concerning the cognitive/moral development of professionals suggests that many faculty members may not be performing at the professional level themselves. The need for mentoring of students, faculty members, and preceptors emerges as a recurring theme. A comprehensive, developmentally anchored plan for professionalization addresses: (1) barriers that must be overcome and strategies to do so; (2) appropriate curriculum content, assessment, and outcomes, and; (3) developmentally appropriate educational interventions

Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed

Internally heated porous convection: an idealised model for Enceladus' hydrothermal activity

Recent planetary data and geophysical modelling suggest that hydrothermal activity is ongoing under the ice crust of Enceladus, one of Saturn's moons. According to these models, hydrothermal flow in the porous, rocky core of the satellite is driven by tidal deformation that induces dissipation and volumetric internal heating. Despite the effort in the modelling of Enceladus' interior, systematic understanding---and even basic scaling laws---of internally-heated porous convection and hydrothermal activity are still lacking. In this article, using an idealised model of an internally-heated porous medium, we explore numerically and theoretically the flows that develop close and far from the onset of convection. In particular, we quantify heat-transport efficiency by convective flows as well as the typical extent and intensity of heat-flux anomalies created at the top of the porous layer. With our idealised model, we derive simple and general laws governing the temperature and hydrothermal velocity that can be driven in the oceans of icy moons. In the future, these laws could help better constraining models of the interior of Enceladus and other icy satellites.Comment: 23 pages, 13 figure

High-Rayleigh-number convection in porous-fluid layers

We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the whole system, as in the canonical Rayleigh-B\'enard problem. Numerical simulations are carried out using a single-domain formulation of the two-layer problem based on the Darcy-Brinkman equations. We explore the dynamics and heat flux through the system in the limit of large Rayleigh number, but small Darcy number, such that the flow exhibits vigorous convection in both the porous and the unconfined fluid regions, while the porous flow still remains strongly confined and governed by Darcy's law. We demonstrate that the heat flux and average thermal structure of the system can be predicted using previous results of convection in individual fluid or porous layers. We revisit a controversy about the role of subcritical "penetrative convection" in the porous medium, and confirm that such induced flow does not contribute to the heat flux through the system. Lastly, we briefly study the temporal coupling between the two layers and find that the turbulent fluid convection above acts as a low-pass filter on the longer-timescale variability of convection in the porous layer.Comment: Accepted for publication in Journal of Fluid Mechanics, 25 pages, 13 figure

The Elastic Landau-Levich Problem on a Slope

The elastic analogue of the Landau-Levich dip-coating problem, in which a plate is withdrawn from a bath of fluid on whose surface lies a thin elastic sheet, is analysed for angle of withdrawal θ to the horizontal. The flow is controlled by the elasticity number, El, which is a measure of the relative importance of viscous and bending stresses, and θ. The leading order solution for small El is a steady profile in which the thickness of the film on the plate is found to vary as El^3/4 /(1 − cos θ)^5/8 . This prediction is confirmed in the limit θ « 1 by comparison with numerical simulation. Finally, the circumstances under which the assumption of a steady solution is no longer valid are discussed, and the time-dependent solution is described

Obstructed and channelized viscoplastic flow in a Hele-Shaw cell

A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with stepwise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interference of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow.D.R.H. is grateful to the Killam Foundation for a Postdoctoral Fellowship.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.

Dewatering of fibre suspensions by pressure filtration

A theoretical and experimental study of dewatering of fibre suspensions by uniaxial compression is presented. Solutions of a one-dimensional model are discussed and asymptotic limits of fast and slow compression are explored. Particular focus is given to relatively rapid compression and to the corresponding development of spatial variations in the solidity and velocity profiles of the suspension. The results of complementary laboratory experiments are presented for nylon or cellulose fibres suspended in viscous fluid. The constitutive relationships for each suspension were measured independently. Measurements of the load for different fixed compression speeds, together with some direct measurements of the velocity profiles using particle tracking velocimetry, are compared with model predictions. The comparison is reasonable for nylon, but poor for cellulose fibres. An extension to the model, which allows for a strain-rate-dependent component in the network stress, is proposed, and is found to give a dramatic improvement in the model predictions for cellulose fibre suspensions. The reason for this improvement is attributed to the microstructure of cellulose fibres, which, unlike nylon fibres, are themselves porous.Akzo Nobel, Valmet Ltd., Natural Sciences and Engineering Council of Canada, Killam Postdoctoral Fellowshi

Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed