Well-resolved direct numerical simulations of 2D Rayleigh-Bénard convection in a porous medium are presented for Rayleigh numbers Ra≤4×10(4) which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu~Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra→∞ by a simple columnar "heat-exchanger" model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k~Ra(0.4).

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. 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 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. 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 CO 2 in a saline aquifer is discussed.

High-resolution numerical simulations of statistically steady convection in a threedimensional porous medium are presented for Rayleigh numbers Ra 2 × 10 4 . Measurements of the Nusselt number Nu in the range 1750 Ra 2 × 10 4 are well fitted by a relationship of the form Nu = α 3 Ra + β 3 , for α 3 = 9.6 × 10 −3 and β 3 = 4.6. This fit indicates that the classical linear scaling Nu ∼ Ra is attained, and that Nu is asymptotically approximately 40 % larger than in two dimensions. The dynamical flow structure in the range 1750 Ra 2 × 10 4 is analysed, and the interior of the flow is found to be increasingly well described as Ra → ∞ by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber k and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by k ∼ Ra 0.52±0.05 , which is distinguishably stronger than the two-dimensional scaling of k ∼ Ra 0.4 .

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.