We consider heat or mass transport from a circular cylinder under a uniform crossflow at small Reynolds numbers, $\mathrm{Re}\ll 1$. This problem has been thwarted in the past by limitations inherent in the classical analyses of the singular flow problem, which have used asymptotic expansions in inverse powers of $\log \mathrm{Re}$. We here make use of the hybrid approximation of Kropinski, Ward & Keller [(1995) SIAM J. Appl. Math. 55, 1484], based upon a robust asymptotic expansion in powers of $\mathrm{Re}$. In that approximation, the “inner” streamfunction is provided by the product of a pre-factor $S$, a slowly varying function of $\mathrm{Re}$, with a $\mathrm{Re}$-independent “canonical” solution of a simple mathematical form. The pre-factor, in turn, is determined as an implicit function of $\log \mathrm{Re}$ via asymptotic matching with a numerical solution of the nonlinear single-scaled “outer” problem, where the cylinder appears as a point singularity. We exploit the hybrid approximation to analyse the transport problem in the limit of large Péclet number, $\mathrm{Pe}\gg 1$. In that limit, transport is restricted to a narrow boundary layer about the cylinder surface – a province contained within the inner region of the flow problem. With $S$ appearing as a parameter, a similarity solution is readily constructed for the boundary-layer problem. It provides the Nusselt number as $0.5799(S\,\mathrm{Pe})^{1/3}$. This asymptotic prediction is in remarkably close agreement with that of the numerical solution of the exact problem [Dennis, Hudson & Smith (1968) Phys. Fluids 11, 933] even for moderate $\mathrm{Re}$-values.

Mathematical models of polyelectrolyte gels are often simplified by assuming the gel is electrically neutral. The rationale behind this assumption is that the thickness of the electric double layer (EDL) at the free surface of the gel is small compared to the size of the gel. Hence, the thin-EDL limit is taken, in which the thickness of the EDL is set to zero. Despite the widespread use of the thin-EDL limit, the solutions in the EDL are rarely computed and shown to match to the solutions for the electrically neutral bulk. The aims of this paper are to study the structure of the EDL and establish the validity of the thin-EDL limit. The model for the gel accounts for phase separation, which gives rise to diffuse interfaces with a thickness described by the Kuhn length. We show that the solutions in the EDL can only be asymptotically matched to the solutions for an electrically neutral bulk, in general, when the Debye length is much smaller than the Kuhn length. If the Debye length is similar to or larger than the Kuhn length, then phase separation can be initiated in the EDL. This phase separation spreads into the bulk of the gel and gives rise to electrically charged layers with different degrees of swelling. Thus, the thin-EDL limit and the assumption of electroneutrality only generally apply when the Debye length is much smaller than the Kuhn length.

We present a mathematical model built to describe the fluid dynamics for the heat transfer fluid in a parabolic trough power plant. Such a power plant consists of a network of tubes for the heat transport fluid. In view of optimisation tasks in the planning and in the operational phase, it is crucial to find a compromise between a very detailed description of many possible physical phenomena and a necessary simplicity needed for a fast and robust computational approach. We present the model, a numerical approach, simulation for single tubes and also for realistic network settings. In addition, we optimise the power output with respect to the operational parameters.

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere’s weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size. Initially, the vapour film transitions from a featureless morphology, where the thickness profile is parabolic, to a neck–bubble morphology, which consists of a uniform pressure bubble bounded by a narrow and much thinner annular neck. Gravity effects then become important in the bubble leading to sequential formation of increasingly smaller neck–bubble pairs near the symmetry axis. This process terminates when the pairs closest to the symmetry axis become indistinguishable and merge. Subsequently, the inner section of that merger transitions into a uniform-thickness film that expands radially, gradually squishing increasingly larger neck–bubble pairs into a region of localised oscillations sandwiched between the uniform film and what remains of the bubble whose radial extent is presently comparable to the uniform film; the neck–bubble pairs farther from the axis remain essentially intact. Ultimately, the uniform film gobbles up the largest outermost bubble, whereby the morphology simplifies to a uniform film bounded by localised oscillations. Overall, the asymptotic analysis describes the continuous evolution of the vapour film from a neck–bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate to a uniform-film morphology which resembles that in the case of a large liquid drop levitating above a liquid bath.

In this work, we introduce an IMEX discontinuous Galerkin solver for the weakly compressible isentropic Euler equations. The splitting needed for the IMEX temporal integration is based on the recently introduced reference solution splitting [32, 52], which makes use of the incompressible solution. We show that the overall method is asymptotic preserving. Numerical results show the performance of the algorithm which is stable under a convective CFL condition and does not show any order degradation.

A continuum hydrodynamic model has been used to characterize flowing active nematics. The behavior of such a system subjected to a weak steady shear is analyzed. We explore the director structures and flow behaviors of the system in flow-aligning and flow tumbling regimes. Combining asymptotic analysis and numerical simulations, we extend previous studies to give a complete characterization of the steady states for both contractile and extensile particles in flow-aligning and flow-tumbling regimes. Another key prediction of this work is the role of the system size on the steady states of an active nematic system: if the system size is small, the velocity and the director angle files for both flow-tumbling contractile and extensile systems are similar to those of passive nematics; if the system is big, the velocity and the director angle files for flow-aligning contractile systems and tumbling extensile systems are akin to sheared passive cholesterics while they are oscillatory for flow-aligning extensile and tumbling contractile systems.