We explore theoretically the aerodynamics of a recently fabricated jellyfish-like flying machine (Ristroph & Childress, J. R. Soc. Interface, vol. 11 (92), 2014, 20130992). This experimental device achieves flight and hovering by opening and closing opposing sets of wings. It displays orientational or postural flight stability without additional control surfaces or feedback control. Our model ‘machine’ consists of two mirror-symmetric massless flapping wings connected to a volumeless body with mass and moment of inertia. A vortex sheet shedding and wake model is used for the flow simulation. Use of the fast multipole method allows us to simulate for long times and resolve complex wakes. We use our model to explore the design parameters that maintain body hovering and ascent, and investigate the performance of steady ascent states. We find that ascent speed and efficiency increase as the wings are brought closer, due to a mirror-image ‘ground-effect’ between the wings. Steady ascent is approached exponentially in time, which suggests a linear relationship between the aerodynamic force and ascent speed. We investigate the orientational stability of hovering and ascent states by examining the flyer’s free response to perturbation from a transitory external torque. Our results show that bottom-heavy flyers (centre of mass below the geometric centre) are capable of recovering from large tilts, whereas the orientation of the top-heavy flyers diverges. These results are consistent with the experimental observations in Ristroph & Childress (J. R. Soc. Interface, vol. 11 (92), 2014, 20130992), and shed light upon future designs of flapping-wing micro aerial vehicles that use jet-based mechanisms.

The total of the gas in shale gas reservoirs is sourced from a combination of free, adsorbed and dissolved/diffused gas. The mechanisms of production of free and adsorbed gas have been studied by numerous researchers. In contrast, the evolution of the dissolved gas and its contribution to the total gas production is not well understood. In this study we model the effect of pore micro-structure in organic matter (OM) on the rate of gas production in shale reservoirs. In this regard, first, we solve the gas-in-solid diffusion equation over a general doubly connected spatial domain with external Neumann and internal Dirichlet boundary conditions. The obtained solution is applied systematically to multi-pore porous OM domains and then the effect of pore morphology on the rate of gas production is studied. Our model results show that pore geometry has a slight effect on the gas diffusion process, while total organic carbon, and OM porosity, pore size distribution and specific surface area, are dominant parameters. An abundance of very small pores in OM tremendously increases the diffuse gas contribution in the total gas reserve and production.

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

Interfacial instabilities of immiscible radial displacements in homogeneous porous media are analysed in the case of sinusoidal injection flows. The analysis is carried out through numerical simulations based on the immersed interface and level set methods. Investigations of the effects of the period of the sinusoidal injection flows revealed a novel resonance effect where, for a critical period, the number of fingers as well as their structures are considerably changed. The resonance in the flow development is clearly identified through the abrupt changes in the Fourier spectrum of the interface as well as quantitative characteristics of the flow in the form of the minimum and maximum radii of the interface. For the range of parameters examined in this study that correspond to instabilities dominated by viscous forces, the resonance period was found to correlate with a characteristic time of the flow and the fluids mobility ratio. This new physical phenomenon offers new perspectives for using the flow instability to determine important physical properties such as the viscosity and the surface tension of fluids.

We show that an electric field parallel to an electrically neutral surface can generate flow of electrolytic mixtures in small channels. We term this solvo-osmotic flow, since the flow is induced by the asymmetric preferential solvation of ions at the liquid–solid interface. The generated flow is comparable in magnitude to the ubiquitous electro-osmotic flow at charged surfaces, but for a fixed surface charge density, it differs qualitatively in its dependence on ionic strength. Solvo-osmotic flow can also be sensitively controlled with temperature. We derive a modified Helmholtz–Smoluchowski equation that accounts for these effects.