Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these phenomena can be observed both in experimental realisations and in numerical simulations based on simple Darcy models of flow and bubble propagation in a Hele-Shaw cell. In this paper, we investigate the corresponding problem for the propagation of a viscous drop (with viscosity $$\nu $$ ν relative to the surrounding fluid) using a Darcy model. We explore the effect of drop viscosity on the steady solution structure for drops in rectangular channels or with imposed height variations. Under the Darcy model in a uniform channel, steady solutions for bubbles map directly on to those for drops with any internal viscosity $$\nu \ne 1$$ ν ≠ 1 . Hence, the solution multiplicity predicted for bubbles also occurs for drops, although for $$\nu >1$$ ν > 1 , the interface shape is reversed with inflection points appearing at the rear rather than the front of the drop. The equivalence between bubbles and drops breaks down for transient behaviour, at the introduction of any height variation, for multiple bodies of different viscosity ratios and for more detailed models which produce a more complicated flow in the interior of the drop. We show that the introduction of topography variations affects bubbles and drops differently, with very viscous drops preferentially moving towards more constricted regions of the channel. Both bubbles and drops can undergo transient behaviour which involves breakup into two almost equal bodies, which then symmetry break before either recombining or separating indefinitely.

A Coupled CFD-DEM Simulation of Immersed Granular Collapse

<p>Natural disasters normally involve the flow of polydispersed granular materials with interstitial fluid which may change the flow dramatically. Here we focus on a typical small-scale case of fluid–particle mixture flows, i.e., the immersed granular collapse using computational fluid dynamics coupled with discrete element method (CFD-DEM). The simulation parameters are calibrated with laboratory experiments and the immersed granular collapse process is reproduced in terms of different aspect ratios. We present a deeper investigation of the collapse based on simulation results. The granular front evolves in three stages, i.e., acceleration, steady propagation, and deceleration. We found that the constant propagation stage is maintained by the transition of particles’ motion from vertical to horizontal and the drag of the fluid. The constant propagation velocity is proportional to the free-fall velocity with a Stokes-number-dependent coefficient and the normalized final runout is linearly correlated with the densimetric Froude number. These conclusions may find its significance in geophysical applications.</p>

Acceleration of Premixed Flames in Obstructed Pipes with Both Extremes Open

Premixed flame propagation in obstructed channels with both extremes open is studied by means of computational simulations of the reacting flow equations with a fully-compressible hydrodynamics, transport properties (heat conduction, diffusion and viscosity) and an Arrhenius chemical kinetics. The aim of this paper is to distinguish and scrutinize various regimes of flame propagation in this configuration depending on the geometrical and thermal-chemical parameters. The parametric study includes various channel widths, blockage ratios, and thermal expansion ratios. It is found that the interplay of these three critical parameters determines a regime of flame propagation. Specifically, either a flame propagates quasi-steady, without acceleration, or it experiences three consecutive distinctive phases (quasi-steady propagation, acceleration and saturation). This study is mainly focused on the flame acceleration regime. The accelerating phase is exponential in nature, which correlates well with the theoretical prediction from the literature. The accelerating trend also qualitatively resembles that from semi-open channels, but acceleration is substantially weaker when both extremes are open. Likewise, the identified regime of quasi-steady propagation fits the regime of flame oscillations, found for the low Reynolds number flames. In addition, the machine learning logistic regression algorithm is employed to characterize and differentiate the parametric domains of accelerating and non-accelerating flames.

Reopening modes of a collapsed elasto-rigid channel

Motivated by the reopening mechanics of strongly collapsed airways, we study the steady propagation of an air finger through a collapsed oil-filled channel with a single compliant wall. In a previous study using fully compliant elastic tubes, a ‘pointed’ air finger was found to propagate at high speed and low pressure, which, if clinically accessible, offers the potential for rapid reopening of highly collapsed airways with minimal tissue damage (Heap & Juel Phys. Fluids, vol. 20 (8), 2008, 081702). The mechanism underlying the selection of that pointed finger, however, remained unexplained. In this paper, we identify the required selection mechanism by conducting an experimental study in a simpler geometry: a rigid rectangular Hele-Shaw channel with an elastic top boundary. The constitutive behaviour of this elasto-rigid channel is nonlinear and broadly similar to that of an elastic tube, but unlike the tube, the channel’s cross-section adopts self-similar shapes from the undeformed state to the point of first near wall contact. The ensuing simplification of the vessel geometry enables the systematic investigation of the reopening dynamics in terms of increasing initial collapse. We find that for low levels of initial collapse, a single centred symmetric finger propagates in the channel and its shape is set by the tip curvature. As the level of collapse increases, the channel cross-section develops a central region of near opposite wall contact, and the finger shape evolves smoothly towards a ‘flat-tipped’ finger whose geometry is set by the strong depth gradient near the channel walls. We show that the flat-tipped mode of reopening is analogous to the pointed finger observed in tubes. Its propagation is sustained by the vessel’s extreme cross-sectional profile at high collapse, while vessel compliance is necessary to stabilise it. A simple scaling argument based on the dissipated power reveals that this reopening mode is preferred at higher propagation speeds when it becomes favourable to displace the elastic channel wall rather than the viscous fluid.

Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow

The focus of this study is to analyse the tip region of a hydraulic fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a fracture through the concept of a hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a hydraulic fracture is analysed by focusing on steady propagation of a semi-infinite hydraulic fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite hydraulic fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.

Propagation regimes of buoyancy-driven hydraulic fractures with solidification

This study investigates the propagation of a semi-infinite buoyancy-driven hydraulic fracture in situations when the fluid is able to solidify along the crack walls. Such problems occur when hot magma ascends from a chamber due to buoyancy forces and solidifies by interacting with colder rock. In the model, the solidification rate is calculated assuming a one-dimensional heat transfer problem, in which case it becomes mathematically equivalent to Carter’s leak-off model, which is commonly used to describe the fluid leak-off from a hydraulic fracture into a porous rock formation. In order to construct a mathematical model for a buoyancy-driven hydraulic fracture with solidification, the aforementioned thermal problem is combined with (i) linear plane-strain elasticity to ensure equilibrium of the rock surrounding the fracture, (ii) linear elastic fracture mechanics to determine the fracture propagation, (iii) lubrication theory to capture the viscous fluid flow inside the crack and to account for the effect of buoyancy, and (iv) volume balance of the magma. To address the problem, the governing equations are first rewritten in terms of one integral equation with a non-singular kernel, which significantly simplifies the analysis and the procedure for obtaining a numerical solution. The latter solution is shown to obey a multiscale behaviour near the fracture tip that is fully resolved by the numerical scheme. In order to understand the structure of the solution and to quantify the regimes of propagation (and the associated transitions), a thorough analysis of the problem has been performed. Finally, the developments are applied to investigate the non-steady propagation of a buoyancy-driven fracture that is fed by a constant flux.

Chemical Gas Generators Based on Mechanically Alloyed Al·Mg Powder

ABSTRACTBecause of the high energy density, easy ignition, and good storability, mechanically alloyed Al·Mg powder has the potential to improve the performance characteristics of various energetic and gas-generating materials. Here, the use of this powder in combustible mixtures for generation of oxygen and hydrogen is explored. The mixtures for oxygen generation consisted of sodium chlorate, nanoscale cobalt oxide catalyst, and Al·Mg powder, while those for hydrogen generation included water, polyacrylamide as a gellant, and Al·Mg powder. To increase hydrogen yield, ammonia borane (NH3BH3) was also added to Al·Mg − water mixtures. Combustion experiments were conducted in an argon environment, using laser ignition. The thermal wave propagation over the oxygen-generating mixtures was studied using infrared video recording. It has been shown that mechanically alloyed Al·Mg material is a promising alternative to currently used iron because significantly smaller amounts of this additive are needed for a steady propagation of the combustion wave. The hydrogen generation experiments have shown that mixtures of mechanically alloyed Al·Mg powder with 10−60 wt% gelled water are combustible, with the front velocities exceeding the values obtained for the mixtures of water with nanoscale Al. Hydrogen yield was measured using mass-spectrometry. In the mixtures that included ammonia borane, D2O was used instead of H2O. Measurements of H2, D2, and HD concentrations in the product gas provided insight into the reaction mechanisms. The isotopic tests have shown that AB participates in two parallel processes − thermolysis and hydrolysis, thus increasing hydrogen yield.