Constant Front Velocity Research Articles

Swelling Kinetics of Hydrogel Beads in Aqueous Glycerin Solutions.

This study examines the swelling kinetics of polyacrylamide hydrogel beads in aqueous glycerin solutions of different concentrations. The total absorbed mass of the hydrogel beads remains nearly constant, independent of glycerin concentration, but the swelling process is markedly slower with increasing glycerin concentration in the aqueous solutions. Absorption capacity curves exhibit universal kinetics when time is rescaled using a characteristic time proportional to the viscosity of the solutions. Additionally, a novel visualization technique is employed to observe the core-shell structure of the hydrogel beads at early times in the swelling process. The evolution of the core-shell structure indicates a constant front velocity, which also reveals universal behavior with the same nondimensional time, suggesting a viscous dominated transport of the solution penetrating the beads.

Synthesis of submicrometric dendritic iron particles in an Electrochemical and Vibrating Hele-Shaw cell: study of the growth of ramified branches

The purpose of this study is to explore a new synthesis way for the production of iron nanoparticles exploiting the nanometric structure of long ramified iron branches formed by electrodeposition in a Hele-Shaw cell. After the growth, these branches are fragmented by the action of a vibrating element (piezoelectric disk) integrated into the cell. The emphasis is put on the growth of the ramified iron branches which is performed by galvanostatic electrodeposition in a stagnant electrolyte (FeCl2) inside the Hele-Shaw cell (50μm deep). The competition between the co-formation of H2 bubbles (H+ reduction) and the growth of ramified iron branches (FeII reduction) is analyzed by varying both the applied current density j and the FeCl2 concentration. Two regimes, depending mainly on j, are highlighted: below a threshold current density of 8mA/cm2 only H2 bubbles are formed, while above this threshold, iron branches grow accompanied by the formation of H2 bubbles which nucleate and grow at the top of the branches during their formation. The H2 bubbles influence the branches growth especially at low j (<24mA/cm2) when the growth velocity of the branches is low compared to the growth rate of the bubbles. At higher j (>24mA/cm2), the branches follow a columnar growth with a constant front velocity, well predicted by the theory. Scanning Electron Microscopy (SEM) of the iron branches shows a dendritic structure constituted of nanometric crystallites, whose size depends on the local growth velocity: increasing the growth velocity from 3.6μm/s to 40μm/s leads to a decrease in the crystallites size, from ∼1μm to ∼10nm. Using the acoustic vibrations (4kHz) of the piezoelectric disk, these fragile branches are successfully fragmented into submicrometric fragments of dendrites exhibiting high specific surfaces S/V (equivalent to the S/V of nanoparticles of 30nm diameter). Advantages/Drawbacks compared to other synthesis ways as well as the optimization of the proposed synthesis are discussed.

One-dimensional collective migration of a proliferating cell monolayer.

The importance of collective cellular migration during embryogenesis and tissue repair asks for a sound understanding of underlying principles and mechanisms. Here, we address recent in vitro experiments on cell monolayers, which show that the advancement of the leading edge relies on cell proliferation and protrusive activity at the tissue margin. Within a simple viscoelastic mechanical model amenable to detailed analysis, we identify a key parameter responsible for tissue expansion, and we determine the dependence of the monolayer velocity as a function of measurable rheological parameters. Our results allow us to discuss the effects of pharmacological perturbations on the observed tissue dynamics.

Collapse of granular-liquid mixtures over rigid, inclined beds

This work deals with the propagation of granular-liquid waves over rigid beds, originated by the sudden removal of a sluice gate in a rectangular, inclined flume. In particular, we experimentally investigate the role of the initial volume ratio of granular material-monodispersed plastic cylinders-to water, the flume width, and the bed roughness on the time evolution of the granular front. Due to the presence of the interstitial liquid, we observed previously unreported types of collapse: (i) discontinuous flows, where the granular material stops after an initial spreading, and then flows again when the liquid, initially slower than the particles, reaches the front and remobilizes it; (ii) flows evolving into uniformly progressive waves at an angle of inclination of the flume well below the angle of repose of the dry granular material. We also noticed an unusual influence of the lateral confinement on the wave propagation. Indeed, the constant front velocity in the uniformly progressive state decreases when the channel width increases. We claim that the latter observation and the presence of discontinuous flows, strongly support the idea that only two-phase, stratified mathematical models can predict the behavior of unsteady, granular-liquid mixtures at high concentration, such as debris flows.

Self-Similar Curling of a Naturally Curved Elastica

We consider the curling of an initially flat but naturally curved elastica on a hard, nonadhesive surface. Combining theory, simulations, and experiments, we find novel behavior, including a constant front velocity and a self-similar shape of the curl that scales in size as t(1/3) at long times after the release of one end of the elastica. The front velocity is selected by matching the self-similar solution with a roll of nearly constant curvature located near the free end.

Tail structure and bed friction velocity distribution of gravity currents propagating over an array of obstacles

AbstractThe bed friction velocity distribution and sediment entrainment potential of Boussinesq compositional gravity currents propagating over a series of obstacles and over a smooth surface, respectively, are analysed based on high-resolution, three-dimensional large-eddy simulations. The investigation focuses on the parameter regime for which currents with a high volume of release go through an extended slumping phase with approximately constant front velocity (Tokyay, Constantinescu &amp; Meiburg, J. Fluid Mech., vol. 672, 2011, 570–605). Under these conditions, a quasi-steady regime is reached between consecutive obstacles that is similar to the steady regime observed for constant-density channel flows over bottom obstacles. At a given location, this quasi-steady regime is reached in the tail of the current after the passage of the front and the associated hydraulic jumps reflected from the first few downstream obstacles. A double-averaging procedure is employed to characterize the global changes in the structure of the tail region between currents with a high volume of release propagating over smooth surfaces and over obstacles. Reynolds-number-induced scale effects on the flow and turbulence structure within the tail region are discussed in some detail. The presence of this quasi-steady regime is significant, since the simulations with obstacles show that most of the sediment is entrained by the tail of the current, rather than by its front. A detailed analysis of the effects of the obstacle shape on the quasi-steady mean flow and turbulence structure is presented, which provides insight into why gravity currents over dunes can entrain more sediment than gravity currents over ribs of comparable size. Finally, the bed friction velocity distributions and the potential to entrain sediment are compared for a compositional current with a high volume of release during the slumping phase, and a current with a low volume of release for which transition to the buoyancy–inertia phase occurs a short time after the release of the lock gate.

Measurement of the temperature profile of an exothermic autocatalytic reaction front

Autocatalytic reactions may propagate as solitary waves, namely, at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. When the reaction is exothermic, a thermal wave is linked to the chemical front. As the thermal diffusivity is nearly two orders of magnitude larger than the molecular one, the temperature profile spreads over length scales (mm) two orders of magnitude larger than the concentration one. Using an infrared camera, we measure the temperature profiles for a chlorite-tetrathionate autocatalytic reaction. The profiles are compared quantitatively to lattice Bhatnagar-Gross-Krook (BGK) numerical simulations. Our analysis also accounts for the lack of observation of the thermal wave for the iodate arsenous acid reaction.

Taylor’s regime of an autocatalytic reaction front in a pulsative periodic flow

Autocatalytic reaction fronts between reacted and unreacted species may propagate as solitary waves, that is, at a constant front velocity and with a stationary concentration profile, which result from a balance between molecular diffusion and chemical reaction. A velocity field in the supporting medium may affect the propagation of such fronts through different phenomena: advection, diffusion enhancement, front shape changes, etc. Here, we report on an experimental study and lattice Bhatnagar–Gross–Krook numerical simulations of the effect of an oscillating flow on the autocatalytic reaction between iodate and arsenous acid in a Hele–Shaw cell. In the low frequency range covered by the experiments, the front behavior is controlled by the flow across the gap and is reproduced with two-dimensional numerical simulations. It is shown that the front velocity oscillates at the frequency of the flow, whereas the front width oscillates at twice that frequency. Moreover, the Taylor regime in the presence of a Poiseuille flow is fully investigated: The description obtained in the case of a stationary flow provides an analytical prediction for the sinusoidal flow. The range of parameters, for which the prediction applies, is delineated and discussed.

Lock-exchange flows in sloping channels

Two-dimensional variable-density Navier–Stokes simulations have been conducted in order to investigate the effects of a slope on the classical lock-exchange flow. Simulations of full lock releases show that the flow goes through an initial quasi-steady phase that is characterized by a constant front velocity. This quasi-steady front velocity has a maximum for slope angles around 40°, and it persists up to a dimensionless time of the order of 10. The flow subsequently undergoes a transition to a second phase with a larger, unsteady, front velocity. These computational findings were confirmed by experimental observations of lock-exchange flows in a tube of circular cross-section.The reason for the observed transition from a quasi-steady front velocity to a larger, unsteady, value is found in the continuous acceleration of the stratified fluid layers connecting the two fronts by the streamwise component of the gravity vector. This acceleration leads to a situation where the fluid layers behind the current front move faster than the front itself. Initially the resulting addition of fluid to the current front from behind affects only the size of the front, while its velocity remains unchanged. Eventually, the current front is unable to absorb more fluid from behind and its velocity has to increase, thereby triggering the transition to the second, unsteady, phase. The transition time is determined as a function of the slope and the density ratio of the two fluids. For increasing density contrast, the transition is seen to occur earlier for the denser current.Conceptually simple models based on the analysis by Thorpe (1968) are compared with simulation results for the flow in the region connecting the fronts. For the early stages of the flow a two-layer stratification model is found to be appropriate, while the later stages require a three-layer stratification model, owing to the intense mixing in the central part of the channel cross-section. These models are employed to estimate the time after which the accelerating stratified fluid layers will affect the velocities of the current fronts. They provide upper and lower estimates for the transition time which are in good agreement with the simulation results.

Lubricating bacteria model for the growth of bacterial colonies exposed to ultraviolet radiation

In this paper, we study the morphological transition of bacterial colonies exposed to ultraviolet radiation by modifying the bacteria model proposed by Delprato Our model considers four factors: the lubricant fluid generated by bacterial colonies, a chemotaxis initiated by the ultraviolet radiation, the intensity of the ultraviolet radiation, and the bacteria's two-stage destruction rate with given radiation intensities. Using this modified model, we simulate the ringlike pattern formation of the bacterial colony exposed to uniform ultraviolet radiation. The following is shown. (1) Without the UV radiation the colony forms a disklike pattern and reaches a constant front velocity. (2) After the radiation is switched on, the bacterial population migrates to the edge of the colony and forms a ringlike pattern. As the intensity of the UV radiation is increased the ring forms faster and the outer velocity of the colony decreases. (3) For higher radiation intensities the total population decreases, while for lower intensities the total population increases initially at a small rate and then decreases. (4) After the UV radiation is switched off, the bacterial population grows both outward as well as into the inner region, and the colony's outer front velocity recovers to a constant value. All these results agree well with the experimental observations [Phys. Rev. Lett. 87, 158102 (2001)]. Along with the chemotaxis, we find that lubricant fluid and the two-stage destruction rate are critical to the dynamics of the growth of the bacterial colony when exposed to UV radiation, and these were not previously considered.

Variable-energy Blast Waves Generated by a Piston Moving in a Dusty Gas

This paper presents a similarity solution for strong blast waves of variable energy propagating in a dusty gas. It is assumed that the equilibrium-flow condition is maintained and the variable energy input is supplied by a driving piston or surface according to a time-dependent power law. Three cases have been investigated: Case I corresponds to a decelerated piston, Case II to a piston of constant velocity, and Case III to a continuously accelerated piston starting from rest. Except in the case of constant front velocity, the similarity solution is valid for adiabatic flow as long as the effect of the counter-pressure is neglected. The effects of a parameter characterizing the various energy input of the blast wave on the similarity solution have been examined. The computations have been performed for various values of mass concentration of the solid particles and for the ratio of density of solid particles to the constant initial density of gas. Tables and graphs of numerical results are presented and discussed.

Pattern of reaction diffusion fronts in laminar flows.

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely, at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice Bhatnagar-Gross-Krook simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.

Evolution of self-similarity, and other properties of waiting-time solutions of the porous medium equation: the case of viscous gravity currents

The one-dimensional porous medium equation ht= (hmhx)x (m&gt;0) admits waiting-time solutions, whose front remains motionless during a finite time interval tw before starting to move. We consider a family of initial value problems, and investigate the asymptotics, close to the front and near start-up, which we expect to be self-similar. We obtain numerical solutions for viscous gravity currents (m=3) and power-law initial conditions (h∝xp, h is proportional to the thickness of the fluid, x is the distance to the front). We find that: (a) if p&lt;2/3 the front starts moving immediately, (b) if p=2/3 the front remains motionless during a finite time, (c) if p&gt;2/3 one obtains waiting-time solutions in which a moving corner layer (a small interval Δx in which hx varies strongly) appears behind the front; the front starts moving when it is overrun by the corner layer. The corner layer strengthens (Δx reduces and the variation of hx increases) as it approaches the front. Our initial conditions produce waiting-time solutions whose front starts moving with nonzero velocity. We determine tw(p) and study the motion of the corner layer and the front, as well as other properties of the solutions. We compare the results with the theoretical upper and lower bounds of tw. We investigate the asymptotics of the numerical solutions for p&gt;2/3, close to the corner layer and the front, and near start-up. To represent this asymptotics various kinds of similarity solutions are available, that can be classified according to the self-similarity exponent δ. We find that only two types (called L and A) are relevant. The L solutions correspond to 1&lt;δ&lt;13/10, and have an infinite series of corner layers that accumulate at the front. The part of these solutions behind the first corner layer of the series represents the asymptotics of the numerical solutions in a domain that excludes the region between the corner layer and the front, for a time interval excluding the neighbourhood of start-up. The A solutions have δ⩽1, and represent the evolution of the strong corner layer that is arriving at the front. The numerical evidence shows that the constant front velocity solution (type A with δ=1) describes the asymptotics close to, and including start-up, so that the motion of the corner layer joins smoothly with that of the front.

Stability and the fractal structure of a spherical flame in a self-similar regime.

Stability of a discontinuous flame front propagating in a self-similar regime R = At-alpha is considered. It is shown that the regime with alpha > 1 is more unstable compared to the flame propagating with a constant front velocity. The destabilizing effec

Thermal propagation of normal zone with increasing temperature level in helium-cooled and high temperature superconductors

Normal zone propagation is investigated above the maximum equilibrium current l ∗, where a superconductor has no stable state in the normal region. This monostable thermal wave is shown to have constant front velocity although its crest grows infinitely with time. Various monostable regimes are analysed by numerical simulation of zone propagation both in helium-cooled and in high T c superconductors (HTSC), and the velocity-current dependences are obtained. Unlike in HTSC, transition to monostable propagation in helium-cooled superconductors is accompanied by jump in velocity at l = l ∗. A constant coefficient model for HTSC is presented which gives analytical expressions for monostable zone velocity. Over a wide range of currents the velocity is given by universal formula dependent on normal substrate properties only. The effect of transient heat transfer is analysed.