The effect of wall slip on the dewetting of ultrathin films on solid substrates: linear instability and second-order lubrication theory

The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely, the weak, intermediate, and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurately predict the linear dynamics of the film for arbitrary slip lengths.This research was funded by the Spanish MINECO, Subdirección General de Gestión de Ayudas a la Investigación, through Project No. RED2018-102829-T and by the Spanish MCIU-Agencia Estatal de Investigación through Project No. DPI2017-88201-C3-3-R, partly financed through FEDER European funds. A.M.-C. also acknowledges support from the Spanish MECD through Grant No. FPU16/02562.Publicad

Universal Free-Fall Law for Liquid Jets under Fully Developed Injection Conditions

We show that verticals lenderjets of liquid injected in air with a fully developed outlet velocity profile have a universal shape in the common case in which the viscous force is much smaller than the gravitational force. The theory of ideal flows with vorticity provides an analytical solution that, under negligible surface tension forces, predicts RjðZÞ¼½ð1þZ=4Þ1=2−ðZ=4Þ1=21=2, where Rj is the jet radius scaled with the injector radius and Z is the vertical distance scaled with the gravitational length, lg¼u2 o=2g, where uo is the mean velocity at the injector outlet and g is the gravitational acceleration. In contrast with Mariotte’s law, Rj¼ð1þZÞ−1=4, previously reported experiments employing long injectors collapse almost perfectly on to the new solution.The authors thank the Spanish MCIU-Agencia Estatal de Investigación through Project No. PID2020–115655GB-C22, partially financed through FEDER European funds

The role of inertia in the rupture of ultrathin liquid films

Theory and numerical simulations of the Navier–Stokes equations are used to unravel the influence of inertia on the dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the self-similar film thinning regimes at finite Ohnesorge numbers is provided, unifying previous findings. We reveal that, for Ohnesorge numbers smaller than one, the structure of the rupture singularity close to the molecular scales is controlled by a balance between liquid inertia and van der Waals forces, leading to a self-similar asymptotic regime with hmin ∝ τ2/5 as τ → 0, where hmin is the minimum film thickness and τ is the time remaining before rupture. The flow exhibits a three-region structure comprising an irrotational core delimited by a pair of boundary layers at the wall and at the free surface. A potential-flow description of the irrotational core is provided, which is matched with the vortical layers, allowing us to present a complete parameter-free asymptotic description of inertia-dominated film rupture.This research was funded by the Spanish MINECO, Subdirección General de Gestión de Ayudas a la Investigación, through Project No. RED2018-102829-T and by the Spanish MCIU-Agencia Estatal de Investigación through Project No. DPI2017-88201-C3-3-R, partly financed through FEDER European funds. A.M.-C. also acknowledges support from the Spanish MECD through the Grant No. FPU16/02562.Publicad

Non-linear dynamics and self-similarity in the rupture of ultra-thin viscoelastic liquid coatings

The influence of viscoelasticity on the dewetting of ultrathin polymer films is unraveled by means of theory and numerical simulations in the inertialess limit. Three viscoelastic models are employed to analyse the dynamics of the film, namely the Oldroyd-B, Giesekus, and FENE-P models. We revisit the linear stability analysis first derived by [Tomar et al., Eur. Phys. J. E., 2006, 20, 185–200] for a Jeffrey's film to conclude that all three models formally share the same dispersion relation. For times close to the rupture singularity, the self-similar regime recently discovered [Moreno-Boza et al., Phys. Rev. Fluids, 2020, 5, 014002], where the dimensionless minimum film thickness scales with the dimensionless time until rupture as hmin = 0.665τ1/3, is asymptotically established independently of the rheological model. The spatial structure of the flow is characterised by a Newtonian core and a thin viscoelastic boundary layer at the free surface, where polymeric stresses become singular as τ → 0. The Deborah number and the solvent-to-total viscosity ratio affect the rupture time but not the length scale of the resulting dewetting pattern and asymptotic flow structure close to rupture, which is thus shown to be universal. Our three-dimensional simulations lead us to conclude that bulk viscoelasticity alone does not explain the experimental observations of dewetting of polymeric films near the glass transition

Large-activation-energy analysis of gaseous reacting flow in pipes

This paper analyzes the exothermic reaction of an initially cold gaseous mixture flowing with a moderately large Reynolds number along a cylindrical pipe with constant wall temperature. An overall irreversible reaction with an Arrhenius rate having a large activation energy is used for the chemistry description. The flow is chemically frozen in the cold entrance region, where the velocity evolves towards the Poiseuille profile as the gas temperature increases towards the wall value, ushering in a reaction stage during which the rate of heat transfer from the wall changes from positive to negative. The subsequent downstream evolution of the flow depends critically on the competition between the heat released by the chemical reaction and the heat-conduction losses to the wall, as measured by the Damkohler number 8, first introduced by Frank-Kamenetskii in his seminal analysis of thermal explosions in cylindrical vessels. For values of delta below the critical value delta &#61; 2 corresponding to the quasi-steady explosion limit, heat losses to the wall keep the gas temperature close to the wall value, so that the chemical reaction occurs slowly along the pipe in a flameless mode, which is analyzed to give an implicit expression for the streamwise reactant distribution. By way of contrast, for delta > 2 the slow reaction rates occur only in an initial ignition region, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a well-defined location, whose computation must account for the temperature found at the end of the entrance region. The predictions of the large-activation-energy analyses, including ignition distances for delta > 2 and flameless reactant consumption rates for delta < 2, show good agreement with numerical computations of the reactive pipe flow for finite values of the activation energy.This work was supported by the Spanish MCINN through project # CSD2010-00011

Mathematical modelling of a membrane-less redox flow battery based on immiscible electrolytes

We present a mathematical model to study the steady-state performance of a membrane-less reversible redox flow battery formed by two immiscible electrolytes that spontaneously form a liquid-liquid system separated by a well defined interface. The model assumes a two-dimensional battery with two coflowing electrolytes and flat electrodes at the channel walls. In this configuration, the analysis of the far downstream solution indicates that the interface remains stable in all the parameter range covered by this study. To simplify the description of the problem, we use the dilute solution theory to decouple the calculation of the velocity and species concentration fields. Once the velocity field is known, we obtain the distribution of the mobile ionic species along with the current and the electric potential field of the flowing electrolyte solution. The numerical integration of the problem provides the variation of the battery current density Iapp with the State of Charge (SoC) for different applied cell voltages Vcell. A detailed analysis of the concentration density plots indicates that the normal operation of the battery is interrupted when reactant depletion is achieved near the negative electrode both during charge and discharge. The effect of the electrolyte flow on the performance of the system is studied by varying the Reynolds, Re and Péclet, Pe, numbers. As expected, the flow velocity only affects the polarization curve in the concentration polarization region, when is well below the equilibrium potential, resulting in limiting current densities that grow with Re......This work has been partially funded by the Spanish Agencia Estatal de Investigación under projects (PID2019-106740RB- I00 and PID2019-108592RB-C41/AEI/10.13039/50110 0 011033), by Grant IND2019/AMB-17273 of the Comunidad de Madrid and by project MFreeB which have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 726217). D. Ruiz-Martín acknowledges the support of an FPI predoctoral fellowship (BES-2016-078629) under project ENE2015-68703-C2-1-R (MINECO/FEDER, UE) and the insigh- ful conversations with professor Mark Blyth during her research visit at the University of East Anglia (UK)

Object-oriented modeling and simulation of the closed loop cardiovascular system by using SIMSCAPE

The modeling of physiological systems via mathematical equations reflects the calculation procedure more than the structure of the real system modeled, with the simulation environment SIMULINK™ being one of the best suited to this strategy. Nevertheless, object-oriented modeling is spreading in current simulation environments through the use of the individual components of the model and its interconnections to define the underlying dynamic equations. In this paper we describe the use of the SIMSCAPE™ simulation environment in the object-oriented modeling of the closed loop cardiovascular system. The described approach represents a valuable tool in the teaching of physiology for graduate medical students

Diffusion-flame flickering as a hydrodynamic global mode

The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.Norbert Peters pointed out the need for the present analysis in his seminal paper with John Buckmaster published thirty years ago (Buckmaster & Peters 1986). It is with great sorrow that we received the news of his passing last year. This paper is devoted to his memory in gratitude for his many outstanding contributions to Combustion Science. The constructive comments of one anonymous referee have led to substantial improvements of the paper and are gratefully acknowledged. This work was supported by the Spanish MCINN through project no. CSD2010-00010 and by the Spanish MINECO through project no. DPI2014-59292-C3-1-P

On the critical conditions for pool-fire puffing

Pool fires are known to undergo a bifurcation to a globally unstable puffing state driven by baroclinic and buoyant vorticity production. Although the supercritical puffing regime away from the bifurcation has been studied extensively in the literature, no detailed account has been given of the critical conditions for its onset, that being the purpose of the present paper. For the relevant canonical case of round liquid pools without swirl, aside from the inherent thermochemical and transport parameters associated with the fuel, pool-fire puffing is governed by a single dimensionless number, the Rayleigh number, which scales with the cube of the pool diameter. Consequently, for a fixed fuel and under fixed ambient conditions, there is a critical fuel pool diameter, associated with a critical value of the Rayleigh number, above which the flame starts puffing. A global linear stability analysis that accounts for the axisymmetry of the prevailing instability mode is developed here to describe the bifurcation. The mathematical formulation employs the limit of infinitely fast reaction, with account taken of the nonunity Lewis number and vaporization characteristics of typical liquid fuels. Predictions of critical puffing conditions, including critical diameters and puffing frequencies, are provided for methanol and for heptane pool fires, and the results are compared with results of new small-scale experiments under controlled laboratory conditions, reported here, yielding reasonably good agreement

The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: transient analysis and explosion limit

In this paper we revisit Frank-Kamenetskii’s analysis of thermal explosions, using also a single-reaction model with an Arrhenius rate having a large activation energy, to describe the transient combustion of initially cold gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. The analysis shows two modes of combustion, including a flameless slowly reacting mode for low wall temperatures or small vessel sizes, when the temperature rise due to the reaction is kept small by the heat-conduction losses to the wall, so as not to change significantly the order of magnitude of the reaction rate. In the second mode of combustion the slow reaction rates occur only in the first ignition stage, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a welldefined ignition time and location, which triggers a flame that propagates across the vessel to consume rapidly the reactant. We define the explosion limits, in agreement with FrankKamenetskii’s analysis, by the limiting conditions for existence of the slowly reacting mode of combustion. In this mode, a quasi-steady temperature distribution is established after a transient reaction stage with small reactant consumption. Most of the reactant is burnt, with nearly uniform mass fraction, in a second long stage, when the temperature follows a quasisteady balance between the rates of heat conduction to the wall and of chemical heat release. The changes in the explosion limits due to the enhanced heat transfer rates by the buoyant motion are described in an accompanying paper.This work was supported by the Spanish MCINN through project # CSD2010- 00010