arXiv subjects

A. Sevilla

Publications and source records attributed to A. Sevilla.

17 recordsLinked to original sources

arXiv2023

Non-axisymmetric modes in ultrathin annular liquid films coating a cylindrical fibre

This paper presents a detailed analysis of the three-dimensional stability properties of an annular liquid film coating a cylindrical fibre in the presence of van der Waals (vdW) interactions, whose influence depends on the wettability of the solid by the liquid. Under wetting conditions, vdW interactions can stabilise a uniform annular film when its thickness is smaller than a critical value that depends only on the fibre radius, the Hamaker constant, and the surface tension coefficient. In contrast, under non-wetting conditions, both surface tension and vdW forces contribute to destabilise the interface, and non-axisymmetric modes may become dominant depending on the thickness of the film and the relative strength of the surface tension and vdW forces. We perform temporal stability analyses of both the Stokes and lubrication equations of motion, allowing us to reveal the dominant azimuthal mode, as well as the optimal axial wavenumber and the corresponding temporal growth rate, as a function of the relevant governing parameters.

physics.flu-dyn↗

arXiv2023

Linear stability of ultrathin spherical coatings

We unravel the linear stability properties of an otherwise stagnant ultrathin non-wetting liquid film of thickness $h_o$ coating a spherical substrate of radius $R$. The configuration is known to be unstable due to the competition of the destabilizing van der Waals (vdW) forces and the stabilizing surface tension force. The governing equations of motion written in the Stokes limit of negligible liquid inertia and an accompanying lubrication model are linearised about the zero-velocity base state and decomposed into normal modes in order to obtain the temporal dispersion relation. Discrete unstable modes are identified and tracked as a function of a capillary number $Ca$ measuring the relative importance of surface tension to vdW forces and the film aspect ratio $η= R/h_o$. For small enough values of the capillary number only the first polar mode is unstable, and the corresponding maximum growth rate is shown to be a universal function of $η$. Lubrication theory is seen to provide a good quantitative prediction of the film stability properties for $η\gg 1$.

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arXiv2023

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

We show that vertical slender jets 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 $R_j(Z)=[(1+Z/4)^{1/2}-(Z/4)^{1/2}]^{1/2}$, where $R_j$ is the jet radius scaled with the injector radius and $Z$ is the vertical distance scaled with the gravitational length, $l_g=u_o^2/2g$, where $u_o$ is the mean velocity at the injector outlet and $g$ is the gravitational acceleration. In contrast with Mariotte's law, $R_j=(1+Z)^{-1/4}$, previously reported experiments employing long injectors collapse almost perfectly onto the new solution.

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arXiv2023

The influence of an outer bath on the dewetting of an ultrathin liquid film

We report a theoretical and numerical investigation of the linear and nonlinear dynamics of a thin liquid film of viscosity $μ$ sandwiched between a solid substrate and an unbounded liquid bath of viscosity $λμ$. In the limit of negligible inertia, the flow depends on two non-dimensional parameters, namely $λ$ and a dimensionless measure of the relative strengths of the stabilizing surface tension force and the destabilizing van der Waals force between the substrate and the film. We first analyze the linear stability of the film, providing an analytical dispersion relation. When the viscosity of the outer bath is much larger than that of the film, $λ\gg 1$, the most amplified wavenumber decreases as $k_{\textrm{m}} \sim λ^{-1/3}$, indicating that very slender dewetting structures are expected when $λ$ becomes large. We then perform fully nonlinear simulations of the complete Stokes equations to investigate the spatial structure of the flow close to rupture revealing that the flow becomes self-similar with the minimum film thickness scaling as $h_{min} = K(λ) τ^{1/3}$ when $τ\to 0$, where $τ$ is the time remaining before the singularity. It is demonstrated that the presence of an outer liquid bath affects the self-similar structure through the prefactor of the film thinning law, $K(λ)$, and the opening angle of the self-similar film shape, which is shown to decrease with $λ$.

physics.flu-dyn↗

arXiv2020

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.

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arXiv2020

Inertial rupture of ultrathin liquid films

Theory and numerical simulations of the Navier-Stokes equations are used to unravel the inertia-driven dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the film thinning regimes at finite Ohnersorge numbers is provided, unifying previous findings. We reveal that, for Ohnesorge numbers smaller than one, the final approach to 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 $h_{\text{min}} \propto τ^{2/5}$, where $h_{\text{min}}$ 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 asymptotically matched with the viscous layers, allowing us to present a complete parameter-free asymptotic description of inertia-driven film rupture.

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arXiv2020

On the flow separation mechanism in the inverse Leidenfrost regime

The inverse Leidenfrost regime occurs when a heated object in relative motion with a liquid is surrounded by a stable vapour layer, drastically reducing the hydrodynamic drag at large Reynolds numbers due to a delayed separation of the flow. To elucidate the physical mechanisms that control separation, here we report a numerical study of the boundary-layer equations describing the liquid-vapour flow around a solid sphere whose surface temperature is above the Leidenfrost point. Our analysis reveals that the dynamics of the thin layer of vaporised liquid controls the downstream evolution of the flow, which cannot be properly described substituting the vapour layer by an effective slip length. In particular, the dominant mechanism responsible for the separation of the flow is the onset of vapour recirculation caused by the adverse pressure gradient in the rearward half of the sphere, leading to an explosive growth of the vapour-layer thickness due to the accumulation of vapour mass. Buoyancy forces are shown to have an important effect on the onset of recirculation, and thus on the separation angle. Our results compare favourably with previous experiments.

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arXiv2020

Stokes theory of thin-film rupture

The structure of the flow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is unraveled by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields $h_{\text{min}} \propto τ^{1/5}$ where $h_{\text{min}}$ is the minimum film thickness and $τ$ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields $h_{\text{min}} \propto τ^{1/3}$, with an opening angle of $37^{\circ}$ off the solid.

physics.flu-dyn↗

arXiv2019

Transition from bubbling to jetting in a co-axial air-water jet

In this Brief Communication we study experimentally the flow regimes that appear in co-axial air-water jets discharging into a stagnant air atmosphere and we propose a simple explanation for their occurrence based on linear, local, spatiotemporal stability theory. In addition to the existence of a periodic bubbling regime for low enough values of the water-to-air velocity ratio, $u=u_w/u_a$, our experiments revealed the presence of a jetting regime for velocity ratios higher than a critical one, $u_c$. In the bubbling regime, bubbles form periodically from the tip of an air ligament whose length increases with $u$. However, when $u> u_c$ a long, slender gas jet is observed inside the core of the liquid coflow. Since in the jetting regime the downstream variation of the flow field is slow, we performed a local, linear spatiotemporal stability analysis with uniform velocity profiles to model the flow field of the air-water jet. Similar to the transition from dripping to jetting in capillary liquid jets, the analysis shows that the change from the bubbling to the jetting regime can be understood in terms of the transition from an absolute to a convective instability.

physics.flu-dyn↗

arXiv2019

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.

physics.flu-dyn↗

arXiv2019

Bubble formation regimes in forced co-axial air-water jets

We report a detailed experimental characterization of the periodic bubbling regimes that take place in an axisymmetric air-water jet when the inner air stream is forced by periodic modulations of the pressure at the upstream air feeding chamber. When the forcing pressure amplitude is larger than a certain critical value, the bubble formation process is effectively driven by the selected frequency, leading to the formation of nearly monodisperse bubbles whose volume is reduced by increasing the forcing frequency. We reveal the existence of two different breakup modes, M1 and M2, under effective forcing conditions. The bubble formation in mode M1 resembles the natural bubbling process, featuring an initial radial expansion of an air ligament attached to the injector, whose initial length is smaller than the wavelength of a small interfacial perturbation induced by the oscillating air flow rate. The expansion stage is followed by a ligament collapse stage, which begins with the formation of an incipient neck that propagates downstream while collapsing radially inwards, leading to the pinch-off of a new bubble. These two stages take place faster than in the unforced case as a consequence of the the air flow modulation induced by the forcing system. The breakup mode M2 takes place with an intact ligament longer than one disturbance wavelength, whereby the interface already presents a local necking region at pinch-off, and leads to the formation of bubbles from the tip of an elongated air filament without an expansion stage. Scaling laws that provide closed expressions for the bubble volume, the intact ligament length, and the transition from the M1 breakup mode to the M2, as functions of the relevant governing parameters, are deduced from the experimental data.

physics.flu-dyn↗

arXiv2019

Natural break-up and satellite formation regimes of surfactant-laden liquid threads

We report a numerical analysis of the unforced break-up of free cylindrical threads of viscous Newtonian liquid whose interface is coated with insoluble surfactants, focusing on the formation of satellite droplets. The initial conditions are harmonic disturbances of the cylindrical shape with a small amplitude $ε$, and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit $ε\to 0$, the problem depends on two dimensionless parameters, namely the Laplace number, $La=ρσ_0 \bar{R}/μ^2$, and the elasticity parameter, $β=E/σ_0$, where $ρ$, $μ$ and $σ_0$ are the liquid density, viscosity and initial surface tension, respectively, $E$ is the Gibbs elasticity and $\bar{R}$ is the unperturbed thread radius. A parametric study is presented to quantify the influence of $La$ and $β$ on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite's surface just prior to pinch-off, $V_{sat}$ and $Σ_{sat}$, respectively. We identify a weak-elasticity regime, $β\lesssim 0.05$, in which the satellite volume and the associated mass of surfactant obey the scaling law $V_{sat} = Σ_{sat} = 0.0042 La^{1.64}$ for $La \lesssim 2$. For $La \gtrsim 10$, $V_{sat}$ and $Σ_{sat}$ reach a plateau of about $3 \%$ and $2.9 \%$ respectively, $V_{sat}$ being in close agreement with previous experiments of low-viscosity threads with clean interfaces. For $La<7.5$, we reveal the existence of a discontinuous transition at a critical elasticity $β_c (La)$, with $β_c \to 0.98$ for $La \lesssim 0.2$, such that $V_{sat}$ and $Σ_{sat}$ abruptly increase. The jumps experienced by both quantities reach a plateau when $La \lesssim 0.2$, while they decrease monotonically as $La$ increases up to $La = 7.5$, where both become zero.

physics.flu-dyn↗

arXiv2019

Start-up flow in shallow deformable microchannels

Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (2018) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modeled as an elastic plate under pure bending satisfying the Kirchhoff-Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter $β$, which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter $γ$ that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, $γ\to 0$, a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with $β$ as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier-Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.

physics.flu-dyn↗

arXiv2019

Temporal stability of free liquid threads with surface viscoelasticity

We analyse the effect of surface viscoelasticity on the temporal stability of a free cylindrical liquid jet coated with insoluble surfactant, extending the results of Timmermans & Lister (J. Fluid Mech., vol. 459, 2002, pp. 289-306). Our development requires, in particular, deriving the correct expressions for the normal and tangential stress boundary conditions at a general axisymmetric interface when surface viscosity is modelled with the Boussinesq-Scriven constitutive equation. These stress conditions are applied to obtain a new dispersion relation for the liquid thread, which is solved to describe its temporal stability as a function of four governing parameters, namely the capillary Reynolds number, the elasticity parameter, and the shear and dilatational Boussinesq numbers. It is shown that both surface viscosities have a stabilising influence for all values of the capillary Reynolds number and elasticity parameter, the effect being more pronounced at low capillary Reynolds numbers. The wavenumber of maximum amplification depends non-monotonically on the Boussinesq numbers, especially for very viscous threads at low values of the elasticity parameter. Finally, two different lubrication approximations of the equations of motion are derived. While the validity of the leading-order model is limited to small enough values of the elasticity parameter and of the Boussinesq numbers, a higher-order parabolic model is able to accurately capture the linearised behaviour for the whole range of values of the four control parameters.

physics.flu-dyn↗

arXiv2018

The nonlinear states of viscous capillary jets confined in the axial direction

We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated that in the absence of axial confinement the steady liquid thread becomes unstable due to an axisymmetric global mode for values of the flow rate, $Q$, below a certain critical value, $Q_c$, giving rise to oscillations of increasing amplitude that finally lead to a dripping regime (Sauter & Buggisch, J. Fluid Mech., 2005; Rubio-Rubio et al., J. Fluid Mech., 2013). Here we focus on the effect of the jet length, $L$, on the transitions that take place for decreasing values of $Q$. The linear stability analysis shows good agreement with our experiments, revealing that $Q_c$ increases monotonically with $L$, reaching the semi-infinite jet asymptote for large values of $L$. Moreover, as $L$ decreases a quasi-static limit is reached, whereby $Q_c \to 0$ and the neutral conditions are given by a critical length determined by hydrostatics. Our experiments have also revealed the existence of a new regime intermediate between steady jetting and dripping, in which the thread reaches a limit-cycle state without breakup. We thus show that there exist three possible states depending on the values of the control parameters, namely steady jetting, oscillatory jetting and dripping. For two different combinations of liquid viscosity, and injector radius, $R$, the boundaries separating these regimes have been determined in the $Q-L$ parameter plane, showing that steady jetting exists for small enough values of $L$ or large enough values of $Q$, dripping prevails for small enough values of $Q$ or sufficiently large values of $L$, and oscillatory jetting takes place in an intermediate region whose size increases with the liquid viscosity and decreases with $R$.

physics.flu-dyn↗

arXiv2017

Global instability of low-density jets

The global stability of laminar axisymmetric low-density jets is investigated in the low Mach number approximation. The linear modal dynamics is found to be characterised by two features: a stable arc branch of eigenmodes and an isolated eigenmode. Both features are studied in detail, revealing that, whereas the former is highly sensitive to numerical domain size and its existence can be linked to spurious feedback from the outflow boundary, the latter is the physical eigenmode that is responsible for the appearance of self-sustained oscillations in low-density jets observed in experiments at low Mach numbers. In contrast to previous local spatio-temporal stability analyses, the present global analysis permits, for the first time, the determination of the critical conditions for the onset of global instability, as well the frequency of the associated oscillations, without additional hypotheses, yielding predictions in fair agreement with previous experimental observations. It is shown that under the conditions of those experiments, viscosity variation with composition, as well as buoyancy, only have a small effect on the onset of instability.

physics.flu-dyn↗

arXiv2014

Global stability analysis of the axisymmetric wake past a spinning bullet-shaped body

We analyze the global linear stability of the axisymmetric flow around a spinning bullet-shaped body as a function of the Reynolds number, $Re=w_{\infty}D/ν$, and of the rotation parameter $Ω=ωD/(2 w_{\infty})$, in the ranges $Re<450$ and $0\leqΩ\leq 1$. Here, $w_{\infty}$ and $ω$ are the free-stream and the body rotation velocities respectively, and $ν$ is the fluid kinematic viscosity. The spectrum and the eigenfunctions obtained allow us to explain the different bifurcations from the axisymmetric state observed in previous numerical studies. Our results reveal that three global eigenmodes, denoted Low-Frequency (LF), Medium-Frequency (MF) and High-Frequency (HF) modes, become unstable in different regions of the $Re-Ω$ parameter plane. We provide precise computations of the corresponding neutral curves, that divide the $Re-Ω$ plane into four different regions: the stable axisymmetric flow prevails for small enough values of $Re$ and $Ω$, while three different frozen states, where the wake structures co-rotate with the body at different angular velocities, take place as a consequence of the destabilization of the LF, MF and HF modes. Several direct numerical simulations of the nonlinear state associated to the MF mode, identified here for the first time, are also reported to complement the linear stability results. Finally, we point out the important fact that, since the axisymmetric base flow is $SO(2)$-symmetric, the theory of equivariant bifurcations implies that the weakly non-linear regimes that emerge close to criticality must necessarily take the form of rotating-wave states. These states, previously referred to as frozen wakes in the literature, are thus shown to result from the base-flow symmetry.

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