Dr. Alejandro Guillermo González

Alejandro G. González, Javier A. Diez, Roberto Gratton, Diego M. Campana, and Fernando A. Saita. Instability of a viscous liquid coating a cylindrical fibre. Journal of Fluid Mechanics, 651:117, March 2010. [ bib | DOI | http ]

The instability of a liquid layer coating the surface of a thin cylindrical wire is studied experimentally and numerically with negligible gravity effects. The initial uniform film is obtained as the residual of a sliding drop, and the thickness measurements are performed with an anamorphic optical system that compresses the vertical scale (allowing to observe several wavelengths) and widens the horizontal one (to follow in detail the evolution of local minima and maxima). Experimental timelines showing the growth and position of the maxima and minima are compared with linear theory and fully nonlinear simulations. A primary mode grows in the early stages of the instability, and its wavelength λ1 is not always in agreement with that corresponding to the maximum growth rate predicted by the linear theory λm. In later stages, a secondary mode appears, whose wavelength is half that of the primary mode. The behaviour of the secondary mode allows us to classify the experimental results into two cases, depending on whether it is linearly stable (case I) or unstable (case II). In case I, the amplitude of the secondary mode remains small compared with that of the primary one, while in case II both amplitudes may become very similar at the end. Thus, the distance between the final drops may be quite different from that seen between initial protuberances. The analysis of the experiments allows us to define a simple criterion based on the comparison between λ1 and λm. Contrary to the predictions of widely used previous quasi-static theories, experiments show that the relation between maximum and minimum of the primary mode is better approximated by a kinematic model based on the assumption that primary maxima increase as fast as the minima decrease. Numerical simulations confirm this hypothesis.

Javier A Diez, Alejandro G González, and Lou Kondic. Stability of a finite-length rivulet under partial wetting conditions. Journal of Physics: Conference Series, 166:012009, May 2009. [ bib | DOI | http ]

We study the stability of a finite-length fluid rivulet at rest on a partially wetting surface. We consider the problem by including the intermolecular force (van der Waals interaction) within the framework of the lubrication approximation. The results are validated by comparison with numerical simulations of the full nonlinear equation. For finite length rivulets, we show that the distance between drops after breakup is very close to the wavelength of maximum growth rate predicted by the linear theory for infinite rivulets. Finally, we compare theoretical and numerical results with reported experimental data.

Keywords: Fluid dynamics,Soft matter,Surfaces,interfaces and thin films,liquids and polymers

Javier A. Diez, Alejandro G. González, and Lou Kondic. On the breakup of fluid rivulets. Physics of Fluids, 21(8):082105, 2009. [ bib | DOI | http ]

We study the stability of rivulets on horizontal substrates. The implemented model includes the effects of capillarity, fluid-solid interaction, and gravity if appropriate, within the framework of the lubrication approximation. We find that the results compare favorably with those in literature, in the regime where previous analyses are valid. By isolating the effect of van der Waals interactions for nanoscale rivulets, and of gravity for macrosize rivulets, we are able to analyze the influence of these forces on the stability. We discuss in detail the scaling of the emerging wavelengths (distance between drops formed after the breakup process) with the rivulet cross-sectional area. Perhaps surprisingly, we uncover close connection between this scaling and the one for the breakup of a free-space fluid jet (Rayleigh–Plateau instability). Finally, we consider rivulets of finite length and find that the finite size effects are considerably different from the ones obtained previously for semi-infinite fluid films.

Keywords: drops,flow instability,jets,lubrication

J. Gomba, J. Diez, R. Gratton, A. González, and L. Kondic. Stability study of a constant-volume thin film flow. Physical Review E, 76(4):046308/1-12, October 2007. [ bib | DOI | http ]

We study the stability of a constant volume of fluid spreading down an incline. In contrast to the commonly considered flow characterized by constant fluid flux, in the present problem the base flow is time dependent. We present a method to carry out consistently linear stability analysis, based on simultaneously solving the time evolution of the base flow and of the perturbations. The analysis is performed numerically by using a finite-difference method supplemented with an integral method developed here. The computations show that, after a short transient stage, imposed perturbations travel with the same velocity as the leading contact line. The spectral analysis of the modes evolution shows that their growth rates are, in general, time dependent. The wavelength of maximum amplitude, λmax, decreases with time until it reaches an asymptotic value which is in good agreement with experimental results. We also explore the dependence of λmax on the cross sectional fluid area A, and on the inclination angle α of the substrate. For considered small A’s, corresponding to small Bond numbers, we find that the dependence of λmax on A is in good agreement with experimental data. This dependence differs significantly from the one observed for the films characterized by much larger A’s and Bond numbers. We also predict the dependence of λmax on the inclination angle α.

A. G. González, J. Diez, R. Gratton, and J. Gomba. Rupture of a fluid strip under partial wetting conditions. Europhysics Letters, 77(February):440011-440015, 2007. [ bib | DOI ]

We study the evolution of a long strip of viscous fluid on a horizontal glass substrate under partial-wetting conditions. This initial condition develops into an array of quasi-equidistant drops. The special feature of this dewetting scenario is that the pearling process, consisting of successive stages of bulge growth and pinching-off, does not occur simultaneously along the strip but propagates from the ends toward the strip center. We find that the footprint of each drop corresponds to two crossed elliptical shapes and report measurements of the breakup process and the dewetting dynamics.

Keywords: Flow instabilities,Liquid thin films,Low-Reynolds number (creeping) flows

J. Diez, A. G. González, J. Gomba, R. Gratton, and L. Kondic. Unstable spreading of a fluid filament on a vertical plane: Experiments and simulations. Physica D: Nonlinear Phenomena, 209(1-4):49-61, September 2005. [ bib | DOI | http ]

We present results of experiments and numerical simulations on the spreading of a constant volume (CV) of fluid flowing down a vertical plate in the form of a micrometric thin film. In the experiments, the initial condition is generated from a horizontal fluid filament (PDMS) of typical diameter ≈ 0.4 mm, and the flow is probed with two optical techniques: one based on an anamorphic system, and the other on the schlieren method. The first one yields the thickness profile and the second one captures the bidimensional pattern of the transversal film instability. The numerical simulations are performed under the lubrication approximation and using a precursor film to overcome the contact line divergence. The comparison between numerical and experimental profiles shows a very good agreement, and therefore allows to estimate the thickness of the precursor film needed to model the flow. We find that this thin precursor (of thickness 43 nm) is very demanding for the numerical description of the instability, since it requires the use of a very fine grid. We show that the use of thicker precursor allows to obtain numerical results which describe qualitatively well the experimental data. In order to study the early times of the instability, we develop a linear model to account for the evolution of the modal amplitudes of the spatial Fourier spectrum of the contact line of the advancing front (frontline). The model is in good agreement with both experiments and simulations for the appropriate precursor film thickness in each case. We find that the precursor film thickness mainly influences the growth rates of the unstable modes, but it does not modify the main features of instability development.

Keywords: Contact line,Instability,Liquid thin films

J. Gomba, J. Diez, A. González, and R. Gratton. Spreading of a micrometric fluid strip down a plane under controlled initial conditions. Physical Review E, 71(1):016304/8-11, January 2005. [ bib | DOI | http ]

We experimentally study the spreading of a small volume of silicon oil down a vertical plane with small Bond number. The initial condition is characterized by a horizontal long fluid strip with cross sectional area A and width w0. We find that the experiments are characterized by a unique nondimensional parameter, R∝w04∕(a2A), where a is the capillary length. An empirical criterium to estimate the onset of the contact line instability is established. The later rivulet formation at the contact line leads to a pattern which is characterized by a dominant wavelength. We find that this wavelength is approximately proportional to R−1∕4.

A. G. González, J. Diez, J. Gomba, R. Gratton, and L. Kondic. Spreading of a thin two-dimensional strip of fluid on a vertical plane: experiments and modeling. Physical Review E – Statistical, Nonlinear and Soft Matter Physics, 70(2 Pt 2):026309, 2004. [ bib | DOI | http ]

We study the thin-film flow of a constant volume of silicon oil (polydymethilsiloxane) spreading down a vertical glass plate. The initial condition is generated from a horizontal fluid filament of typical diameter 0.4 mm. Two optical diagnostic methods are used: One based on an anamorphic system, and the other on the Schlieren method. The first one allows for a detailed characterization of the early stable stage of the spreading which is used to estimate the thickness of the precursor film needed to model the flow. The second one captures the bidimensional pattern of the transversal film instability. We use these techniques to determine the film thickness profiles, and the evolution of the moving contact line, including its shape and Fourier spectra. The numerical simulations of the stable stage of spreading are in good quantitative agreement with the experimental results. We develop a model based on linear stability theory that predicts the evolution of the modes present in the linear stage of the instability.

Alejandro G. González, G. Julio, Fausto T. Gratton, and Charles J. Farrugia. Compressible kelvin-helmholtz instability at the terrestrial magnetopause. Brazilian Journal of Physics, 32(4):945, 2002. [ bib | DOI | http ]

The compressible magnetohydrodynamic Kelvin-Helmholtz instability occurs in two varieties, one that can be called incompressible as it exists in the limit of vanishing compressibility (primary instability), while the other exists only when compressibility is included in the model (secondary instability). In previous work we developed techniques to investigate the stability of a surface of discontinuity between two different uniform ows. Our treatment includes arbitrary jumps of the velocity and magnetic fields as well as of density and temperature, with no restriction on the wave vector of the modes. Then it allows stability analyses of complex configurations not previously studied in detail. Here we apply our methods to investigate the stability of various typical situations occurring at different regions of the front side, and the near anks of the magnetopause. The physical conditions of the vector and scalar fields that characterize the equilibrium interface at the positions considered are obtained both from experimental data and from results of simulation codes of the magnetosheath available in the literature. We give particular attention to the compressible modes in configurations in which the incompressible modes are stabilized by the magnetic shear. For configurations of the front of the magnetopause, which have small relative velocities, we find that the incompressible MHD model gives reliable estimates of their stability, and compressibility effects do not introduce significant changes. However, at the anks of the magnetopause the occurrence of the secondary instability and the shift of the boundary of the primary instability play an important role. Consequently, configurations that are stable if compressibility is neglected turn out to be unstable when it is considered and the stability properties are quite sensitive on the values of the parameters. Then compressibility should be taken into account when assessing the stability properties of these configurations, since the estimates based on incompressible MHD may be misleading. A careful analysis is required in each case, since no simple rule of thumb can be given.

Alejandro G. González, Marisa González, and Julio Gratton. The kelvin-helmholtz instability in compressible plasmas with magnetic field shear. AIP Conference Proceedings, 563(1):47-52, April 2001. [ bib | DOI | http ]

We investigate the effect of compressibility and magnetic field shear on the Kelvin-Helmholtz instability in compressible stratified plasmas. We obtain two main results. First, for sufficiently low velocities the compressibility stabilizes the unstable modes present in an incompressible model (called main modes). This represents an important difference with the case without magnetic field shear. Second, new unstable modes appear (called secondary) which owe their existence to compressive perturbations. The secondary modes (of compressive character) determine the stability for values of velocity of the unperturbed flow that correspond to stable primary modes. In these cases the compressive modes do not disappear and may have appreciable growth rates. Therefore, compressibility effects may be relevant when discussing the stability of problems with magnetic field shear. Diagrams of stability and growth rates are shown thatallow an easy visualization of the stability properties of aconfiguration.

Keywords: compressible flow,magnetic fields,plasma instability,plasma magnetohydrodynamics,plasma simulation,shear flow

Alejandro G. González and Julio Gratton. Reaction forces on a ladder leaning on a rough wall. American Journal of Physics, 64(8):1001-1005, August 1996. [ bib | DOI | http ]

The determination of the reactions on a ladder is discussed including friction against the wall. In a recent article, this problem was studied considering elastic compression and it was argued that an additional condition holds that allows one to find all the reactions. We show that this condition is incorrect for typical ladders, when flexion is important. We clarify the issues of static determinacy by means of an analysis that takes into account both compression and flexion. We find that when the climber arrives at the top, the result depends on which deformation prevails. We conclude that the reactions can never be determined using only statics, because there is no way to ascertain which kind of deformation dominates, and so which limiting condition will be attained, if any.

AG González and J. Gratton. The role of a density jump in the kelvin—helmholtz instability of compressible plasma. Journal of Plasma Physics, 32(2):223-244, 1994. [ bib | DOI | http ]

The hydromagnetic Kelvin–Helmholtz instability is relevant in many complex situations in astrophysical and laboratory plasmas. Many cases of interest are very complicated, since they involve the combined role of velocity shear, of density and magnetic field stratification, and of various geometries in compressible plasmas. In the present work we continue investigating the influence of various physical and geometrical parameters of the plasma on the Kelvin–Helmholtz modes. We use the general dispersion relation for the ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas. We study analytically the existence and properties of the modes and their stability, for a velocity jump combined with a density jump, and for any relative orientation of B, u and k (B is continuous). Stability is analysed by means of a general procedure that allows discussion of any configuration and all kinds of perturbations. The boundaries between modes of different kinds are discussed. In contrast to the case of uniform density, for a density jump there are no monotonically unstable modes, only overstabilities. The unstable modes belong to two types. Those with the largest growth rates tend to monotonically unstable modes in the limit of uniform density, and are related to the torsional Alfvén mode. The other overstable modes have no analogue among the purely incompressible modes, and occur in a range of U that is stable in the incompressible limit. We derive bounds for the growth rate of the instability. The present results may serve as a guide to interpret results in more complicated and realistic situations as those occurring in laboratory and natural plasmas.

AG González and J. Gratton. The kelvin–helmholtz instability in a compressible plasma: the role of the orientation of the magnetic field with respect to the flow. Journal of Plasma Physics, 51(01):43-60, 1994. [ bib | DOI | http ]

The hydromagnetic Kelvin–Helmholtz instability is relevant in many complex situations in astrophysical and laboratory plasmas. Many cases of interest are very complicated, since they involve the combined roles of velocity shear, density and magnetic field stratification, and various geometries in compressible plasmas. The present work is part of a systematic investigation of the influence of the various physical and geometrical parameters characterizing the plasmas on the Kelvin–Helmholtz modes. The general dispersion relation for ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas is derived. The existence and characteristics of the modes and their stability are studied analytically for any relative orientation of B, u and k, for continuous B and ρ. It is shown that the stability of a given configuration cannot be determined by considering only special orientations of k (say flute or parallel modes). The results obtained here may serve as a guide to interpret results in more complicated and realistic situations, such as those occurring in experiments and natural plasmas.

AG Gonzalez and Julio Gratton. Compressibility effects on the gravitational instability of a plasma-vacuum interface. Plasma Physics and Controlled Fusion, 32(1):3-19, 1990. [ bib | DOI | http ]

The stability of gravitational compressible surface modes of a plasma-vacuum interface is investigated. Stratified equilibrium profiles of density and magnetic field in the plasma are considered. The corresponding boundary conditions for magnetohydrodynamic linear perturbations are deduced. Three types of surface normal modes (slow, intermediate and fast) may appear. The slow mode is unstable below a critical wavenumber. The stability criterion is affected in general by the compressibility. The growth rate of the unstable modes is increased by compressibility. It is shown that for ‘flute’ or pure interchange modes with respect to the vacuum magnetic field (but not with respect to the equilibrium magnetic field in the plasma) the compressibility enlarges the instability domain of surface modes. The interval of existence of unstable surface perturbations, as well as their growth rates, are larger than those of the internal unstable modes. Intervals of non-existence of surface modes appear for the flute perturbations with respect to the plasma magnetic field. The critical values of the wavenumber below which the modes are unstable, are discussed in general.

Alejandro G. González and Julio Gratton. Comments on “linear waves and stability in ideal magnetohydrodynamics” [phys. fluids 30, 3673 (1987)]. Physics of Fluids B: Plasma Physics, 1(6):1339, 1989. [ bib | DOI | http ]

It is shown that the most dangerous modes for stability of the slab geometry case considered by Eckhoff are not flute modes but quasi‐interchange perturbations

Keywords: FLUIDS,MAGNETOHYDRODYNAMICS,OSCILLATION MODES,SLABS,STABILITY

J. Gratton, FT Gratton, and AG González. Convective instability of internal modes in accelerated compressible plasmas. Plasma Physics and Controlled Fusion, 30(4):435, 1988. [ bib | DOI | http ]

A compact second order differential equation for small amplitude magnetohydrodynamic modes of a plasma stratification in a uniform effective gravity field is derived. The steady state includes non-uniform density, mass motion, magnetic shear and non-isotropic pressure, given by arbitrary profiles. The perturbation treatment is of the magnetohydrodynamic class, with two closure equations for the time evolution of the pressure, in order to encompass ideal MHD, the Chew et al. (1956) and other non-isotropic models. As an application a detailed study of the compressible, convective-gravity modes in the ideal isotropic MHD case is presented. Local criteria for the convective instability are first obtained by means of physically intuitive arguments for unidirectional and for sheared magnetic field. In both instances a rigorous variational energy treatment is then provided. In the second case, a criterion analogous to that of B.R. Suydam (1958) for the pinch is shown to hold for plasma atmospheres. Global internal modes for an isothermal equilibrium with unidirectional magnetic field are then analysed. Stability criteria and growth rates of the unstable modes are studied. Areas of application of the reported results are indicated.

FT Gratton and AG Gonzalez. The influence of viscosity and magnetic shear on rayleigh-taylor modes of plasma. Plasma Physics and Controlled Fusion, 28(1976):18071821, 1986. [ bib | DOI | http ]

The equations of gravitational modes of stratified, incompressible and ideally conducting fluids, with a viscous tensor in a sheared magnetic field are given. Boundary conditions at fluid discontinuities are derived. Properties of the frequency spectrum are obtained from variational principles. A detailed description of the modes and the Rayleigh-Taylor instability is given for a plasma-vacuum interface, with different magnetic fields on each side, in three cases: isotropic viscous properties, vc>> omega ci( omega ci, ion cyclotron frequency; vc, ion collision frequency) and non isotropic viscous properties in the limit omega ci>>vc for k//B0, which is dominated by dissipative forces and for k perpendicular to B0, which is governed by gyroscopic forces. Applications of the theory to accelerated plasmas are discussed

Fausto T. Gratton and Alejandro G. González. A minimum dissipation principle for the rayleigh-taylor problem in viscous magnetohydrodynamics. Physics Letters A, 105(7):365-367, October 1984. [ bib | DOI | http ]

A variational principle for magnetohydrodynamic gravitational modes, including isotropic viscosity and the shear of magnetic field lines, is given. It is shown to imply a minimum dissipation requirement for the modes. A sufficient condition for stability given in the literature for the case of ordinary fluids is corrected here.

Keywords: GRAVITATIONAL FIELDS,LAGRANGE MULTIPLIERS,MAGNETOHYDRODYNAMIC FLOW,MAGNETOHYDRODYNAMIC STABILITY,PLASMA TURBULENCE,PLASMA-ELECTROMAGNETIC INTERACTION,REYNOLDS NUMBER,TAYLOR INSTABILITY,VARIATIONAL PRINCIPLES,VISCOUS FLOW