A regular perturbation approach to surface tension driven flows

Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed

Surface tension and microgravity

The behaviour of confined liquids on board an orbiting spacecraft is mainly driven by surface tension phenomena, which cause an apparently anomalous response of the liquid when compared with the behaviour that can be observed on an Earth laboratory provided that the amount of liquid is high enough. The reason is that in an orbiting spacecraft the different inertial forces acting on the bulk of the liquid are almost zero, causing thus capillary forces to be the dominant ones. Of course, since gravity forces are proportional to the liquid volume, whereas surface tension forces are proportional to the liquid surface, there are situations on Earth where capillarity can be the dominant effect, as it happens when very small volume liquid samples are considered. However, work with small size samples may require the use of sophisticated optical devices. Leaving aside the neutral buoyancy technique, a way of handling large liquid interfaces is by using drop towers, where the sample falls subjected to the action of Earth's gravity. This approach is suitable when the characteristic time of the problem under consideration is much smaller than the drop time. In this work the transformation of an out-of-use chimney into a drop tower is presented. Because of the miniaturization, hardiness and low cost of current electronic devices, a drop tower can be used as an inexpensive tool for undergraduate students to experimentally analyse a large variety of surface tension driven phenomena.

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications

Evaluation of the surface free energy of plant surfaces: toward standardizing the procedure

Plant surfaces have been found to have a major chemical and physical heterogeneity and play a key protecting role against multiple stress factors. During the last decade, there is a raising interest in examining plant surface properties for the development of biomimetic materials. Contact angle measurement of different liquids is a common tool for characterizing synthetic materials, which is just beginning to be applied to plant surfaces. However, some studies performed with polymers and other materials showed that for the same surface, different surface free energy values may be obtained depending on the number and nature of the test liquids analyzed, materials' properties, and surface free energy calculation methods employed. For 3 rough and 3 rather smooth plant materials, we calculated their surface free energy using 2 or 3 test liquids and 3 different calculation methods. Regardless of the degree of surface roughness, the methods based on 2 test liquids often led to the under- or over-estimation of surface free energies as compared to the results derived from the 3-Liquids method. Given the major chemical and structural diversity of plant surfaces, it is concluded that 3 different liquids must be considered for characterizing materials of unknown physico-chemical properties, which may significantly differ in terms of polar and dispersive interactions. Since there are just few surface free energy data of plant surfaces with the aim of standardizing the calculation procedure and interpretation of the results among for instance, different species, organs, or phenological states, we suggest the use of 3 liquids and the mean surface tension values provided in this study.

Influence of acrylic adhesive viscosity and surface roughness on the properties of adhesive joint

In adhesion, the wetting process depends on three fundamental factors: the surface topography of the adherend, the viscosity of the adhesive, and the surface energy of both. The aim of this paper is to study the influence of viscosity and surface roughness on the wetting and their effect on the bond strength. For this purpose, an acrylic adhesive with different viscosities was synthesized and some properties, such as viscosity and surface tension, were studied before adhesive curing took place. Furthermore, the contact angle and the lap-shear strength were analyzed using aluminum adherends with two different roughnesses. Scanning electron microscopy was used to determine the effect of the viscosity and the roughness on the joint interface. The results showed that the adhesive exhibits an optimal value of viscosity. Below this value, at low viscosities, the low neoprene content produces poor bond strength due to the reduced toughness of the adhesive. Additionally, it also produces a high shrinkage during curing, which leads to the apparition of residual stresses that weakens the interfacial strength. However, once the optimum value, an increase in the viscosity produces a negative effect on the joint strength as a result of an important decrease in the wettability.

Similarities between ion waves in plasmas and gravity waves in incompressible fluids

Some similarities between ion waves in plasmas and gravity waves in incompressible fluids are investigated. It is shown that for zero ion temperature the ion-wave dispersion relation is similar to that of gravity waves in a stratified liquid between rigid, horizontal walls; for large wavelength the ion waves behave as the surface gravity waves of shallow-water theory. The general character of the pattern of ion waves arising in steady plasma flows is analyzed for arbitrary ion temperature, wavelength, and acoustic mach number (which is based on the ion-acoustic speed), and is compared to the pattern of surface gravity waves in steady water flows when surface tension is taken into account.

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids.

The stability of a liquid layer with an undeformable interface open to the atmo- sphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature dif- ference applied on the system. Depending on the liquid depth, this basic flow is desta- bilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturba- tions are driven by the basic flow and therefore one must distinguish between convec- tive and absolute thresholds. The instability mechanisms as well as the di¿erent re- gimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr 1?4 10Þ. In partic- ular, it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally

Statistical distributions obtained from the compression of monodisperse, soft and frictionless particles

The cyclic compression of several granular systems has been simulated with a molecular dynamics code. All the samples consisted of bidimensional, soft, frictionless and equal-sized particles that were initially arranged according to a squared lattice and were compressed by randomly generated irregular walls. The compression protocols can be described by some control variables (volume or external force acting on the walls) and by some dimensionless factors, that relate stiffness, density, diameter, damping ratio and water surface tension to the external forces, displacements and periods. Each protocol, that is associated to a dynamic process, results in an arrangement with its own macroscopic features: volume (or packing ratio), coordination number, and stress; and the differences between packings can be highly significant. The statistical distribution of the force-moment state of the particles (i.e. the equivalent average stress multiplied by the volume) is analyzed. In spite of the lack of a theoretical framework based on statistical mechanics specific for these protocols, it is shown how the obtained distributions of mean and relative deviatoric force-moment are. Then it is discussed on the nature of these distributions and on their relation to specific protocols.

Ultrastructure of Plant Leaf Cuticles in relation to Sample Preparation as Observed by Transmission Electron Microscopy

The leaf cuticular ultrastructure of some plant species has been examined by transmission electron microscopy (TEM) in only few studies. Attending to the different cuticle layers and inner structure, plant cuticles have been grouped into six general morphological types. With the aim of critically examining the effect of cuticle isolation and preparation for TEM analysis on cuticular ultrastructure, adaxial leaf cuticles of blue-gum eucalypt, grey poplar, and European pear were assessed, following a membrane science approach. The embedding and staining protocols affected the ultrastructure of the cuticles analysed. The solubility parameter, surface tension, and contact angles with water of pure Spurr's and LR-White resins were within a similar range. Differences were however estimated for resin : solvent mixtures, since Spurr’s resin is combined with acetone and LR-White resin is mixed with ethanol. Given the composite hydrophilic and lipophilic nature of plant cuticles, the particular TEM tissue embedding and staining procedures employed may affect sample ultrastructure and the interpretation of the results in physicochemical and biological terms. It is concluded that tissue preparation procedures may be optimised to facilitate the observation of the micro- and nanostructure of cuticular layers and components with different degrees of polarity and hydrophobicity.

The breaking of axisymmetric slender liquid bridges

Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems

Stability of slender, axisymmetric liquid bridges between unequal disks

The stability of slender, axisymmetric liquid bridges held by surface tension forces between two coaxial, parallel solid disks having different radii is studied by using standard perturbation techniques. The results obtained show that the behaviour of such configurations becomes similar to that of liquid bridges between equal disks when subject to small axial gravity forces.

Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray

La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.

On the use of liquid bridges as accelerometers

The shape of the interface of a drop of liquid held by surface tension forces between two solid disks,a liquid bridge, depends on the geometry of the supporting disks, the volume of liquid and the external forces acting on the drop. Therefore, once the geometry of the supporting disks and the volume of liquid are fixed, and assuming that the value of the surface tension is known, a way to measure such external forces could be by measuring the deformation of the liquid bridge interface.

Estudio de la movilidad que presenta el diésel en un suelo contaminado empleando surfactantes

La contaminación de suelos con hidrocarburos de petróleo en México es un problema que se ha vuelto muy común en nuestros días, debido principalmente a derrames, así como a las actividades propias de la industria petrolera. Algunos suelos contaminados, principalmente en el sureste de México, contienen concentraciones de hidrocarburos hasta de 450,000 mg/kg. Por dichas razones, una de las preocupaciones de las autoridades ambientales es el desarrollo de tecnologías eficientes y económicamente factibles que permitan la eliminación de este tipo de contaminantes. El saneamiento del sitio se puede lograr a través de diversos procedimientos, como son la aplicación de métodos físicos, químicos y biológicos (o combinaciones de ellas). La elección de un método depende de la naturaleza del contaminante, su estado físico, concentración, tipo de suelo, espacio físico disponible, tiempo destinado para su tratamiento, así como de los recursos económicos disponibles. Previa a la aplicación de la tecnología es necesario la realización de un diagnóstico de la contaminación del suelo, con el fin de conocer el tipo, concentración y distribución de los contaminantes presentes, así como el volumen de suelo a tratar, las condiciones climáticas de la zona, y características físicas del lugar (vías de acceso y servicios, entre otros). En la presente tesis, el empleo de surfactantes, se ha propuesto como una técnica para incrementar la movilidad de contaminantes orgánicos hidrofóbicos (HOCs) como hidrocarburos totales del petróleo (HTPs), bifenilos policlorados (PCBs), Benceno, Tolueno, Xilenos, explosivos, clorofenoles, pesticidas, entre otros, y así facilitar su degradación. Los surfactantes debido a que reducen la tensión superficial del agua, son moléculas formadas por grupos polares hidrofílicos y largas cadenas carbonadas hidrofóbicas. Sus grupos polares forman puentes hidrógeno con las moléculas de agua, mientras que las cadenas carbonadas se asocian a los hidrocarburos debido a interacciones hidrofóbicas que estos presentan. En soluciones acuosas, los surfactantes forman estructuras esféricas organizadas llamadas micelas. La solubilización de los contaminantes se lleva a cabo solamente cuando se forma la fase micelar, la cual se obtiene cuando la concentración del surfactante es superior a la concentración micelar crítica (CMC), es decir, arriba de la concentración de la cual el monómero se comienza a auto-agregar. La eficiencia de desorción de diésel por un surfactante depende de su naturaleza, de la dosis empleada, de la hidrofobicidad del contaminante, de la interacción surfactante-suelo y del tiempo de contacto surfactante-suelo. Sin embargo, la mejor eficiencia de desorción no está siempre relacionada con la mejor eficiencia de movilidad o solubilidad, debido principalmente a que el empleo de una alta concentración de surfactante puede inhibir la movilización. De acuerdo con información proporcionada por la Procuraduría Federal de Protección al Ambiente (PROFEPA), a la fecha no se ha llevado a cabo en México ninguna restauración de sitios específicamente contaminados con diésel, la técnica de lavado de suelos. Por lo anterior existe la necesidad de emplear la técnica de lavado de suelos ex situ. Específicamente en el suelo extraído de la ex refinería 18 de marzo ubicada en el Distrito Federal México y empleando una solución de surfactantes con agua desionizada, la cual consiste ponerlos en contacto con el suelo contaminado con diésel por medio de columnas de lavado cilíndricas, para lograr la remoción del contaminante. Se emplearon como surfactantes el lauril sulfato de sodio, lauril éter sulfato de sodio y Glucopon AV-100 a diferentes concentraciones de 0.5 a 4.0 [g/L], lográndose obtener una eficiencia del 80 % con este último surfactante. El lavado de suelos contaminados con diésel empleado surfactantes, es una tecnología que requiere que se profundice en el estudio de algunas variables como son el tipo de surfactante, concentración, tiempo de lavado, fenómenos de difusión, desorción, propiedades termodinámicas, entre otros. Los cuales determinarán el éxito o fracaso de la técnica empleada. Nowadays, soil pollution with oil in Mexico is a very common issue due mainly to both oil spill and oil activities. For example, mainly in the southeast area of Mexico, polluted soil contains high concentrations of hydrocarbons, up to 450,000 mg/kg. For these reasons, enviromental authorities have the concern in developing economically feasible and efficient technology that allow the elimination of these type of contaminants. The sanitation in sites can be achieved through several procedures such as physical, chemical and biological methods (or a combination among them). The choice of a method depends on the nature and physical state of the contaminant, the concentration, type of soil, physical space available, time consumption and financial resources. Before any technological application, a diagnostic of the polluted soil is necessary in order to know the type, concentration and distribution of contaminants as well as the soil volume, climatic conditions and physical features of the place (access routes and services, among others). In this thesis, surfactants has been proposed as a technique to increase the mobility of hydrophobic-organic contaminants (HOCs), e.g. total hydrocarbons of petroleum, polychlorinated biphenyls, benzene, toluene, xylenes, explosives, chlorophenols, pesticides, among others, and, hence, to facilitate degradation. Since surfactants reduce the water surface tension, they are molecules comprised of hydrophilic polar groups and long-hydrophobic carbon chains. Surfactant’s polar groups form hydrogen bonding with water molecules while carbon chains, i.e. hydrocarbon chains, have hydrophobic interactios. In aqueous solutions, surfactants form self-organised spherical structures called micelles. The solubilisation of contaminants is carried out only when the micellar phase is formed. This is obtained when the surfactant concentration is higher than the crítical micelle concentration (CMC), i.e. above the concentration where the surfactant monomer begins to self-aggregate. The diesel efficiency desorption by surfactants depends on their nature, the dose use, the contaminant hydrophobicity, the surfactant-soil interaction and the contact time with surfactant soil. However, the best desorption is not always related with the best either mobility or solubility efficiency since high concentration of surfactant can inhibit mobilisation. According to information of the Federal Bureau of Environmental Protection (PROFEPA), up today, there is not any restauration of diesel-polluted sites using the washing-soil technique. Due to the above, there exist the necessity of employing the waching-soil technique ex situ. More specifically, a sample soil from the oil-refinery of “18 de marzo” in Mexico city was extracted and a surfactant solution with deionised water was put in contact with the diesel contaminated soil by means of cylindrical waching columns in order to remove the contaminant. The surfactants employed in this work were sodium lauryl sulfate, sodium lauryl ether sulfate and Glucopon AV-100 at different concentrations of 0.5 to 4 [g/L], obtaining a efficiency of 80 % with this last surfactant. The washing of diesel-polluted soil using surfactants is a technology which requires a deeper study of some variables such as the type of surfactant, concentration, washing time, difusión phenomena, desorption, thermodynamic properties, among others. These parameters determine the succes or failure of the employed technique.

Hydrostatic instabilities in floating zone cristal growth process

If only Fluid Mechanics aspects are considered, the configuration appearing in the floating zone technique for crystal growth can be modelled as a mass of liquid spanning between two solid rods. Besides, if now the influence of temperature gradients and heat flow are not considered, the simplest fluid model consists of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart: the so called liquid bridge. As it is well known, if both supporting disks were parallel, coaxial and of the same diameter, 2R, the volume of liquid, V, were equal to that of a cylinder of the same L and R (V=KR~L) and no body forces were acting on the liquid column, the fluid configuration (under these conditions of cylindrical shape) will become unstable when the distance between the disks equals the length of the circumference of the supporting disks (L=2KR, the so-called Rayleigh stability limit). One should be aware that the Rayleigh stability limit can be dramatically modified when the geometry differs from the above described cylinder (due to having non-coaxial disks, different diameter disks, liquid volume different from the cylindrical one, etc) or when other external effects like accelerations either axial or lateral are considered. In this paper the stability limits of liquid bridges considering different types of perturbations are reviewed.