Theory of wetting-induced fluid entrainment by advancing contact lines on dry surfaces

R. Ledesma-Aguilar, A. Hernández-Machado, I. Pagonabarraga

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We report on the onset of fluid entrainment when a contact line is forced to advance over a dry solid of arbitrary wettability. We show that entrainment occurs at a critical advancing speed beyond which the balance between capillary, viscous, and contact-line forces sustaining the shape of the interface is no longer satisfied. Wetting couples to the hydrodynamics by setting both the morphology of the interface at small scales and the viscous friction of the front. We find that the critical deformation that the interface can sustain is controlled by the friction at the contact line and the viscosity contrast between the displacing and displaced fluids, leading to a rich variety of wetting-entrainment regimes. We discuss the potential use of our theory to measure contact-line forces using atomic force microscopy and to study entrainment under microfluidic conditions exploiting colloid-polymer fluids of ultralow surface tension.

AFM measurements and lipid rearrangements: evidence from red blood cell shape changes

K. A. Melzak, G. R. Lázaro, A. Hernández-Machado, I. Pagonabarraga, J. M. Cadenas Díaz de Espada, J. L. Toca-Herrera

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Application of force to echinocytes during atomic force microscopy measurements was shown to be able to convert the cells to stable discocyte shapes. The echinocyte shape is associated with a relative excess of the area of the outer leaflet of the cell membrane; the AFM measurements are therefore associated with a change in the relative areas of the inner and outer membrane leaflets. It was hypothesized that localised damage in the lipid bilayer that is caused by an AFM tip can permit the lipids to flip-flop between the two membrane leaflets, thus changing their relative areas. The conditions in which AFM measurements on cells could induce shape changes were investigated both experimentally and by modelling. The relative area change of the membrane leaflets, attributed here to lipid movement, was characterised in terms of the membrane energy levels; membrane energy was calculated using a version of the area-difference-elasticity model that was applied to predetermined shapes, rather than being used to generate shapes as solutions found at the energy minima. Shapes were generated by rotation of Cassini ovals with a superimposed undulation in order to generate spikes similar to those of the echinocytes. The membrane energy was considered as a function of the membrane curvature, the area difference between the two membrane leaflets, and the deformation of the cytoskeleton. This led to the conclusions that the minimisation of the membrane energy causes the lipid translocation, with the relaxation of the cytoskeleton being a significant driving force.

Phase-field model for the morphology of monolayer lipid domains

F. Campelo, A. Cruz, J. Pérez-Gil, L. Vázquez, A. Hernández-Machado

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Phase-separated domains exist in multicomponent lipid monolayers and bilayers. We present here a phase-field model that takes into account the competition between lipid dipole-dipole interactions and line tension to define the domain morphology. A dynamic equation for the phase-field is solved numerically showing stationary non-circular shapes like starfish shapes. This phase-field model could be applied to study the dynamic properties of complex problems like phase segregation in pulmonary surfactant membranes and films.

Controlling viscoelastic flow in microchannels with slip

Bravo-Gutiérrez, M.E, Castro, M, Hernández-Machado, A, Corvera-Poiré, E

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Growth saturation of unstable thin films on transversed-striped hydrophilic-hydrophobic micropatterns;

R. Ledesma-Aguilar, A. Hernández-Machado, I. Pagonabarraga

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Curvature multiphase-field model for phase separation on a membrane

C. Varea, R.A. Barrio, A. Hernández-Machado

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Tumor angiogenesis and vascular patterning: A mathematica model;

R.D.M. Travasso, E. Corvera Poiré, M. Castro, J.C. Rodriguez-Manzanreque, A. Hernández-Machado

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Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools.

Pinning and avalanches in hydrophobic microchanels;

M. Queralt-Martin, M. Pradas, R. Rodriguez-Trujillo, E. Arundell, A. Hernández-Machado

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Rare events appear in a wide variety of phenomena such as rainfall, floods, earthquakes, and risk. We demonstrate that the stochastic behavior induced by the natural roughening present in standard microchannels is so important that the dynamics for the advancement of a water front displacing air has plenty of rare events. We observe that for low pressure differences the hydrophobic interactions of the water front with the walls of the microchannel put the front close to the pinning point. This causes a burstlike dynamics, characterized by series of pinning and avalanches, that leads to an extreme-value Gumbel distribution for the velocity fluctuations and a nonclassical time exponent for the advancement of the mean front position as low as 0.38.

Controlled drop emission by wetting properties in driven liquid filaments;

R. Ledesma-Aguilar, R. Nistal, A. Hernandez-Machado, I. Pagonabarraga

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The controlled formation of micrometre-sized drops is of great importance to many technological applications 1, 2, 3, 4, 5. Here we present a wetting-based destabilization mechanism of forced microfilaments on either hydrophilic or hydrophobic stripes that leads to the periodic emission of droplets. The drop emission mechanism is triggered above the maximum critical forcing at which wetting, capillarity, viscous friction and gravity can balance to sustain a stable driven contact line. The corresponding critical filament velocity is predicted as a function of the static wetting angle, which can be tuned through the substrate behaviour, and shows a strong dependence on the filament size. This sensitivity explains the qualitative difference in the critical velocity between hydrophilic and hydrophobic stripes, and accounts for previous experimental results of splashing solids6. We demonstrate that this mechanism can be used to control independently the drop size and emission period, opening the possibility of highly monodisperse and flexible drop production techniques in open microfluidic geometries.

Flower development as an interplay between dynamical physical field and genetic networks;

R.A. Barrio, A. Hernández-Machado, C. Varea, J.R. Romero-Arias, E.R. Alvarez-Buylla

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Dynamics of gravity driven three dimensional thin films on hydrophilic-hydrophobic patterned substrates;

Rodrigo Ledesma-Aguilar, Aurora Hernandez-Machado, Ignacio Pagonabarrag

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We investigate numerically the dynamics of unstable gravity driven three-dimensional thin liquid films on hydrophilic-hydrophobic patterned substrates of longitudinal stripes and checkerboard arrangements. The thin film can be guided preferentially on hydrophilic longitudinal stripes, while fingers develop on adjacent hydrophobic stripes if their width is large enough. On checkerboard patterns, the film fingering occurs on hydrophobic domains, while lateral spreading is favoured on hydrophilic domains, providing a mechanism to tune the growth rate of the film. By means of kinematical arguments, we quantitatively predict the growth rate of the contact line on checkerboard arrangements, providing a first step towards potential techniques that control thin film growth in experimental setups.

Activity statistics, avalanche kinetics and velocity correlations in surface growth;

J.M. López, M. Pradas, A. Hernandez-Machado

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Constricting force of filamentary protein rings evaluated from experimental results.

I. Horger, F. Campelo, A. Hernández-Machado, P. Tarazona

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Frequency-induced stratification in viscoelastic microfluidics;

E. Corvera Poire, A Hernández-Machado

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Avalancha dynamics in fluid imbibition near the depinning transition

Marc Pradas, Juan M. López, A. Hernández-Machado

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Single-phase-field model of stepped surfaces

M. Castro, A. Hernández-Machado, R. Cuerno

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We formulate a phase-field description of step dynamics on vicinal surfaces that makes use of a single dynamical field, at variance with previous analogous works in which two coupled fields are employed, namely, a phase-field proper plus the physical adatom concentration. Within an asymptotic sharp interface limit, our formulation is shown to retrieve the standard Burton-Cabrera-Frank model in the general case of asymmetric attachment coefficients Ehrlich-Schwoebel effect. We confirm our analytical results by means of numerical simulations of our phase-field model. Our present formulation seems particularly well adapted to generalization when additional physical fields are required.

Dynamics of driven three-dimensional thin films: From hydrophilic to superhydrophobic regimes

R. Ledesma-Aguilar, A. Hernández-Machado, I. Pagonabarraga

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We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Influence of disorder strength on phase-field models of interfacial growth

T. Laurila, M. Pradas, A. Hernández-Machado, T. Ala-Nissila

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We study the influence of disorder strength on the interface roughening process in a phasefield model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Polymer-induced tubulation in lipid vesicles

F. Campelo, A. Hernández-Machado

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A mechanism of extraction of tubular membranes from a lipid vesicle is presented. A concentration gradient of anchoring amphiphilic polymers generates tubes from bud-like vesicle protrusions. We explain this mechanism in the framework of the Canham-Helfrich model. The energy profile is analytically calculated and a tube with a fixed length, corresponding to an energy minimum, is obtained in a certain regime of parameters. Further, using a phase-field model, we corroborate these results numerically. We obtain the growth of tubes when a polymer source is added, and the bud-like shape after removal of the polymer source, in accordance with recent experimental results.

Dynamic characterization of permeabilities and flows in microchannels

M. Castro, M. E. Bravo-Gutiérrez, A. Hernández-Machado, E. Corvera Poiré

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We make an analytical study of the nonsteady flow of Newtonian fluids in microchannels. We consider the slip boundary condition at the solid walls with Navier hypothesis and calculate the dynamic permeability, which gives the system’s response to dynamic pressure gradients. We find a scaling relation in the absence of slip that is broken in its presence. We discuss how this might be useful to experimentally determine—by means of microparticle image velocimetry technology—whether slip exists or not in a system, the value of the slip length, and the validity of Navier hypothesis in dynamic situations.