Numerical simulations of a falling film on the inner surface of a rotating cylinder.

A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and 3D direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterized by the Reynolds, Froude, Weber, and Ekman numbers. The variation of the Ekman number (Ek), defined to be proportional to the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of Ek values (0≤Ek≤484) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing Ek, which leads to a rise in the magnitude of centrifugal forces, produces a stabilizing effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilization and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally and centrifugally driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

Local damage detection by nonlinear coda wave interferometry combined with time reversal.

Coda wave interferometry (CWI) is a sensitive ultrasound method for the detection of weak and local changes in complex inhomogeneous media. In a nonlinear modification of the method discussed here, a high-frequency probe coda is compared to its replica obtained in the presence of low-frequency pumping. If, after the filtering-out of low frequencies, the coda signals are different, this is attributed to nonlinear pump-probe interaction induced by contact acoustical nonlinearity in the damaged zone. Actually, the CWI methods are used for global inspection of complex media, such as for example, concrete structures. In this work, a step forward is made; it consists in combining the CWI with the time-reversal (TR) technique in order to allow one to focus the pump wave on a selected area in the structure and to detect and localize a flaw. Time-reverse pump is possible only in pulsed mode due to the spatio-temporal wave compression. By this reason, the particularities of coda wave mixing in conventionally used continuous and pulsed pump mode are considered. It has been experimentally observed that an aftereffect of a pulsed pump provides a nonlinear interaction between pump and probe waves of a sufficient overall level for defect detection with TR. Finally, it was shown that a TR focusing even with the minimal available quality i.e., with only one transducer produces a sufficient contrast allowing to distinguish intact and damaged zones with nonlinear CWI.

Relationship between renal capacity to reabsorb glucose and renal status in patients with diabetes.

AIMS: Interindividual variability in capacity to reabsorb glucose at the proximal renal tubule could contribute to risk of diabetic kidney disease. Our present study investigated, in patients with diabetes, the association between fractional reabsorption of glucose (FRGLU) and degree of renal disease as assessed by urinary albumin excretion (UAE) and estimated glomerular filtration rate (eGFR). METHODS: FRGLU [1-(glucose clearance/creatinine clearance)] was assessed in 637 diabetes patients attending our tertiary referral centre, looking for correlations between FRGLU and UAE (normo-, micro-, macro-albuminuria) and Kidney Disease: Improving Global Outcomes (KDIGO) eGFR categories: >90 (G1); 90-60 (G2); 59-30 (G3); and<30-16 (G4) mL/min/1.73 m2. Patients were stratified by admission fasting plasma glucose (FPG) into three groups: low (<6mmol/L); intermediate (6-11mmol/L); and high (>11mmol/L). RESULTS: Median (interquartile range, IQR) FRGLU levels were blood glucose-dependent: 99.90% (0.05) for low (n=106); 99.90% (0.41) for intermediate (n=288); and 96.36% (12.57) for high (n=243) blood glucose categories (P<0.0001). Also, FRGLU increased with renal disease severity in patients in the high FPG group: normoalbuminuria, 93.50% (17.74) (n=135); microalbuminuria, 96.56% (5.94) (n=77); macroalbuminuria, 99.12% (5.44) (n=31; P<0.001); eGFR G1, 94.13% (16.24) (n=111); G2, 96.35% (11.94) (n=72); G3 98.88% (7.59) (n=46); and G4, 99.11% (2.20) (n=14; P<0.01). On multiple regression analyses, FRGLU remained significantly and independently associated with UAE and eGFR in patients in the high blood glucose group. CONCLUSION: High glucose reabsorption capacity in renal proximal tubules is associated with high UAE and low eGFR in patients with diabetes and blood glucose levels>11mmol/L.

Fluid-solid phase transition of n-alkane mixtures: Coarse-grained molecular dynamics simulations and diffusion-ordered spectroscopy nuclear magnetic resonance.

Wax appearance temperature (WAT), defined as the temperature at which the first solid paraffin crystal appears in a crude oil, is one of the key flow assurance indicators in the oil industry. Although there are several commonly-used experimental techniques to determine WAT, none provides unambiguous molecular-level information to characterize the phase transition between the homogeneous fluid and the underlying solid phase. Molecular Dynamics (MD) simulations employing the statistical associating fluid theory (SAFT) force field are used to interrogate the incipient solidification states of models for long-chain alkanes cooled from a melt to an arrested state. We monitor the phase change of pure long chain n-alkanes: tetracosane (C24H50) and triacontane (C30H62), and an 8-component surrogate n-alkane mixture (C12-C33) built upon the compositional information of a waxy crude. Comparison to Diffusion Ordered Spectroscopy Nuclear Magnetic Resonance (DOSY NMR) results allows the assessment of the limitations of the coarse-grained models proposed. We show that upon approach to freezing, the heavier components restrict their motion first while the lighter ones retain their mobility and help fluidize the mixture. We further demonstrate that upon sub-cooling of long n-alkane fluids and mixtures, a discontinuity arises in the slope of the self-diffusion coefficient with decreasing temperature, which can be employed as a marker for the appearance of an arrested state commensurate with conventional WAT measurements.

Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation.

The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications.

A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics.

Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.

Dynamics of sessile and pendant drops excited by surface acoustic waves: Gravity effects and correlation between oscillatory and translational motions.

When sessile droplets are excited by ultrasonic traveling surface acoustic waves (SAWs), they undergo complex dynamics with both oscillations and translational motion. While the nature of the Rayleigh-Lamb quadrupolar drop oscillations has been identified, their origin and their influence on the drop mobility remains unexplained. Indeed, the physics behind this peculiar dynamics is complex with nonlinearities involved both at the excitation level (acoustic streaming and radiation pressure) and in the droplet response (nonlinear oscillations and contact line dynamics). In this paper, we investigate the dynamics of sessile and pendant drops excited by SAWs. For pendant drops, so-far unreported dynamics are observed close to the drop detachment threshold with the suppression of the translational motion. Away from this threshold, the comparison between pendant and sessile drop dynamics allows us to identify the role played by gravity or, more generally, by an initial or dynamically induced stretching of the drop. In turn, we elucidate the origin of the resonance frequency shift, as well as the origin of the strong correlation between oscillatory and translational motion. We show that for sessile drops, the velocity is mainly determined by the amplitude of oscillation and that the saturation observed is due to the nonlinear dependence of the drop response frequency on the dynamically induced stretching.

The effect of adsorption kinetics on the rate of surfactant-enhanced spreading.

A comparison of the kinetics of spreading of aqueous solutions of two different surfactants on an identical substrate and their short time adsorption kinetics at the water/air interface has shown that the surfactant which adsorbs slower provides a higher spreading rate. This observation indicates that Marangoni flow should be an important part of the spreading mechanism enabling surfactant solutions to spread much faster than pure liquids with comparable viscosities and surface tensions.

Fluoro- vs hydrocarbon surfactants: why do they differ in wetting performance?

Fluorosurfactants are the most effective compounds to lower the surface tension of aqueous solutions, but their wetting properties as related to low energy hydrocarbon solids are inferior to hydrocarbon trisiloxane surfactants, although the latter demonstrate higher surface tension in aqueous solutions. To explain this inconsistency available data on the adsorption of fluorosurfactants on liquid/vapour, solid/liquid and solid/vapour interfaces are discussed in comparison to those of hydrocarbon surfactants. The low free energy of adsorption of fluorosurfactants on hydrocarbon solid/water interface should be of a substantial importance for their wetting properties.

Nonequilibrium hysteresis and Wien effect water dissociation at a bipolar membrane.

As in electrochemical cyclic voltammetry, time-periodic reverse voltage bias across a bipolar membrane is shown to exhibit hysteresis due to transient effects. This is due to the incomplete depletion of mobile ions, at the junction between the membranes, within two adjoining polarized layers; the layer thickness depends on the applied voltage and the surface charge densities. Experiments show that the hysteresis consists of an Ohmic linear rise in the total current with respect to the voltage, followed by a decay of the current. A limiting current is established for a long period when all the mobile ions are depleted from the polarized layer. If the resulting high field within the two polarized layers is sufficiently large, water dissociation occurs to produce proton and hydroxyl traveling wave fronts which contribute to another large jump in the current. We use numerical simulation and asymptotic analysis to interpret the experimental results and to estimate the amplitude of the transient hysteresis and the water-dissociation current.

Dynamics of a climbing surfactant-laden film--I: base-state flow.

The dynamics of a surfactant-laden film climbing up an inclined plane is investigated through a two-dimensional (2-D), nonlinear evolution equation for the interface coupled to convective-diffusion equations for the surfactant, derived using lubrication theory. One-dimensional (1-D) solutions, representing the base-state flow, are investigated for constant flux and constant volume configurations; these flows are parameterised by capillarity, gravity, convection-diffusion ratios (represented by Péclét numbers at the surface and bulk), a solubility parameter, sorption kinetics constants, the number of surfactant monomers in a micelle, and the nonlinearity of the surfactant equation of state. In both configurations studied, a front develops spreading up the substrate against the direction of gravity whereby the leading edge of the front follows a power-law as a function of time. The effect of system parameters on the base-state flow is explored through an extensive parametric study, while the stability of the above-mentioned system to spanwise perturbations is the focus of Part II.

Dynamics of a climbing surfactant-laden film II: stability.

The linear and nonlinear stability of a spreading film of constant flux and a drop of constant volume, discussed in [1], are examined here. A linear stability analysis (LSA) is carried out to investigate the stability to spanwise perturbations, by linearisation of the two-dimensional (2-D) evolution equations derived in [1] for the film thickness and surfactant concentration fields. The latter correspond to convective-diffusion equations for the surfactant, existing in the form of monomers (present at the free surface and in the bulk) and micelles (present in the bulk). The results of the LSA indicate that the thinning region, present upstream of the leading front in the constant flux case, and the leading ridge in the constant volume case, are unstable to spanwise perturbations. Numerical simulations of the 2-D system of equations demonstrate that the above-mentioned regions exhibit finger formation; the effect of selected system parameters on the fingering patterns is discussed.

Breakup of an electrified, perfectly conducting, viscous thread in an AC field.

We study the axisymmetric breakup and satellite formation of slender jets surrounded by a concentrically placed cylindrical electrode and subjected to time-dependent AC electric fields. The jet is assumed to be a perfectly conducting viscous fluid and surrounded by a dielectric inviscid gas. We use the long-wave approximation to derive coupled evolution equations for the interface position and the axial velocity component, which accounts for electrostatic forcing. The electrostatic force in this case is large and competes with capillary forces near the rupture point, causing the interface to oscillate and the satellite to have shapes that are distinct from the DC case. In particular, our results indicate that it may be possible to use the AC field to control the number of satellites accompanying breakup as well as their size.

Droplet displacements and oscillations induced by ultrasonic surface acoustic waves: a quantitative study.

We present an experimental study of a droplet interacting with an ultrasonic surface acoustic wave. Depending on the amplitude of the wave, the drop can either experience an internal flow with its contact line pinned, or (at higher amplitude) move along the direction of the wave also with internal flow. Both situations come with oscillations of the drop free surface. The physical origins of the internal mixing flow as well as the drop displacement and surface waves are still not well understood. In order to give insights of the underlying physics involved in these phenomena, we carried out an experimental and numerical study. The results suggest that the surface deformation of the drop can be related to a combination between acoustic streaming effect and radiation pressure inside the drop.

Surfactant-enhanced rapid spreading of drops on solid surfaces.

We study the surfactant-enhanced spreading of drops on the surfaces of solid substrates. This work is performed in connection with the unique ability of aqueous trisiloxane solutions to wet highly hydrophobic substrates effectively, which has been studied for nearly two decades. We couple a lubrication model to advection-diffusion equations for surfactant transport. We allow for micelle formation and breakup in the bulk and adsorptive flux at both the gas-liquid and liquid-solid interfaces and use appropriate equations of state to model variations in surface tension and wettability. Our numerical results show the effect of basal adsorption, kinetic rates, and the availability of surfactant on the deformation of the droplet and its spreading rate. We demonstrate that this rate is maximized for intermediate rates of basal adsorption and the total mass of surfactant.

Pinning, retraction, and terracing of evaporating droplets containing nanoparticles.

We consider the dynamics of a slender, evaporating droplet containing nanoparticles. We use lubrication theory to derive a coupled system of equations that govern the film thickness and the concentration of nanoparticles. These equations account for capillarity, Marangoni stresses, evaporation, and disjoining pressure; the nanoparticle-induced structural component of the disjoining pressure is also considered. Contact line singularities are avoided through the adsorption of ultrathin films wherein evaporation is suppressed by the disjoining pressure; a similar approach has recently been used by Ajaev [J. Fluid Mech. 2005, 528, 279-296] who has built on the previous work of Moosman and Homsy [J. Colloid Interface Sci. 1980, 73, 212-223]. The results of our numerical simulations indicate that, depending on the value of system parameters, the droplet exhibits a variety of different behaviours, which include spreading, evaporation-driven retraction, contact line pinning, and "terrace" formation.

Explosive dynamics and localization of wave triads in a coupled magnetoelastic system.

The dynamics of three-wave parametric coupling is considered on an example of nonequilibrium magnetostrictive medium under electromagnetic pumping. Subthreshold and supercritical mode of three-wave excitation are described analytically and simulated numerically for a triad of magnetoelastic waves. Theoretical analysis of the supercritical mode shows that space-time development of three-wave excitation in such a nonequilibrium system has the character of explosive instability and localization of "positive energy" waves.

Interfacial dynamics in pressure-driven two-layer laminar channel flow with high viscosity ratios.

The large-scale dynamics of an interface separating two immiscible fluids in a channel is studied in the case of large viscosity contrasts. A long-wave analysis in conjunction with the Kármán-Polhausen method to approximate the velocity profile in the less viscous fluid is used to derive a single equation for the interface. This equation accounts for the presence of interfacial stress, capillarity, and viscous retardation as well as inertia in the less viscous fluid layer where the flow is considered to be quasistatic; the equation is shown to reduce to a Benney-type equation and the Kuramoto-Sivashinskiy equation in the relevant limits. The solutions of this equation are parametrized by an initial thickness ratio h0 and a dimensionless parameter S , which measures the relative significance of inertial to capillary forces. A parametric continuation technique is employed, which reveals that nonuniqueness of periodic solutions is possible in certain regions of (h0,S) space. Transient numerical simulations are also reported, whose results demonstrate good agreement with the bifurcation structure obtained from the parametric continuation results.

On autophobing in surfactant-driven thin films.

Recent experiments (Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Langmuir 2004, 20, 7575-7582) on the spreading of aqueous droplets containing cationic surfactants over thin aqueous films supported by negatively charged substrates demonstrated trends in the spreading behavior with either increasing surfactant concentration or increasing film thickness. Although the substrate is initially hydrophilic and the droplet spreads, surfactant adsorption at the substrate renders it hydrophobic leading to droplet retraction. We generate a model here using lubrication theory that allows the effect of the surfactant on the wettability to be taken into account. Our numerical results show that due to basal adsorption of surfactant at the interface, the initially hydrophilic solid substrate is rendered hydrophobic. This then drives droplet retraction and dewetting, which is in agreement with the experimentally observed trends.

Falling films on flexible inclines.

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.