Enrique Rame

On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation

Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested. The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region. Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13 a . and O.17 a , where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10 -4 and 8.3 × 10 -3 . Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.

The velocity field near moving contact lines

The dynamics of a spreading liquid body are dictated by the interface shape and flow field very near the moving contact line. The interface shape and flow field have been described by asymptotic models in the limit of small capillary number, Ca. Previous work established the validity and limitations of these models of the interface shape (Chen et al.). Here, we study the flow field near the moving contact line. Using videomicroscopy, particle image velocimetry, and digital image analysis, we simultaneously make quantitative measurements of both the interface shape and flow field from 30 μm to a few hundred microns from the contact line. We compare our data to the modulated-wedge solution for the velocity field near a moving contact line (Cox 1986). The measured flow fields demonstrate quantitative agreement with predictions for Ca ≤ 0.1, but deviations of ∼ 5% of the spreading velocity at Ca 0.4. We observe that the interface shapes and flow fields become geometry independent near the contact line. Our experimental technique provides a way of measuring the interface shape and velocity field to be used as boundary conditions for numerical calculations of the macroscopic spreading dynamics.

The breakdown of asymptotic hydrodynamic models of liquid spreading at increasing capillary number

Complex hydrodynamics near the moving contact line control spreading of a fluid across a solid surface. In the confined region near the contact line, velocity gradients in the fluid are large and viscous forces control the shape of the fluid/fluid interface. The present model for liquid spreading describes the viscous effect on the dynamic interface shape to lowest order in capillary number, Ca. Using videomicroscopy and image analysis techniques, we have examined the shape of liquid/air interfaces very near moving contact lines for Ca≥0.10 where the interfaces are in capillary depression. We find that the theory correctly describes the data up to Ca=0.10 for distances from 20 to 400 μm from the contact line. As Ca increases, the model fails to describe the data in a region near the contact line, which grows as Ca increases. In this expanding region, the model predicts too large a curvature for the interface. We explore the origins of this breakdown by examining the fundamental assumptions of the model. T...

Dip-coated films of volatile liquids

We examine experimentally the hydrodynamics of dip-coated, finite-length films of evaporative fluids, from the film tip through the film body all the way to the connection with the main meniscus. The characteristic film thickness has a power-law dependence on the withdrawing speed similar to that for the thickness of “infinite” films formed by nonvolatile liquids. The film length and cross-sectional area have power-law dependence on the withdrawing speed as well, but the prefactors of the power laws are controlled by the evaporation rate of the fluid. These power laws are consistent with the global mass balance over the film between mass lost by evaporation and mass input by the solid motion. We have also found that the apparent contact angle and the curvature at the film tip both have power-law dependencies on the withdrawing speed that are consistent with those found for the length and the film thickness. Film shape measurements near the film tip reach thicknesses ∼100 A from the solid; but we did not d...

EFFECTS OF INERTIA ON THE HYDRODYNAMICS NEAR MOVING CONTACT LINES

We investigate the effects of inertia on the hydrodynamics in the microscopic vicinity of moving contact lines. These hydrodynamics control the macroscopic shape and spreading of fluid bodies across solid surfaces. We perform experiments at low capillary number (Ca<0.1) and negligible (10−4) to moderate (Re∼1) Reynolds number. On a microscopic scale, inertia decreases the dynamic curvature of the free surface near the contact line compared to the case with Re=0 at the same Ca. On a macroscopic scale, inertia lowers the apparent contact angle of the static-like macroscopic interface compared to the situations with the same Ca but negligible Re.

The effects of thin films on the hydrodynamics near moving contact lines

We explore the effects of thin films on the hydrodynamics of macroscopic fluid bodies spreading over solid surfaces. To examine these effects, we measure the interface shape within microns of moving contact lines and compare those measurements to two asymptotic models in the limit of small capillary number, Ca. One model requires that the films affect the hydrodynamics only in a microscopic region near the contact line and allows the macroscopic meniscus to exhibit a nonzero effective contact angle. The other model describes the film as containing mobile fluid and specifically models the flow as fluid moves into or out of the film as the contact line moves. We examine fluids advancing and receding on wetting and nonwetting surfaces with spontaneously forming (molecular scale) and pre-existing (micron scale) films. Our results emphasize the importance of the mobility of the molecules in these very thin films in determining the hydrodynamics governing the moving contact line. The first model, which describes fluids advancing over dry surfaces, also accounts for the hydrodynamics of liquids advancing over very thin, immobile films. Surprisingly, the same model fails when fluid recedes on a nonwetting surface and no film is present. For mobile pre-existing films, the second model, based on Landau and Levich’s theory, accounts for the hydrodynamics in the limit of small Ca.

Dynamic wetting of shear thinning fluids

The impact of non-Newtonian behavior on dynamic wetting is critical since many fluids exhibit such behavior somewhere in the high-shear environment inherent in the wedge flow near a moving contact line. This impact will be different for two broad categories of non-Newtonian behavior, shear thinning, and elasticity. In this paper, we discuss the steady-state wetting of a fluid, aqueous solutions of xanthan gum, dominated by shear thinning but with negligible elasticity. In the shear thinning fluid, viscous bending near the contact line is greatly reduced compared to a Newtonian fluid having the same zero-shear viscosity. Concomitant with this reduction in viscous bending, the effective dynamic contact angle has a much weaker dependence on capillary number, Ca, than is observed in, or predicted for, Newtonian fluids. A simple lubrication model using a constitutive relation with power-law shear thinning at high shear rates and a Newtonian plateau at low shear rates mimics the trends seen in our data and eluc...

The spreading of surfactant-laden liquids with surfactant transfer through the contact line

We examine the spreading of a liquid on a solid surface when the liquid surface has a spread monolayer of insoluble surfactant, and the surfactant transfers through the contact line between the liquid surface and the solid. We show that, as in surfactant-free systems, a singularity appears at the moving contact line. However, unlike surfactant-free systems, the singularity cannot be removed by the same assumptions as long as surfactant transfer takes place. In an attempt to avoid modelling difficulties posed by the question of how the singularity might be removed, we identify parameters which describe the dynamics of the macroscopic spreading process. These parameters, which depend on the details of the fluid motion next to the contact line as in the pure-fluid case, also depend on the state of the spread surfactant in the macroscopic region, in sharp contrast to the pure-fluid case where actions at the macroscopic scale did not affect material spreading parameters. A model of the viscous-controlled region near the contact line which accounts for surfactant transfer shows that, at steady state, some ranges of dynamic contact angles and of capillary number are forbidden. For a given surfactant–liquid pair, these disallowed ranges depend upon the actual contact angle and on the transfer flux of surfactant. We also examine a possible inner model which accounts for the transfer via surface diffusivity and regularizes the stress via a slip model. We show that the asymptotic behaviour of this model at distances from the contact line large compared to the inner length scale matches to the viscous-controlled region. An example of how the information propagates is given.

Experimental studies on the parametrization of liquid spreading and dynamic contact angles

The dynamics of a spreading liquid are controlled by the details of the fluid motion very near the moving contact line. Modeling this motion is not trivial. The classical hydrodynamic model has a singular stress field at the moving contact line. This singularity prevents the use of the contact angle in dynamic conditions and predicts that an infinite force would be needed to sink a solid into a fluid. A model, valid in the small capillary number (Ca) limit, describes the fluid motion and viscous interfacial deformation near the moving contact line. The model contains a single free parameter, ω o , which can be related to material parameters and must be determined experimentally. Experiments are reported that tested the range of validity of this asymptotic hydrodynamic model. The fluid-vapor interface shape and fluid velocity field produced by a glass tube entering a bath of polydimethylsiloxane at constant speed were measured near and far from the contact line. They were compared with the model using the free parameter ω o as a fitting constant. This procedure established the validity of the theory and provided a means of measuring ω o . The ranges (in capillary number and in space) of validity of the theory were established. The model fails near the contact line at Ca ≥ 0.1. This failure starts near the contact line, propagates out and increases in magnitude as Ca increases. For Ca ≤ 0.1, the model with viscous deformation fails far from the contact line but describes the interface shape within ∼400 μm from the contact line. The model begins to fail at distances where the interface shape ceases to be controlled by geometry-independent viscous forces but responds instead to a competition between viscous and gravitational forces. At even larger distances from the contact line, viscous forces become negligible and the interface looks static-like. The experiments showed that the contact angle formed by the extrapolation to the solid surface of the static-like interface far from the contact line equals ω o as predicted by the theory. Comparisons of ω o and apparent dynamic contact angles based on meniscus height measurements, θ app , are presented. Small but systematic errors were found which increase with Ca. In contrast to ω o , θ app cannot be related to material parameters and hence cannot be used to generate archival modeling information for spreading dynamics.

Flow Visualization of Liquid Hydrogen Line Chilldown Tests

We present experimental measurements of wall and fluid temperature during chill-down tests of a warm cryogenic line with liquid hydrogen. Synchronized video and fluid temperature measurements are used to interpret stream temperature profiles versus time. When cold liquid hydrogen starts to flow into the warm line, a sequence of flow regimes, spanning from all-vapor at the outset to bubbly with continuum liquid at the end can be observed at a location far downstream of the cold inlet. In this paper we propose interpretations to the observed flow regimes and fluid temperature histories for two chilldown methods, viz. trickle (i.e. continuous) flow and pulse flow. Calculations of heat flux from the wall to the fluid versus wall temperature indicate the presence of the transition/nucleate boiling regimes only. The present tests, run at typical Reynolds numbers of approx O(10 (exp 5)), are in sharp contrast to similar tests conducted at lower Reynolds numbers where a well-defined film boiling region is observed.