Session PG: Free Surface Flows III

Numerical study of the convection induced by evaporation in cylindrical geometry

During very short times, at the beginning of the drying of a polymer/solvent solution contained in a cylindrical crucible, experimental results have shown that the origin of convective cells is essentially linked to bouyancy- and/or surface tension-driven instabilities. In order to understand the relative importance of the two mechanisms, a 3D numerical study is performed. Convection is considered as significant when the Peclet number value (Pe) is greater than 1. The evolution of Pe as a function of the initial perturbation is intended to explore the transient character of the problem. The impact of the viscosity and thickness of the fluid on the convective regime and instability thresholds will also be presented and a comparison with experimental data performed. Convective patterns during the quasi-steady regime (slow evolution of the cells) will be shown for various aspect ratios.   

Experimental and Numerical Investigation of Convective Dominated Capillary Channel Flow in Microgravity

In this work we investigated experimentally and numerically liquid flows through open capillary channels under microgravity conditions. The experimental investigations focus on the free surface contour and the maximum flow rate through the channel. Due to convective and viscous momentum transport the pressure along the flow path of the liquid decreases and causes the collapse of the free surface. This stability limit depends on the geometry of the channel and the properties of the liquid. We present an experimental setup which is used in the low gravity environment of the Bremen Drop Tower. High-Resolution Experiments with convective dominated systems have been performed where the flow rate was increased up to the maximum value. In comparison to this we present unique three-dimensional computations to determine important characteristics of the flow, such as the free surface shape and the limiting flow rate. The good agreement validates the capabilities of the numerical solver.   

Investigation of capillary flow in channels with polygonal cross sections: Simulations and experiments

A series of simulations and experiments will be presented which systematically investigate the flows in channels having polygonal cross sections through capillary action. Specific attention is focused on the evolution and shape of the resulting menisci. Simulations are preformed using Surface Evolver in which several important parameters were varied including the number of sides, the characteristic length scale, the contact angle, and the curvature of the channel corners. The results are used to guide and compare with corresponding experiments of capillary force lithography (CFL). The elastomeric molds used in CFL are made by casting PDMS on a rigid patterned master previously fabricated by electron beam lithography combining with reactive ion etching to incorporate precise patterns of polygonal capillaries with the size of around 100nm. Products of CFL are characterized by atomic force microscopy as well as scanning electron microscopy. The results demonstrate that it is possible and practical to fabricate hierarchic structures of sub-100nm features on top of sub-micron patterns.   

Multifunctional superhydrophobic coatings for large area applications

Formulation of flexible superhydrophobic coatings (water droplet contact angles above 150 deg and roll-off angles below 10 deg) with high durability and electrical conductivity, and their fabrication using scalable techniques is a major challenge. The current work lays their foundation using solution processed polymer nanocomposites. Carefully selected polymer(s) are used to disperse filler particles and the dispersions are applied by spraying process. The filler particle size, surface energy and other functionalities are varied to produce the coatings. Sub-micron poly(tetrafluoroethylene) (PTFE) particles and carbon black or other nanoparticles are jointly used to obtain hierarchical morphology (micro-to-nanoscale roughness) and superhydrophobicity. As examples, firstly, acrylonitrile-co-butadiene rubber based nanocomposites are shown to maintain superhydrophobicity up to 200{\%} linear and for 100 cycles of reversible 0 to 100{\%} uniaxial stretching. Secondly, poly(vinylidene fluoride) and poly(methyl methacrylate) blend based nanocomposites containing carbon nanofibers are demonstrated as superhydrophobic coatings with electrical conductivity up to 300 S/m.   

Dynamics of complete wetting liquid under evaporation

We study the dynamics of a contact line under evaporation and complete wetting conditions taking into account the divergent nature of evaporation near the border of the liquid, as evidenced by Deegan et al.~[Nature \textbf{389}, 827]. The model we propose shows the existence of a precursor film at the edge of the liquid. The length of the precursor film is controlled by Hamacker constant and evaporative flux. Past the precursor film, Tanner's law is generalized accounting for evaporative effects.   

Micron-scale measurements of the flow field near a moving contact line

It has long been known that a continuum hydrodynamic description using a no-slip boundary condition breaks down near a moving contact line. Theoretical models including microscopic effects, such as velocity slip and a diffuse interface, have been proposed to relieve the contact line singularity. Although experimental testing of the theoretical models has been attempted by measuring the apparent dynamic contact angle, few efforts have been made to map the flow field close to a moving contact line. We experimentally investigated the flow motion near the moving contact line of a liquid bridge, which is trapped between a stationary hanging rod and a glass substrate which can be moved at a controlled speed. The flow field was seeded with nano-scale fluorescent particles visualized using both flood illumination and evanescent wave (TIRF). The motion was captured using a high speed camera equipped with a high-magnification microscopic objective. These experimental arrangements enable to resolve the flow field within 10 microns of the contact line and as close as 100nm above the moving substrate. The characteristics of the flow, including slip lengths as a function of distance from the contact line can be calculated from the flow field.   

Experimental Investigation of the Effects of Surface Conditions on Natural Convection-Driven Evaporation

Presented are the results from an experimental investigation of the effects of surface conditions at an air/water interface on transport phenomena within the context of natural convection-driven evaporation. Experiments were conducted using tanks of heated water under several different surface conditions: 1) contamination with an oleyl alcohol monolayer, 2) contamination with a stearic acid monolayer, and 3) ``clean'' or surfactant-free. These surface conditions create the following hydrodynamic boundary conditions: 1) constant elasticity, 2) no-slip, and 3) shear-free. The effect of these boundary conditions on evaporation and air-side natural convection heat transfer is presented via the power law relationships between the Sherwood and Rayleigh numbers (for evaporation) and the Nusselt and Rayleigh numbers (for natural convection heat transfer). Additionally, infrared imagery of the water surface was collected during these experiments, yielding qualitative information on the effect of these boundary conditions on the flow near the interface. Few studies exist in which the effects of surface conditions on interfacial heat and mass transfer are investigated, making this work particularly relevant.   

The existence of longitudinal vortices in the flow of air above an air/water interface

Many researchers have observed the formation of longitudinal vortices in boundary layers developing over heated solid surfaces. In the present work, such vortices were observed in an air boundary layer developing over a heated water surface. The existence of these vortices was documented via infrared imaging of the water surface, which showed a consistent pattern of hot and cold streaks, coinciding with the vortex position. These vortices were also visualized through smoke injected into the air-side flow. The onset position $X_c$ and lateral vortex spacing $\lambda$ were investigated for a range of wind speeds (0.1 - 1 m/s) and air/water temperature differences (26 - 42 $^{\circ}$C). Plots of $X_c/\lambda$ versus the Reynolds number exhibit power-law behavior similar to that of prior work on boundary layers over heated solid surfaces. However, plots of $X_c/\lambda$ versus the Grashof number show significant differences from the power-law behavior observed for heated solid plates. A theory explaining the similarity and difference between the present results and those for heated solid plates is discussed which is based on differences in the thermal boundary conditions.   

On hydrostatic free surface flows

We consider the hydrostatic Euler equations in a strip bounded by two free surfaces. We show that the initial value problem is well-posed only if the horizontal velocity is uniform in every cross section of the strip.   

Stretching bridges and bubbles: The effect of air bubbles on liquid transfer

The transfer of liquid from one surface to another is important in a wide variety of both natural and industrial settings. A potential complication in an application such as printing is the entrapment of air bubbles, which can alter the amount of liquid transferred to the substrate, and can produce defects if the bubbles do not burst before drying. To better understand this effect, we use flow visualization to study the stretching of liquid bridges at low capillary numbers. The bridges are visualized from beneath the drop to track the motion of the contact lines, and from beside the drop to enable image analysis to quantify liquid transfer. The dynamics of the outer gas-liquid interface, between the drop and the surrounding air, are found to be the same during stretching both with and without a bubble; thus, the volume of fluid (liquid or liquid plus bubble) transferred to the moving surface is the same in both cases, regardless of the dynamics of the bubble. Therefore, the liquid transfer will increase if the bubble remains on the stationary surface after breakup, or decrease if it transfers to the moving surface. The effect of the wettability of the surfaces on the breakup behavior of the liquid bridge is also discussed.