Session GJ: Surface Tension Effects I

A Novel Method to Measure Contact Angle

A liquid drop on a solid semi-infinite wall is bounded by the wall edge when the component of gravity tangential to the wall points towards the edge. Such drops are called wall-edge-bound-drops and have been studied recently and shown to exhibit a critical wetting behavior, where for a given orientation of the wall the liquid spreads along the edge of the wall forming a rivulet. Such rivulets are always stable when the contact angle of the liquid is below a certain critical value. Limiting cases of the wall-edge-bound-drop are the pendent drop and the sessile drop for which the critical contact angles are zero and 180 degrees respectively. The uniqueness of the critical contact angle corresponding to the orientation of the wall gives rise to a simple method to measure the contact angle of the fluid/solid system. Experiments demonstrating the approach are presented.   

Early growth of condensing water droplets on a superhydrophobic surface

Water droplets placed on dry superhydrophobic surfaces have very large contact angles and very small critical inclination angles, making their behavior especially interesting. However, very few systematic investigations are available on the behavior of droplets condensing on such surfaces. We report on the early growth of water droplets condensing from humid air on a cooled superhydrophobic surface created with a micro-post surface topology. The evolution of individual droplets is monitored via confocal microscopy as they nucleate between and on the micro-posts, grow and coalescence. A model is developed to investigate the effect that surface micro-topography has on the configuration of a condensing droplet, and the model indicates that the post aspect ratio determines whether a condensing droplet will fill the cavity between posts or span adjacent posts. Further study of condensing water droplets on cooled substrates with a variety of designed micro-structures is underway.   

Polyhedral spreading by imbibition of liquids on micro-decorated surfaces

We report on the dynamics of imbibition of liquid droplets on topographically patterned surfaces, i.e. assemblies of cylindrical posts arranged on square lattices. In the case of partially wetting fluids, spreading proceeds by imbibition of the textured part of the surface without spreading of the macroscopic drop. By varying the liquid/substrate equilibrium contact angle and the topography features (height of the posts), we obtain various final shapes of the spreading droplets (octagons, squares, circles) and rationalize these observations using simple physical arguments.   

The Stability of Droplets Dragged Across Surfaces

The stability of a droplet pressed between a stationary and moving cylindrical surface is studied experimentally and theoretically. This so-called ``drag-a-drop'' method has been proposed as a means to suspend a droplet of high index of refraction fluid between a mask blank and lens in a laser mask writing system to greatly enhance the resolution in microelectronic lithographic mask writing. The droplet of fluid is held between the moving lens and the mask due to surface tension forces and must be to stable at large velocities and accelerations. Experimental measurements and theoretical calculations show that a stable droplet can be held onto a 6 mm diameter lens translating at velocities up to 600 mm/s. The maxima of these stable velocities is determined by several factors including the surface energies of the fluid and lens and mask surfaces, the fluid viscosity and density and the thickness of the gap between the cylindrical lens and stationary surface. The droplets are found to break-up by two different mechanisms. In the receding edge instability a thin film pulled behind the lens breaks up into a trail of smaller droplets. In an advancing edge instability, the front edge of the droplet initial shows signs of partial detachment from the lens followed by complete break-up of the attached droplet. A stability map is presented that correlates the onset of these two instabilities as a function of the dimensionless capillary number and Weber number.   

Pattern Formation of Bubbles due to Combined Buoyancy and Thermocapillary Forces

Bubbles/drops in the presence of a temperature field occur in many engineering applications. Examples include materials processing, energy generation by liquid/vapor phase change, and microelectromechanical systems (MEMS). In these applications, often a key question is to understand the particle-induced motion and to manipulate the motion of the particles for a better control of fluid flow and heat transfer. A salient feature of these flows is a tendency for bubbles to form short term and/or long term patterns. This will affect the macroscopic behavior of the system, depending on the type of the pattern. Here, we will examine the motion of freely evolving (mm-sized) air bubbles (in silicon oil) under combined buoyancy and thermocapillarity using direct numerical simulations. The free parameter here is a nondimensional number which characterizes the relative importance of buoyancy and thermocapillary. In the range of parameters used here, the purely buoyancy-driven bubbles tend to distribute randomly, the purely thermocapillary-driven bubbles tend to form horizontal layers, and the bubbles under the combined effects tend to form large clusters. The goal is to understand the mechanism of pattern formation and to quantify the motion using appropriate measures.   

Analysis and Numerical Simulation of EWOD of a Droplet for Application in a Variable Focus Microlens

Modification of the curvature of the interface between a conductive (water) and isolating (oil) liquids is used in order to design a tunable microlens. Electrowetting on Dielectric (EWOD), the modification of surface energy of a conductive droplet on an isolated electrode, is employed in order to change the interface curvature and tune the microlens. Several features of the microlens design are addressed. These includes: the drop-centering mechanism, matching of the density of the two immiscible liquids, refractive indexes of the two liquids, and planar electrodes for electrowetting. A dimensional analysis is performed to identify the relevant nondimensional parameters. Direct numerical simulation of the hydrodynamic and electric fields is carried out. It is found that the focal length of the microlens changes continuously from negative to positive by applying a voltage from 0 to 200 volts. The focusing speed of the microlens is calculated to be around 10 milli-seconds. A successfully fabricated microlens device has been demonstrated.   

Shear- and Thermocapillary-Induced Migration of Bubbles in a Channel

Bubbles/drops in the presence of a temperature field occur in many engineering applications. Examples include materials processing, energy generation by liquid/vapor phase change, and microelectromechanical systems (MEMS). In these applications, often a key question is to understand the particle-induced motion and to manipulate the motion of the particles for a better control of fluid flow and heat transfer. A salient feature of these flows is a tendency for bubbles to form short term and/or long term patterns. This will affect the macroscopic behavior of the system, depending on the type of the pattern. In the case of bubbles moving near the wall, the velocity gradient will also influence the motion. To explore the effect of velocity gradient on the pattern formation, we impose a shear force on the thermocapillary-driven suspension of bubbles. We use a front tracking/finite difference method to solve the momentum and energy equations in both fluids. Dynamics of binary- and multi-bubble interactions will be studied as a function of different shear rates. The goal is to understand the mechanism of pattern formation and to quantify the motion using appropriate measures.   

Agglomeration of floating particles

Floating particles attract by surface tension. The energy of attraction of two individual particles has been investigated before (D. Vella and L. Mahadevan, {\it {Am. J. Phys.}}, {\bf {73}}, 817-825, 2005). The energy of an arbitrary particle clump can be derived from binary interactions for small densities; for high densities, no explicit formula for the energy is known. We develop a highly accurate numerical scheme based on the boundary integral formulation. This numerical scheme is used to analyze the statistics of energies for many-particle clumps for dense configurations. An empirical formula for the energy which seems to be highly accurate for an arbitrary configuration of particles is proposed. To confirm the theory, experiments were conducted by placing particles in a given configuration on a stretched fabric net that was immersed in a water bath, with evolution of particle positions recorded by a digital camera. Results for the evolution of the second moment of the configuration of 10-25 particles show good agreement with theoretical predictions using a single parameter fit characterizing the unknown particle mobility.   

Formation of dynamic particle accumulation structures in oscillatory thermocapillary flow in liquid bridges

We report on the behaviour of small particles of dilute concentration in time-dependent (oscillatory) thermocapillary flow in cylindrical liquid bridges (LB). For certain aspect ratios and Marangoni numbers particles are found to accumulate in a dynamic particle string. This was observed for isodense particles and for ones with density larger and smaller than that of the fluid .The particle string is wound m times (m = mode number of the oscillatory flow field) around the thermocapillary vortex as a deformed spiral and is rotating around its ring- axis. We present a hypothesis about the mechanisms of PAS-formation. Particles in the outer layers of the surface flow are gathered by the cold phase of the hydrothermal wave (HTW) and particle-rich fluid is injected in m azimuthally travelling spots into the return flow. PAS occurs for resonance between the HTW and the ``turn over time of the PAS-string'' in the thermocapillary vortex. Repeated in-phase injection of particle-rich fluid at the m rotating spots forms PAS. We present evidence for the gathering of particles and the injection mechanism. We varied particle radius and density to measure the time for the formation of PAS and discuss particle migration. Experiments under microgravity excluded gravity as PAS-forming mechanism. *Supported by ESA and BMBF under DLR-contract No. 50WM0350.