Surface-Tension-Driven Dynamic Contact Line in Microgravity.

Deposition of colloidal material in evaporating droplets is important in many applications including DNA sequencing and medical diagnostic testing. When colloidal droplets evaporate, the majority of material is often deposited at the periphery of the resultant deposition in a coffee-ring pattern. Formation of this pattern is the result of contact line pinning and the interplay between evaporative and surface tension effects in the droplet. When the contact line is pinned and the evaporative flux in the droplet is highest at the periphery, a radially outward flow is generated to conserve mass that deposits particles in the fluid at the contact line. Evaporation at the contact line can also create a temperature gradient across the droplet. This gradient gives rise to a surface tension driven flow that can resuspend particles in the droplet. When the evaporative flow dominates, particles are deposited at the contact line in a coffee-ring pattern. The presence of the coffee-ring pattern is undesirable in many printing and medical diagnostic processes. Suppression of the coffee-ring effect has been achieved by addition of surfactant, enhancement of surface tension flow, surface modification, alteration of particle shape, and application of an electric field. Manipulation of the coffee-ring effect has been achieved through the application of both AC and DC electric fields. One result of the presence of this field is the electrowetting force at the contact line which acts to reduce the contact angle and increase contact area. Since this force acts at the contact line, it may disrupt typical contact line dynamics, including evaporative dynamics, which are responsible for the formation of the coffee-ring effect. This work will experimentally examine contact line dynamics of evaporating droplets in the presence of DC electric fields. Droplets of water will be desiccated on a device with a photolithographically patterned electrode covered with a thin layer of SU8-3005. Experimental cases with applied DC fields will be compared with unactuated control cases to examine changes in transient interface shape and contact diameter.

Chemical Affinity Tensor and Chemical Reaction Front Propagation: Theory and FE-Simulations

When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving contact line processes. The calculations reveal that up to Capillary number Ca=0.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale) from the dynamic contact line is independent of the macroscopic length scale a for a>103Li, and compares well to the leading order analytical “modulated-wedge” flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca<0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1<Ca<0.15, caused by the inadequacy of the leading order analytical solution over this range of Ca. Meniscus shapes produced from calculations in a truncated domain, where the modulated-wedge velocity field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] is used as a boundary condition along an arc of radius R=10−2a from the dynamic contact line, agree well with those using two inner slip models for Ca<0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on velocity profiles in the vicinity of dynamic contact lines. These calculations show that over an appropriate range of Ca, the velocity field and the meniscus slope in a geometry-independent region can potentially serve as material boundary conditions for models of processes containing dynamic contact lines.

Local heating effect on thermal Marangoni flow and heat transfer characteristics of an evaporating droplet

A comprehensive numerical and experimental investigation on micrometer-sized water droplet impact dynamics and evaporation on an unheated, flat, dry surface is conducted from the standpoint of spray-cooling technology. The axisymmetric time-dependent governing equations of continuity, momentum, energy, and species are solved. Surface tension, wall adhesion effect, gravitational body force, contact line dynamics, and evaporation are accounted for in the governing equations. The explicit volume of fluid (VOF) model with dynamic meshing and variable-time stepping in serial and parallel processors is used to capture the time-dependent liquid-gas interface motion throughout the computational domain. The numerical model includes temperature- and species-dependent thermodynamic and transport properties. The contact line dynamics and the evaporation rate are predicted using Blake's and Schrage's molecular kinetic models, respectively. An extensive grid independence study was conducted. Droplet impingement and evaporation data are acquired with a standard dispensing/imaging system and high-speed photography. The numerical results are compared with measurements reported in the literature for millimeter-size droplets and with current microdroplet experiments in terms of instantaneous droplet shape and temporal spread (R/D(0) or R/R(E)), flatness ratio (H/D(0)), and height (H/H(E)) profiles, as well as temporal volume (inverted A) profile. The Weber numbers (We) for impinging droplets vary from 1.4 to 35.2 at nearly constant Ohnesorge number (Oh) of approximately 0.025-0.029. Both numerical and experimental results show that there is air bubble entrapment due to impingement. Numerical results indicate that Blake's formulation provides better results than the static (SCA) and dynamic contact angle (DCA) approach in terms of temporal evolution of R/D(0) and H/D(0) (especially at the initial stages of spreading) and equilibrium flatness ratio (H(E)/D(0)). Blake's contact line dynamics is dependent on the wetting parameter (K(W)). Both numerical and experimental results suggest that at 4.5 < We < 11.0 the short-time dynamics of microdroplet impingement corresponds to a transition regime between two different spreading regimes (i.e., for We < or = 4.5, impingement is followed by spreading, then contact line pinning and then inertial oscillations, and for We > or = 11.0, impingement is followed by spreading, then recoiling, then contact line pinning and then inertial oscillations). Droplet evaporation can be satisfactorily modeled using the Schrage model, since it predicts both well-defined transient and quasi-steady evaporation stages. The model compares well with measurements in terms of flatness ratio (H/H(E)) before depinning occurs. Toroidal vortices are formed on the droplet surface in the gaseous phase due to buoyancy-induced Rayleigh-Taylor instability that enhances convection.

Combustion regime of a reacting front propagating into an auto-igniting mixture

Partially wetting drops sliding down an inclined plane develop a “corner singularity” at the rear, consisting of two dynamic contact lines that intersect. We analyze the three-dimensional flow in the vicinity of this singularity by exploring similarity solutions of the lubrication equations. These predict a self-similar structure of the velocity field, in which the fluid velocity does not depend on the distance to the corner tip; this is verified experimentally by particle image velocimetry. The paper then addresses the small-scale structure of the corner, at which the singularity is regularized by a nonzero radius of curvature R of the contact line. Deriving the lubrication equation up to the lowest order in 1∕R, we show that contact line curvature postpones the destabilization of receding contact lines to liquid deposition, and that 1∕R increases dramatically close to the “pearling” instability. The general scenario is thus that sliding drops avoid a forced wetting transition by forming a corner of two inclined contact lines, which is regularized by a rounded section of rapidly decreasing size.

Spiral motifs are pervasive in nature, art, and technology due to their functional property of providing compact length. Nature is particularly adept at spiral patterning, and yet, the spirals observed in seashells, hurricanes, rams' horns, flower petals, etc. all evolve via disparate physical mechanisms. Here, we present a mechanism for the self-guided formation of spirals from evaporating saline drops via a coupling of crystallization and contact line dynamics. These patterns are in contrast to commonly observed patterns from evaporation of colloidal drops, which are discrete (rings, concentric rings) or continuous (clumps, uniform deposits) depending on the particle shape, contact line dynamics, and evaporation rate. Unlike the typical process of drop evaporation where the contact line moves radially inward, here, a thin film pinned by a ring of crystals ruptures radially outward. This motion is accompanied by a nonuniform pinning of the contact line due to crystallization, which generates a continuous propagation of pinning and depinning events to form a spiral. By comparing the relevant timescales of evaporation and diffusion, we show that a single dimensionless number can predict the occurrence of these patterns. These insights on self-guided crystallization of spirals could be used to create compact length templates.

The interaction of pure capillary waves with boundaries that constrain the contact line are of interest for problems involving liquids contained by minimal solid contact for applications in low gravity and at small scales in normal gravity. Time-harmonic capillary waves on a liquid cylinder axially incident on and scattered by an infinitesimal concentric barrier are considered theoretically in the inviscid limit. The barrier is taken to be infinitesimally small in the sense that its immersed depth is of the order of the amplitude of contact-line motion. Edge conditions on the barrier that are investigated include a pinned contact line and a moving contact line by an effective-slip model, assuming that contact-line velocity is proportional to the deviation of the contact angle from equilibrium multiplied by a slip coefficient. The incident waves are taken to be those with wavelengths short enough to be stable on the liquid cylinder. Scattering and dissipation by the contact line are determined as a function of wavenumber and slip coefficient. Zero transmission is approached in the long-wave limit. The short-wave limit agrees with established results for the scattering of planar gravity–capillary waves on a deep liquid by a surface-piercing vertical barrier in the limit of zero barrier depth and zero gravity. We find that contact-line dissipation at the barrier is a maximum for incident waves whose phase speed is of the order of the slip coefficient, which is interpreted as an effect of impedance matching. Transmission past an infinitesimal barrier is found to be low over all parameter space, illustrating the importance of contact-line constraints.

A biharmonic stream function equation is solved analytically in axisymmetric toroidal coordinates for Stokes flow in a sessile droplet with a surface tension gradient and diffusive evaporation on the surface. Four different types of streamlines are defined and utilized to predict particle deposition either at the center or at the contact line of the droplet. The impact of UV light radius, droplet's contact angle, and humidity level on the flow pattern is investigated. When the relative humidity is high, the formation of Moffatt eddies is observed. However, the eddy size and the number of eddies decrease with an increase in UV light radius or droplet contact angle. As humidity decreases, the Moffatt eddies are restricted to a specific region, decrease in number and size, and ultimately disappear. Under lower humidity, the Marangoni flow near the contact line is dominated by capillary action. The toroidal streamlines are broken from outside and turned into transporting streamline to deposit more particles on the contact line. The region near the droplet center, where the surface tension gradient is significant, is always dominated by toroidal streamlines.

The dynamics of the triple gas-liquid-solid contact line is analyzed for the case where the gas is the saturated vapor corresponding to the liquid. For partial wetting conditions, a nonstationary contact line problem where the contact line motion is caused by evaporation or condensation is treated. It is shown that the Navier slip condition alone is not sufficient to relax the hydrodynamic contact line singularity: the Marangoni term is equally important when the heat transfer is involved. The transient heat conduction inside the heater is accounted for. A multiscale problem of drop evaporation with freely moving contact line is solved in the lubrication approximation as an illustration of the proposed approach.

In this paper we present a set of wave flume experiments for a solitary wave reflecting off a vertical wall. A particle tracking velocimetry (PTV) technique is used to measure free-surface velocity and the velocity field in the vicinity of the moving contact line. We observe that the free surface undergoes the so-called rolling motion as the contact line moves up and down the vertical wall, and fluid particles on the free surface almost always flow toward the wall except at the end of the reflection process. As the contact line descends along the wall, wall boundary layer flows move in a downward direction and therefore the boundary layer acts like a conduit through which the surface-rolling-induced flow escapes from the meniscus. However, during the last phase of the reflection process flow reversal occurs inside the wall boundary layer. An approximate analytical solution is developed to explain the flow reversal feature. Very good agreement between the approximate theory and measured data is obtained. Because of the flow reversal, boundary layer flows collide with the surface-rolling-induced flows. The collision gives rise to a jet ejecting from the meniscus into the water body, which later evolves into a small eddy. It is noticed that the fluid particles in different regions such as the free stream, the free-surface boundary layer and the wall boundary layer, can be transported to other regions by passing through the meniscus.

Evaporation of fluid from a pinned drop placed on solid surface proceeds via constant contact radius (CCR) mode, with a continuous reduction in the contact angle. The reduction of contact angle leads to an imbalance of interfacial tensions at the three-phase contact line. When the unbalanced force is sufficiently strong, the drop slips from the pinned contact line and slides inward. Depinning of the drop alters the mode of evaporation to constant contact angle (CCA) mode till it repins onto the surface. The change in evaporation mode from CCR to CCA is usually achieved by tuning the pinning energy barrier by controlling the surface properties of the substrate. Here, we demonstrate that the evaporation mode can be controlled by solely tailoring the surface tension of the drop, which is achieved in microgel particle-laden sessile drops that show spontaneous adsorption of microgels to the air/water interface, leading to a decrease in the interfacial tension. We show that droplets containing a sufficient number of microgels evaporate predominantly in CCR mode even on a hydrophobic surface, and the contact line remains pinned throughout the evaporation of the drop. Interestingly, the contact line dynamics can be controlled by tuning the softness of the microgels and the particle concentration in the drops.

Static nanodroplets and dynamic contact line (CL) movements were visualized by an in situ transmission electron microscope (TEM) liquid cell technique at nanometer spatial resolution. Crawling and sliding movements of nanoscale CL were observed. The crawling happened at a capillary number (Ca) range of ∼10-9 to ∼10-8, and the sliding happened at a Ca range of ∼10-8 to ∼10-7. Three dimensional (3D) image construction had been employed to study static and dynamic contact angles (CAs) at nanoscale. CA hysteresis at nanoscale was observed in the sliding but not in the crawling. The energies associated with sliding were analyzed to investigate the CA hysteresis. An empirical model of the relationship between nanoscale CAs and Ca was developed. Both the experimental observation and the empirical analysis suggested that the competition among substrate defect, CL elastic, and molecular activation energies dictated different CL movements at nanoscale.

Surface tension gradient driven spreading of trisiloxane surfactant solution on hydrophobic solid