Sessile drops: spreading versus evaporation–condensation

We experimentally and theoretically investigate a distinct problem of spreading, evaporation, and the associated dried deposits of a colloidal particle-laden aqueous sessile droplet on a surface in a saturated alcohol vapor environment. In particular, the effect of particle size on monodispersed suspensions and efficient self-sorting of bidispersed particles have been investigated. The alcohol vapor diffuses toward the droplet's curved liquid-vapor interface from the far field. The incoming vapor mass flux profile assumes a nonuniform pattern across the interface. The alcohol vapor molecules are adsorbed at the liquid-vapor interface, which eventually leads to absorption into the droplet's liquid phase due to the miscibility. This phenomenon triggers a liquid-vapor interfacial tension gradient and causes a reduction in the global surface tension of the droplet. This results in a solutal Marangoni flow recirculation and spontaneous droplet spreading. The interplay between these phenomena gives rise to a complex internal fluid flow within the droplet, resulting in a significantly modified and strongly particle-size-dependent dried colloidal deposit. While the smaller particles form a multiple ring pattern, larger particles form a single ring, and additional "patchwise" deposits emerge. High-speed visualization of the internal liquid-flow revealed that initially, a ring forms at the first location of the contact line. Concurrently, the Marangoni flow recirculation drives a collection of particles at the liquid-vapor interface to form clusters. Thereafter, as the droplet spreads, the smaller particles in the cluster exhibit a "jetlike" outward flow, forming multiple ring patterns. In contrast, the larger particles tend to coalesce together in the cluster, forming the "patchwise" deposits. The widely different response of the different-sized particles to the internal fluid flow enables an efficient sorting of the smaller particles at the contact line from bidispersed suspensions. We corroborate the measurements with theoretical and numerical models wherever possible.

This chapter discusses mainly about five important physical concepts in liquid and gas systems, which are phase equilibrium, phase transition, interface, contact angle, and cluster. Phase refers to the physically distinctive form of a substance. From the view of thermodynamics, the states and conditions for phase equilibrium are described and some fundamentals for phase transition are introduced. A liquid-vapor interface is considered to be a very thin region having rapid changes in fluid or material properties from the bulk liquid to bulk vapor. Using surface excess quantity, the thermodynamic analysis can be conducted to explore the interfacial effects. Interface tension and Young-Laplace equation are discussed here. The contact angle, which is used to quantify the wettability of liquid, is defined as the angle between the liquid-vapor interface and the solid surface at the contact line. Contact angle equilibrium, hysteresis and dynamic are discussed. Clusters consisting of tens and hundred of atoms or molecules are a new class of compounds called atomic or molecular clusters. The number balance equation is formulated for activated molecules in clusters, with a comprehensive investigation of the dynamics of clusters formed with internal or external perturbations.

Although the contact angle between a liquid/vapor interface and a flat homogeneous solid at equilibrium is well explained at equilibrium, the motion of the triple line line is still not well understood. A mobility equation relates the deviation of the contact angle out of its equilibrium value and its speed on the solid. As the line moves on the solid thanks to an evaporation/condensation process, this introduces a dynamical Arrhenius factor small enough to make the mobility of the contact line the limiting factor of the dynamics, the smallness of the mobility being a well known experimental fact. Outside of the neighborhood of the moving contact line, the liquid-vapor interface is at equilibrium for capillary forces. This approach predicts well the cusps observed on the rear edge of droplets sliding on a tilted plane. A more microscopic theory is sketched that couples van der Waals phase field and Stokes-like fluid equations. For very small Arrhenius factors, this set of equations yields a dynamical change of the functions in the van der Waals phase field equation. The motion of the contact line may thus even lead to a wetting transition, that is to a continuous variation of the contact angle from a finite to a zero value as the receding velocity increases. This may be related to the observation of a limit contact angle in liquid flowing down a plate [1], [7] as well as to the known sensitivity of contact line mobility to vapor pressure.

Spreading of nanofluids driven by the structural disjoining pressure gradient.

Dynamics of dewetting

The behavior of a fluid inside a closed narrow slit between solid walls is examined on the basis of the density functional theory. It is shown that the constraint of constant number of molecules leads to interesting effects which are absent when the slit is open and in contact with a reservoir. If the slit walls are identical, the density profiles at low temperatures or at high average densities rhoav of the fluid molecules in the slit have a sharp maximum in the middle of the slit, the value of the density at maximum being comparable to that of a liquid. The density of fluid at the walls is in this case comparable to the density of a vapor phase. At high temperatures or at low rhoav the fluid density in the middle of the slit is of the same order of magnitude as at the walls. For nonidentical walls the density maximum is shifted towards the wall with a stronger wall-fluid interaction. The transition between the two types (with and without the sharp maximum) of density profiles with the change of temperature in the slit occurs in a narrow range of temperatures, this range being larger for narrower slits. The pressures which the fluid exerts on the walls as well as the forces per unit area arising due to stresses in the sidewalls of the system can decrease with increasing rhoav. Such a behavior is not possible for homogeneous systems and can be explained by analyzing the fluid density at the walls when rhoav increases. The normal and transversal components of the pressure tensor were calculated as functions of the distance from the wall using the equation of hydrostatic equilibrium and direct calculation of the forces between molecules, respectively. The normal component decreases with increasing distance near the wall in contrast to the normal component near the liquid-vapor interface reported previously in the literature. The behavior of the transverse component does not depend on the fluid-solid interaction and is comparable to that for a liquid-vapor interface.

Water emerging from micrometer-sized pores into millimeter-sized gas-flow channels forms drops. The drops grow until the force from the flowing gas is sufficient to detach the drops as either (1) slugs that completely occlude the cross section of the channel and move at the superficial gas velocity, (2) drops that partially occlude the channel and move at a velocity that is less than the gas velocity, or (3) films that flow continuously, occluding part of the channel. At steady state, small residual water droplets, ∼100 μm in diameter, left in corners and on surface defects from previous drops, are key in determining the shape of water drops at detachment. Slugs are formed at low-gas-phase Reynolds numbers (ReG) in both hydrophilic and hydrophobic channels. Drops are shed in Teflon-coated hydrophobic channels for ReG > 30. Films are formed in acrylic hydrophilic channels for ReG > 30. Slugs form when growing drops encounter residual water droplets that nucleate the drop to slug transition. Drops are shed when the force exerted by the flowing gas on growing drops exceeds the force needed to advance the gas/liquid/solid contact line before they grow to the critical size for the drop to slug transition. Drops grow by "stick-slip" of the solid-liquid-gas contact lines and with pinned contact lines until the force on the drops results in either the downstream contact angle becoming greater than the dynamic advancing contact angle or the upstream contact angle becoming less than the dynamic receding contact angle. The upstream contact line never detaches for hydrophilic channels, which is why films form. The shape of water drops and the detachment energies are shown to be well approximated by the force balance between the force needed to advance the drop's contact lines and the force that the flowing gas exerts on a stationary drop.

The effect of three-phase contact line speed on local evaporative heat transfer: Experimental and numerical investigations

Review: 214 refs.

Molecular dynamics simulation on bubble formation in a nanochannel

Evaporating sessile drops remain pinned at the contact line during much of the evaporation process, and leave a ring of residue on the surface upon dryout. The intensive mass loss near the contact line causes solute particles to flow to the edge of the droplet and deposit at the contact line. The high vapor diffusion gradient and the low thermal resistance of the film near the contact line are responsible for very efficient mass transfer in this region. Although heat and mass transfer at the contact line have been extensively studied, well-characterized experiments remain scarce. The local mass transport in a 100-400 microm region near the contact line of a water droplet of radius 1810 microm on a glass substrate is experimentally quantified in the present work. Microparticle image velocimetry measurements of the three-dimensional flow field near the contact line are conducted to map the velocity field. Combined with high-resolution transient liquid profile shapes, the measured velocity field yields transient local evaporative mass fluxes near the contact line. The spatial and temporal distribution of the local evaporative flux is also documented. The temperature distribution in the droplet near the contact line is deduced from the local evaporative fluxes and interface mass transport theory.

An integrated microchannel heat sink consisting of shallow, nearly rectangular microchannels has been fabricated using standard micromachining techniques to highlight the effects of the micrometer sized channel shape on the evolving flow patterns and, consequently, on the thermal performance of the microsystem. An integrated heater serves as a local heat source, while an array of micro thermistors is used for temperature distribution measurements. The working fluid, DI water, is pressurized through the microchannels for forced convection heat transfer studies. Boiling curves for different flow rates have been recorded and analyzed based on the visualized flow patterns. Local nucleation, including bubble formation and bubble dynamics, is documented and found to be negligible. Although detected, in contrast with triangular microchannels, annular flow is observed to be unstable. Instead, the dominant flow pattern is an unsteady transition region connecting an upstream vapor zone to a downstream liquid zone with an average location depending on the input power. A physical mechanism based on the force balance across the vapor–liquid interface, and the development of a restoring force, is proposed to explain the flow visualization results.

In the present study, the effect of contact-line mobility on the natural oscillations of sessile drops is investigated through interface-resolved simulations. A hyperbolic tangent function is employed to model the variation of contact angle (CA) with contact-line (CL) velocity. The range of CL mobility considered is sufficient to recover the free contact-line (FCL) and pinned contact-line (PCL) limits. For finite CL mobility between these asymptotic limits, the CL can move, and the CA varies with CL velocity. The equilibrium CA and CL mobility are systematically varied to investigate their effects on oscillation frequency, energy dissipation, and oscillation decay rate. The results show that the oscillation frequency increases monotonically with CL mobility, transitioning from the FCL to the PCL limit. The CL dissipation is zero at the FCL and PCL limits and exhibits a non-monotonic dependence on CL mobility. The oscillation decay rate generally decreases with increasing equilibrium CA. However, due to the non-monotonic variation of CL dissipation with CL mobility, the decay rate initially increases and then decreases as CL mobility increases.

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.

Droplet detachment in cross-flow membrane emulsification: Comparison among torque- and force-based models