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•Heat flux caused by droplet impingement has weaker dependence on surface temperature.•Conduction and surface evaporation are the two most dominant modes of heat transfer.•For ...subcooled impinging droplets, the effect of oscillatory motion is negligible.•Heat flux at droplet interface increases with impact velocity or surface temperature.•Heat flux upon impact is 12x the dry state and 4.5x higher than in the receding MCL.
A comprehensive understanding of heat transfer mechanisms and hydrodynamics during droplet impingement on a heated surface and subsequent evaporation is crucial for improving heat transfer models, optimizing surface engineering, and maximizing overall effectiveness. This work showcases findings related to heat transfer mechanisms and simultaneous tracking of the moving contact line (MCL) for subcooled impinging droplets across a range of surface temperatures, utilizing a custom MEMS device, at multiple impact velocities. Experimental results show that heat flux caused by droplet impingement has a weaker dependence on surface temperature than receding MCL heat transfer due to evaporation, which is significantly surface temperature dependent. The measurements also demonstrate that when a droplet impacts a heated surface and evaporates, the process can be divided into two segments based on the effective heat transfer rate: an initial conduction-dominated segment followed by another segment dominated by surface evaporation. For subcooled impinging droplets, the effect of oscillatory motion is found to be negligible, unlike in a superheated regime; hence, heat conduction into the droplet entirely governs the first segment. Results also show that heat flux at the solid-liquid interface of an impinging droplet increases with the rise of either impact velocity or surface temperature. In the subcooled regime, droplets impacting a heated surface have approximately 1.6 times higher vertical heat flux values than gently deposited droplets. Furthermore, this study quantifies the contributions of buoyancy and thermocapillary convection within the droplet to the overall heat transfer.
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•A novel microdevice combines phase interface and temperature sensing schemes.•MCL precedes the actual change in local surface temperature during evaporation.•Time lag between MCL ...passage and associated thermal response depends on MCL's speed.•The passage of MCL contributes more than 70% of the overall temperature change.•Maximum local heat flux values occurred at the three-phase contact line region.
Despite the important and pervasive nature of evaporative heat transfer phenomena, fundamental questions still remain about the microscopic processes that occur in and around individual droplets on a surface. In order to understand the underlying physics behind evaporative heat transfer, it is critical to have information at the individual droplet level regarding the surface temperature distribution with time as well as the location and speed of the moving multiphase contact line (MCL). In this work, a multifunctional microscale device comprised of a resistance heater, an array of spatially distributed thin-film resistance temperature detectors, and a phase interface sensing capacitance micro-sensor array has been utilized to measure the local heat transfer characteristics and MCL behavior simultaneously for the evaporation of individual sessile water droplets on a horizontal heated surface. The resistance- and capacitance-based operating principles of the micro-device means that it is capable of detecting temperature changes and tracking MCL at the microscale in real time even for applications with limited or no visibility such as within thermal management hardware or processing equipment. Importantly, having knowledge of the MCL’s location and speed with microscale precision allows for its influence on surface temperature and heat transfer to be directly studied rather than inferred. Results show that the MCL passage precedes the change in local surface temperature and the duration of the time difference between these events depends on the MCL’s speed. In addition, the passage of the MCL accounts for more than 70% of the overall temperature change during the evaporation process.
In this paper, we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line. The model is a coupled system that consists of incompressible ...Navier–Stokes equations with a generalized Navier boundary condition and Cahn–Hilliard equation in conserved form. In both schemes the projection method is used to deal with the Navier–Stokes equations and stabilization approach is used for the non-convex Ginzburg–Landau bulk potential. By some subtle explicit–implicit treatments, we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions. An efficient spectral-Galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed schemes are very efficient and accurate.
•We proposed two linear energy stable numerical schemes for a phase field moving contact line model.•Discrete energy laws that are consistent to the continuous ones are proved.•The efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified.
Heat and mass transfer at a droplet impinging on a hot wall is investigated experimentally and numerically. The experiments are conducted with refrigerant FC-72 within a saturated vapour atmosphere. ...The droplet dynamics and the heater temperature very close to the solid–fluid interface are captured with high spatial and temporal resolution. The boundary conditions for the numerical simulations are chosen according to the experiments. The simulation accounts for the complex two-phase flow including evaporative mass transfer. Special attention is given to the local heat and mass transfer close to the moving three-phase contact line. Numerical and experimental results are compared to give insight into the basic heat transport mechanisms occurring during drop impact and to quantify their relevance for the overall heat transfer. It turns out that convective heat transfer is dominant during the initial stage of the impact corresponding to the droplet spreading, while at the final stage of the impact, corresponding to evaporation of a sessile droplet, a considerable part of the total heat transfer occurs in the direct vicinity of the three-phase contact line.
The interplay between phase separation and wetting of multicomponent mixtures is ubiquitous in nature and technology and recently gained significant attention across scientific disciplines, due to ...the discovery of biomolecular condensates. It is well understood that sessile droplets, undergoing phase separation in a static wetting configuration, exhibit microdroplet nucleation at their contact lines, forming an oil ring during later stages. However, very little is known about the dynamic counterpart, when phase separation occurs in a nonequilibrium wetting configuration, i.e., spreading droplets. Here we show that liquid-liquid phase separation strongly couples to the spreading motion of three-phase contact lines. Thus, the classical Cox-Voinov law is not applicable anymore, because phase separation adds an active spreading force beyond the capillary driving. Intriguingly, we observe that spreading starts well before any visible nucleation of microdroplets in the main droplet. Using high-speed ellipsometry, we further demonstrate that the evaporation-induced enrichment, together with surface forces, causes an even earlier nucleation in the wetting precursor film around the droplet, initiating the observed wetting transition. We expect our findings to improve the fundamental understanding of phase separation processes that involve dynamical contact lines and/or surface forces, with implications in a wide range of applications, from oil recovery or inkjet printing to material synthesis and biomolecular condensates.
•A finite force is identified for the no-slip hydrodynamic solution of the MCL.•Microscopic dynamic contact angle is modeled using a new dynamic Young’s equation.•MCL force and angle are a function ...of viscosity, velocity, and surface tension only.
In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young’s equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox’s model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.
We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The ...model is a nonlinear, coupled system that consists of incompressible Navier–Stokes equations with the generalized Navier boundary condition, and the Cahn–Hilliard equations with moving contact line boundary conditions. By some subtle explicit–implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectral-Galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate.
We consider the thin-film equation ∂th+∇⋅(h2∇Δh)=0 in physical space dimensions (i.e., one dimension in time t and two lateral dimensions with h denoting the height of the film in the third spatial ...dimension), which corresponds to the lubrication approximation of the Navier–Stokes equations of a three-dimensional viscous thin fluid film with Navier-slip at the substrate. This equation can have a free boundary (the contact line), moving with finite speed, at which we assume a zero contact angle condition (complete-wetting regime). Previous results have focused on the 1+1-dimensional version, where it has been found that solutions are not smooth as a function of the distance to the free boundary. In particular, a well-posedness and regularity theory is more intricate than for the second-order counterpart, the porous-medium equation, or the thin-film equation with linear mobility (corresponding to Darcy dynamics in the Hele-Shaw cell). Here, we prove existence and uniqueness of classical solutions that are perturbations of an asymptotically stable traveling-wave profile. This leads to control on the free boundary and in particular its velocity.
When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might ...be a liquid film or an arrangement of droplets depending on the receding speed of the meniscus and the wetting properties of the system. For complex liquids with volatile components as, e.g., polymer solutions and particle or surfactant suspensions, the deposit might be a homogeneous or structured layer of solute — with structures ranging from line patterns that can be orthogonal or parallel to the receding contact line via hexagonal or square arrangements of drops to complicated hierarchical structures. We review a number of recent experiments and modelling approaches with a particular focus on mesoscopic hydrodynamic long-wave models. The conclusion highlights open question and speculates about future developments.
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•Experimental results and modelling approaches for deposition patterns emerging at moving contact lines are reviewed.•Relations between onset of patterned deposition and depinning transitions in other soft matter systems are highlighted.•Outlook sketches how to derive long-wave models for coupled fields in a systematic and thermodynamically consistent manner.
Droplet motions fill a periodic table Steen, Paul H.; Chang, Chun-Ti; Bostwick, Joshua B.
Proceedings of the National Academy of Sciences - PNAS,
03/2019, Volume:
116, Issue:
11
Journal Article
Peer reviewed
Open access
Drawing parallels to the symmetry breaking of atomic orbitals used to explain the periodic table of chemical elements; here we introduce a periodic table of droplet motions, also based on symmetry ...breaking but guided by a recent droplet spectral theory. By this theory, higher droplet mode shapes are discovered and a wettability spectrometer is invented. Motions of a partially wetting liquid on a support have natural mode shapes, motions ordered by kinetic energy into the periodic table, each table characteristic of the spherical-cap drop volume and material parameters. For water on a support having a contact angle of about 60°, the first 35 predicted elements of the periodic table are discovered. Periodic tables are related one to another through symmetry breaking into a two-parameter family tree.
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