# Poster session

Tuesday, March 27, 2018 - 4:40pm - 6:00pm

Lind 400

**Droplet breakup in a stagnation point flow**

Alireza Hooshanginejad (University of Minnesota, Twin Cities)

Recent studies by Hooshanginejad and Lee (2017) have demonstrated complex depinning behaviors of a partially wetting droplet under wind. Motivated by this study, we examine the coupled evolution of a 2D thin drop and external wind, when it is initially held against a fast stagnation point flow. Our drop lubrication model employs the potential flow and Prandtl boundary layer theory for outer flow to compute the internal drop flow corresponding to drop deformations. Furthermore, both the analytical and numerical steady state solutions provide a partial prediction for the drop’s final shape and help identify the range of droplet sizes that undergo a breakup for the given flow condition.**Moving contact-line mobility measured**

Paul Steen (Cornell University)

Contact-line mobility characterizes how fast a liquid can wet or unwet a solid support by relating the contact angle Δα to the contact-line speed $U_{CL}$. The contact angle changes dynamically with contact-line speeds during rapid movement of liquid across a solid. Speeds beyond the region of stick–slip are the focus of this experimental paper. For these speeds, liquid inertia and surface tension compete while damping is weak. The mobility parameter $M$ is defined empirically as the proportionality, when it exists, between Δα and $U_{CL}$, $MΔα = U_{CL}$. We discover that $M$ exists and measure it. The experimental approach is to drive the contact line of a sessile drop by a plane-normal oscillation of the drop’s support. Contact angles, displacements and speeds of the contact line are measured. To unmask the mobility away from stick–slip, the diagram of Δα against $U_{CL}$, the traditional diagram, is remapped to a new diagram by rescaling with displacement. This new diagram reveals a regime where Δα is proportional to $U_{CL}$ and the slope yields the mobility $M$. The experimental approach reported introduces the cyclically dynamic contact angle goniometer. The concept and method of the goniometer are illustrated with data mappings for water on a low-hysteresis non-wetting substrate.**Role of surface tension gradient in determining microscopic dynamic contact angle**

Joseph Thalakkottor (University of Florida)

Following Gibb's interpretation of an interface as a dividing surface, the force balance is rewritten for a control volume encompassing the interface and the contact line. We find that in addition to surface tension of respective interfaces, the gradient of surface tension also plays an important role in determining the dynamic contact angle. The surface tension gradient not only contributes towards an additional force, but it also accounts for the deviation of local surface tension from its static equilibrium value. This gradient in surface tension is attributed to convective acceleration in the vicinity of the contact line, which in turn is a direct result of varying degree of slip in that region. In addition, we provide evidence that the surface tension gradient is one of the key factors responsible for difference in contact angles at the leading and trailing edge of a steadily moving contact line. These finding are validated using molecular dynamics simulations.**Breakup of finite size liquid filaments including substrate effects**

Shahriar Afkhami (New Jersey Institute of Technology)

This work studies the breakup of finite size liquid filaments on substrates, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension surfaces, the liquid filament aspect ratio, and a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up into one or multiple droplets or collapses into a single droplet on the substrate. The results are compared with the ones available in the literature for free standing liquid filaments. The findings show that the presence of the substrate promotes breakup of the filament. The effect of the degree of slip on the breakup is also discussed. Finally, direct numerical simulations reveal striking new details into the breakup pattern for low Ohnesorge numbers, where the dynamics are fast and the experimental imaging is not available; our results therefore significantly extend the range of Ohnesorge number over which filament breakup has been considered.**Who needs Herakles? A finite force at the moving contact line**

Peter Zhang (University of Florida)

It is widely known that the Stokes solution to the moving contact line (MCL) problem yields an infinite stress if the no-slip boundary condition is enforced. In the past, this infinite stress has been associated with a logarithmically infinite force, which led Huh & Scriven (1971) to state: “not even Herakles could sink a solid if the physical model were entirely valid”. Revisiting previous analyses of the MCL reveals that an infinite force is obtained through integral equations that are derived for smooth interfacial surfaces. However, the MCL is a corner singularity that cannot be treated in the same way as a smooth interface. In order to capture the complete force balance, we define an infinitesimally small cylindrical control volume that encloses the entire contact line and captures the forces acting along all three interfaces. A summation of the forces acting on this volume yields a finite force despite a singular stress. This finite force analysis extends Young’s equation to MCLs and provides a theoretical model for the microscopic dynamic contact angle. When the current model is combined with Cox’s model for dynamic contact angle, we eliminate the microscopic contact angle as an empirical fitting parameter and obtain good agreement with published experimental measurements.**Direct numerical simulation of variable surface tension flows using a Volume-of-Fluid method**

Lou Kondic (New Jersey Institute of Technology)

A general methodology for the inclusion of a variable surface tension coefficient into a Volume-of-Fluid based Navier–Stokes solver is presented. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation is applicable to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. We demonstrate the applicability of our method to the thermocapillary migration of bubbles and the coalescence of drops characterized by a different surface tension coefficient. General methodology can be found in J. Comp. Phys. vol. 352, 615 (2018), and application to modeling thermal Marangoni effect in the context of liquid metals in Phys. Fluids, vol. 30, 012109 (2018). This project is supported by the NSF Grant No. DMS-1320037 and CBET-1604351.**Sweeping by Sessile Drop Coalescence**

Jon Ludwicki (Cornell University)

Condensation is a ubiquitous heat transfer process that manifests as either dropwise or filmwise, depending on the wettability of the condensing surface. In practice, the condensation mode is often filmwise due to its easier control. However, dropwise condensation has gained recent attention due to its higher heat transfer coefficient. During dropwise condensation, vapor condenses as drops onto a cooled surface. Maximal heat transfer is favored by condensing onto fresh surface since smaller drops have a higher heat flux per unit footprint. An important mechanism of fresh surface generation is the sweeping up of nearby drops by a coalescence event. We report on sweeping by sessile drop coalescence, specifically how static contact angle and contact angle hysteresis influence the surface area swept by dynamic motion. Experiments are used in conjunction with numerical simulations to show how different surface types affect coalescence sweeping for a solid-water-air system.**A combined experimental and multi-scale modeling approach to determine phase change coefficients of cryogenic propellants**

Kishan Bellur (Michigan Technological University)

Prediction and control of evaporation/condensation of cryogenic propellants is one of the key factors limiting long-term space missions. Modeling propellant behavior and predicting phase change rates require models that need to be calibrated with experimental data. However, no such data is available on controlled phase change of cryogenic propellants. Neutron imaging is employed as a means to visualize the condensed propellant inside opaque metallic containers at temperatures as low as 17 K. These are the first known images of liquid hydrogen and methane. Evaporation/condensation tests were conducted using containers of different sizes, shapes and materials. A CFD thermal model is used determine the inner wall solid-fluid temperature distribution from discrete experimental outer wall measurements. A multi-scale phase change model is used to evaluate the non-uniform evaporation flux along the liquid-vapor interface. A technique to determine the phase change coefficients using a combination of neutron imaging experiments, a CFD thermal model and a multi-scale phase change model is presented. The onset of condensation is investigated and the results show that both liquid hydrogen and methane are perfectly wetting to Al 6061 and SS 316. A new technique to probe length scales lower than the imaging resolution is developed and discussed.**Drying of Droplets of Colloidal Suspensions on Rough Substrates**

Truong Pham (University of Minnesota, Twin Cities)

In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.**Transfer of Rate-thinning and Rate-thickening Liquids Between Separating Plates and Cavities**

Jyun-Ting Wu (University of Minnesota, Twin Cities)

One promising technology for fabricating low-cost printed electronics on a large scale is roll-to-roll gravure, which involves transfer of inks from microscale cavities to a second surface. Although printing inks containing functional additives usually exhibit non-Newtonian rheological behavior, the influence of ink rheology on liquid transfer is not yet well understood. To address this issue, an axisymmetric model is used to develop fundamental understanding of how ink rheology affects liquid transfer between vertically separating surfaces. Liquids whose rheological behavior is described by Carreau-type models are considered, inertial and gravitational forces are neglected, and the nonlinear governing equations are solved with the Galerkin finite-element method. For liquid transfer between two flat plates, the results reveal that rate-thinning (rate-thickening) rheology leads to reduced (enhanced) viscosities near the less-wettable surface where stronger pressure gradients arise. The reduced (enhanced) viscous forces further assist (hinder) the slip of the moving contact line, allowing more (less) liquid to be transferred from the less-wettable surface to the more-wettable one. For liquid transfer between a flat plate and a trapezoidal cavity, the amount of liquid transferred to the flat plate is found to increase with a larger cavity angle and this phenomenon is observed for both Newtonian and rate-dependent liquids. In addition, the influence of rate-dependent rheology is found to primarily occur near the flat plate. This behavior is attributed to the presence of the cavity wall, which reduces the interface deformation, the associated capillary pressure gradients, and thus the effect of rate-dependent rheology. As a consequence, rate-thickening (rate-thinning) tends to increase (decrease) the amount of liquid transferred from the cavity.**Dynamics of moving contact lines: From the nano- to the macroscale**

Serafim Kalliadasis (Imperial College London)

Reviewed in this poster are selected recent advances made by our group at Imperial towards the resolution of the highly controversial 50 year old moving contact line problem. In particularly we report on the derivation of new multiscale unified continuum model that retains the fundamental elements of any fluid across all length- and timescales: from detailed information on the microscale and intermolecular interactions with the fluid and between the fluid and boundaries (thus accounting for the effects of confinement) to hydrodynamic interactions and inertia. The model is mathematically well-posed and versatile, i.e. analytically accessible and computationally tractable. It is used to offer fundamental insight on the intricate physics occurring in the immediate vicinity of a moving contact line.**High Reynolds number oscillatory contact lines**

William Schultz (University of Michigan)**Electrostatic Assist of Liquid Transfer between Flat Surfaces**

Chung-Hsuan Huang (University of Minnesota, Twin Cities)

Transfer of liquid from one surface to another plays a vital role in printing processes. During liquid transfer, a liquid bridge is formed and subjected to substantial extension, but incomplete liquid transfer can produce defects that are detrimental to the operation of printed electronic devices. One strategy for minimizing these defects is to apply an electric field, a technique known as electrostatic assist (ESA). However, the physical mechanisms underlying ESA remain a mystery. To better understand these mechanisms, slender-jet models are developed for both perfect dielectric and leaky dielectric axisymmetric Newtonian liquid bridges with moving contact lines. Nonlinear partial differential equations describing the evolution of the bridge radius and interfacial charge are derived, and then solved using finite-element methods. For perfect dielectrics, application of an electric field enhances liquid transfer to the more wettable surface over a wide range of capillary numbers. The electric field modifies the pressure differences inside the liquid bridge, and as a consequence, drives liquid toward the more wettable surface. For leaky dielectrics, charge can accumulate at the liquid-air interface. Application of an electric field can augment or oppose the influence of wettability differences, depending on the direction of the electric field and the sign of the surface charge. Flow visualization experiments reveal that when an electric field is applied, more liquid is transferred to the more wettable surface due to a modified bridge shape that causes depinning of the contact line. The measured values of the amount of liquid transferred are in good agreement with predictions of the perfect dielectric model.