Challenges in Nanoscale Physics of Wetting Phenomena

We investigate the transition between different regimes of lubrication, and present a new method to directly observe the thickness of the nanometric lubrication films with a sensitivity of a single molecular layer between rough surfaces. This allows for measurement of the structure of the lubrication film in three dimensions and with unprecedented resolution. We use a novel definition of the specific film thickness successfully captures the transition from full elastohydrodynamic lubrication to mixed and boundary lubrication.

Determining the lifetime of an evaporating sessile droplet on a solid substrate is an important part of understanding many industrial processes, such as ink-jet printing, coating, and spray cooling, as well as drug delivery systems and chemical spill containment. Consequently, in recent years there has been a rapid growth of experimental and theoretical research into droplet evaporation. Previous authors [1] have shown that the instantaneous evaporation rate of a droplet depends on the thermal conductivity of the substrate. In the present work we use a combination of analytical and numerical methods to study the effect of the thermal conductivity of the substrate on the evolution, and hence the lifetime, of an evaporating droplet. In the limit of a thin droplet on a thin substrate we obtain analytical expressions for the lifetimes of droplets evaporating in various modes of evaporation [3]. In the general case of a non-thin droplet we use numerical methods to calculate the lifetimes of droplets evaporating in various modes of evaporation on substrates of various thermal conductivities. In general, droplets on less conductive substrates are found to have longer lifetimes than those on more conductive ones.

References
[1] Dunn G. J., Wilson S. K., Duffy, B. R., David, S. and Sefiane K. "The strong influence of substrate conductivity on droplet evaporation" Journal of Fluid Mechanics, 2009, 623, 329-351.
[2] Stauber J. M., Wilson S. K., Duffy, B. R. and Sefiane K. "On the lifetimes of evaporating droplets" Journal of Fluid Mechanics, 2014, 744, R2.
[3] Schofield F. G. H., Wilson S. K., Pritchard, D. and Sefiane K. "The lifetimes of evaporating sessile droplets are significantly extended by strong thermal effects" Journal of Fluid Mechanics, 2018, 851, 231-244.

The resolution of the moving contact line

The moving contact line problem occurs when modelling one fluid replacing another as it moves along a solid surface, a situation widespread throughout industry and nature. Classically, the no-slip boundary condition at the solid substrate, a zero-thickness interface between the fluids, and motion at the three-phase contact line are incompatible - leading to the well-known shear-stress singularity. At the heart of the problem is its multiscale nature: a nanoscale region close to the solid boundary where the continuum hypothesis breaks down, must be resolved before phenomenological macroscale parameters such as contact line friction and slip, often adopted to alleviate the singularity [1], can be obtained.
Here we will review recent progress made by our group to rigorously analyse the moving contact line problem and related physics from the nano- to macroscopic lengthscales. Specifically, to capture nanoscale properties very close to the contact line and to establish a link to the macroscale behaviour, we employ elements from the statistical mechanics of classical fluids, namely density-functional theory (DFT) [2,3]. We formulate a new and general dynamic DFT (DDFT) [4]that carefully and systematically accounts for the fundamental elements of any classical fluid and soft matter system, a crucial step towards the accurate and predictive modelling of physically relevant systems. In a certain limit, our DDFT reduces to a non-local Navier-Stokes-like equation [5]: an inherently multiscale model, bridging the micro- to the macroscale, and retaining the relevant fundamental microscopic information (fluid temperature, fluid-fluid and wall-fluid interactions) at the macroscopic level.
Work analysing the contact line in both equilibrium and dynamics will be presented [6,7]. The new model allows us to benchmark existing phenomenological models and reproduce some of their key ingredients. But its multiscale nature also allows us to unravel the underlying physics of moving contact lines, not possible with any of the previous approaches, and indeed show that the physics is much more intricate than the previous models suggest. For instance, a key property captured by our theory is the fluid layering at the wall-fluid interface, amplified as the contact angle decreases. But also the existence of compressive interfacial regions on the vapor side of the vapor-liquid interface and a large shear region close to the wall in which effective slip can be generated. We demonstrate that the stratified fluid structure in the vicinity of the wall has a large effect on the compression and shearing properties of the fluid and determines the width of the shear region on the wall. We also scrutinize the effect of stratification on contact line friction and the dependence of the latter on the imposed temperature of the fluid and motion orientation [8].

Selected references
[1] D.N. Sibley, A. Nold and S. Kalliadasis 2015 "The asymptotics of the moving contact line: cracking an old nut," J. Fluid Mech. 764, 445-462.
[2] P. Yatsyshin, N. Savva and S. Kalliadasis 2015 "Wetting of prototypical one- and two-dimensional systems: Thermodynamics and density functional theory," J. Chem. Phys. 142, Art. No. 034708.
[3] P. Yatsyshin, A.O. Parry and S. Kalliadasis 2016 "Complete prewetting," J. Phys.: Condens. Matter 28, Art. No. 275001.
[4] B.D. Goddard, A. Nold, N. Savva, G.A. Pavliotis and S. Kalliadasis 2012 "General dynamical density functional theory for classical fluids," Phys. Rev. Lett. 109, Art. No. 120603.
[5] B.D. Goddard, A. Nold, N. Savva, P. Yatsyshin and S. Kalliadasis 2013 "Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments," J. Phys.: Condens. Matter 25, Art. No. 035101.
[6] A. Nold, D.N. Sibley, B.D. Goddard and S. Kalliadasis 2014 "Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory," Phys. Fluids 26, Art. No. 072001.
[7] A. Nold, D.N. Sibley, B.D. Goddard and S. Kalliadasis 2015 "Nanoscale fluid structure of liquid-solid-vapor contact lines for a wide range of contact angles," Math. Model. Nat. Phenom. 10, 111-125.
[8] A. Nold, PhD Thesis, Imperial College London (2016).

Drops sliding down an inclined wall can have very different shapes, depending on their composition. This is a simple everyday example of the complex interplay between drop shape, substrate properties and dynamics of wetting. In static situations, liquid surfaces are characterized by a surface tension that depends on thermodynamic quantities like temperature and composition of the liquid. For dynamic situations, the surfaces tension becomes additionally a function of, e.g., the deformation rate of the surface. A tutorial example is sitting drop on a deformable immiscible substrate. I will discuss changes in drop shape, condensation, and drop motion. The surface tension exerts a vertical force to the substrate. For soft enough substrates (low elastic modulus of the substrate) this leads to a deformation of the substrate under the drop. Not only quasi-static properties, like nucleation barrier [1] or drop shape are influences, also the dynamics of the drop (sliding) is strongly changed [2]. Here, the viscosity or viscoelasticity of the substrate influences the drop motion. Liquid surfaces have rheological properties that are independent of the bulk properties. The surface alone can exhibit elastic or viscoelastic restoring forces against shear or extensional deformation. Even at identical static surfaces properties, the dynamics behavior of drops strongly differ due to surface rheology of the liquid. I will give some examples on this and discuss, e.g., dynamic receding contact angles [3].

References
1. Sokuler, M., G. K. Auernhammer, M. Roth, C. Liu, E. Bonacurrso and H.-J. Butt (2009). "The Softer the Better: Fast Condensation on Soft Surfaces." Langmuir 26(3): 1544-1547.
2. Karpitschka, S., S. Das, M. van Gorcum, H. Perrin, B. Andreotti and J. H. Snoeijer (2015). "Droplets move over viscoelastic substrates by surfing a ridge." Nat Commun 6.
3. Henrich, F., D. Fell, D. Truszkowska, M. Weirich, M. Anyfantakis, T.-H. Nguyen, M. Wagner, G. K. Auernhammer and H.-J. Butt (2016). "Influence of surfactants in forced dynamic dewetting." Soft Matter 12: 7782 - 7791.

Modeling of evaporation in the microregion separating an adsorbed film and a macroscopic meniscus is important for a number of applications such as pool boiling and micro heat pipes. We develop a model of a moving microregion incorporating the effects of evaporation, viscous flow, surface tension, and two-component disjoining pressure and apply it to study contact line motion over heated surfaces with wettability defects or patterns. Substantial heat transfer enhancement is found when a receding microregion passes over the portion of the substrate with higher wettability than the surrounding areas. The effect is explained in physical terms by widening of the part of the microregion with low thermal resistance. To achieve sustained heat transfer enhancement, we then consider a configuration in which the substrate is patterned by an array of high-wettability stripes and investigate the evaporative flux as a function of the geometry of the pattern. The effects of Marangoni stress at the interface are also studied and found to result in slight reduction of the average evaporative flux, as the tangential stress at the interface reduces the liquid supply into the micro region. Joint work with E. Gatapova and O. Kabov.

Phase separation generates functional, subcellular condensates with fluid-like properties. The mechanisms that degrade fluid phases in cells, however, are not fully understood. Clearance of condensates involves autophagy, a conserved pathway in which membrane sheets isolate portions of the cytosol to form autophagosomes, which then fuse with lysosomes for cargo breakdown. Here, we studied the assembly of autophagic membranes at fluid interfaces in both living and synthetic cells. A minimal physical model shows that interfacial tension determines whether isolation membranes will sequester the condensate entirely, or will prematurely close and degrade the condensate in a piece-meal fashion. In the latter case, curvature-inducing proteins confer a regulatory switch that associates isolation membranes with condensates, however, without degrading them. Thus, condensates persist and serve as a platform to assemble cytosol-degrading autophagosomes repeatedly. Our findings suggest that the autophagic breakdown of fluids - fluidophagy - is a wetting phenomenon, which is controlled by elasto-capillary feedback between the phase-separated condensate and the isolating membrane.

We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds $Ca = U\eta/\gamma$ of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp’s tip scales with the slip length multiplied by an exponential of $−Ca$. The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is ‘wetting failure'. We develop an analytical theory of the threshold to air entrainment, which predicts the critical capillary number to depend logarithmically on the viscosity ratio, with corrections coming from the slip in the gas phase.

The use of inkjet printing to manufacture printed electronics has been receiving increasing attention due to the technique's potential for roll-to-roll manufacturing, lower cost and flexibility. As the droplets used for printing become smaller O(10um), substrate topographical features (designed or due to minor variations) can affect the dynamics and equilibrium morphologies of the printed liquid. Here, the interaction of droplets with a surface featuring an open microchannel are explored. Such a feature could represent a designed structure and allow us to investigate the effect of its dimensions on the printed morphology. A 3D GPU-enabled multiphase Lattice Boltzmann Method is used. The GPU speed-up enables running parametric studies in affordable simulation time. This implementation also captures partial wetting and contact angle hysteresis. The latter is significant as stable continuous printed lines form only if the receding contact angle is very low or zero. The model is validated using experimental data from the literature. The effect on dynamics and equilibrium morphologies of a single droplet as the depth and width of the feature change is investigated using the developed simulation methodology. Varying the width and depth of the microchannel relative to the droplet size reveals six different morphologies varying from complete imbibition into the microchannel to almost just a spherical cap. In addition, a series of droplets that form a continuous printed line are simulated to ascertain what depths and widths of the feature cause breaks in continuity of the line.

We analyze the near-rolling motion of two-dimensional nonwetting drops down a gently inclined plane. Inspired by the scaling analysis of Mahadevan & Pomeau, we focus upon the limit of small Bond numbers, $B\ll1$, where the drop shape is nearly circular {and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop.} Our analysis reveals that the leading-order dissipation is contributed by both the flow in the flat-spot region and the correction to rigid-body rotation in the remaining liquid domain. The resulting leading-order approximation for the drop velocity $\mathcal{U}$ is given by $\mu\, \mathcal{U}/{\gamma} \sim {\alpha}/{2B\ln\frac{1}{B}}$, wherein $\mu$ is the liquid viscosity, $\gamma$ the interfacial tension and $\alpha$ the inclination angle.

A few tricks (hydrophobic texture, Leidenfrost state, etc.) allow us to keep water drops with a spherical shape, which induces spectacular properties. We describe a few of them. We also challenge the water mobility in the cases where it is expected to be impeded - for instance by reducing the drop size or by increasing the water temperature.

We investigate the moving contact line problem for two-phase incompressible flows by means of a kinematic approach, where the key point is an evolution equation for the contact angle assuming the transporting velocity field to be given. The resulting equation expresses the time derivative of the contact angle in terms of the gradients of the fluid velocity and the local mass transfer rate at the solid wall. Combined with the impermeability condition at the solid wall and exploiting the interfacial transmission condition for the viscous stress, we derive an explicit form of the contact angle evolution for sufficiently smooth solutions. This has severe consequences for the qualitative behavior of solutions to standard wetting models: their solutions necessarily have singularities at the contact line or they behave unphysical.

Periodic wetting and dewetting of liquid on a superheated wall is a complex process that occurs in several applications such as nuclear boiling or spray impingement cooling. The wall superheat causes the liquid to evaporate. The local evaporation rate and local heat flux distribution strongly depends on the hydrodynamics of the wetting or dewetting flow and vice versa. Generic experimental setups were designed to understand and characterize these mutual interactions. High spatial and temporal resolution gives insights to the local and transient phenomena. These experiments were cloned with numerical simulations based on the fundamental transport and balance equations using a VOF-based numerical method. The numerical results, once validated against the experiments, allow very detailed evaluation of the local transient temperature and flow profiles. It is observed that the evaporation rate of the liquid is much higher during dewetting situations compared to wetting situations. The dynamic contact line evolution is also strongly dependent on the wall superheat. The complex mutual interactions of local heat transport, temperature gradients, fluid flow, and wetting characteristics are described for different configurations.

We investigate the transition to a Landau–Levich–Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier–Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle θ∆ called the numerical contact angle. Despite the well-known contact line singular- ity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from 15◦ to 110◦ and capillary numbers from 0.00085 to 0.2 where the mesh size ∆ is varied in the range of 0.0035 to 0.06 of the capillary length lc. To interpret the results, we use Cox’s theory which involves a microscopic distance rm and a microscopic angle $θ_e$. In the numerical case, the equivalent of θe is the angle θ∆ and we find that Cox’s theory also applies. We introduce the scaling factor or gauge function φ so that rm = ∆/φ and estimate this gauge function by comparing our numerics to Cox’s theory. The comparison provides a direct assessment of the agreement of the numerics with Cox’s theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on θ∆ and the viscosity ratio q. In the case of small $θ_e$, we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau– Levich–Derjaguin forced dewetting transition. We generalize this prediction to large θe and arbitrary q and express the critical capillary number as a function of θe and rm. This implies also a prediction of the critical capillary number for the numerical case as a function of θ∆ and φ. The theory involves a logarithmi- cally small parameter ε = 1/ln(lc/rm) and is thus of moderate accuracy. Thenumerical results are however in approximate agreement in the general case, while good agreement is reached in the small θ∆ and q case. An analogy can be drawn between the numerical contact angle condition and a regularization of the Navier–Stokes equation by a partial Navier-slip model. The analogy leads to a value for the numerical length scale rm proportional to the slip length. Thus the microscopic length found in the simulations is a kind of numerical slip length in the vicinity of the contact line. The knowledge of this microscopic length scale and the associated gauge function can be used to realize grid-independent sim- ulations that could be matched to microscopic physics in the region of validity of Cox’s theory.

We consider a charged droplet sitting on a dielectric substrate and study the static profile of the interface near the contact line. We first derive the governing equations using the principle of minimum energy, then discuss the distinguished limit of the model as the dimensionless parameters β and d go to zero with d/β = O(1), where β measures the strength of the electrical potential force relative to the curvature force, and d is the thickness of the insulator. Analysis of the inner problem, which governs the interface profile near the contact line, shows the existence of a well-defined apparent contact angle. Significant bending of the interface is observed near the contact line. The apparent contact angle depends on the applied electrical potential and the thickness of the insulator, and the relation agrees well with the Young-Lippmann equation. This work was supported by Singapore MOE AcRF grants and NSFC (No.11871365, NUSRI(Suzhou)).

We present direct numerical simulations for a porous media model consisting of two immiscible fluids in a micro-geometry filled with randomly sized and randomly distributed cylinders. First, interface instability and penetration modes are presented when varying the wetting features of the porous medium, showing that the displacement patterns not only change with the capillary number, but also are a function of the contact angle, even for a viscosity ratio of unity. This is an important conclusion suggesting that capillary number and viscosity ratio alone cannot completely describe the pore-scale displacement. Second, rapid pore-scale displacement is considered, where the displacements are accompanied by sudden interface jumps from one site to another, known as Haines jumps. The characteristic time and length scales of a Haines jump are examined. This work is in collaboration with Adam O’Brien and Markus Bussmann from the University of Toronto.

A crucial part of the numerical simulation of dynamic wetting is the transport of the contact angle, which is typically prescribed by a boundary condition in the mathematical model. In a recent paper (see separate talk by Dieter Bothe), we proved a fundamental kinematic relationship between the change in the contact angle and the transporting velocity field. Besides its implications for the mathematical modeling of dynamic wetting, this "kinematic evolution equation" also serves as a reference to validate the numerical methods. We employ the geometrical Volume-of-Fluid (VOF) method to solve the hyperbolic transport equation for the interface being in contact with the domain boundary. Generalizations of the Youngs and ELVIRA methods to reconstruct the interface close to the boundary are introduced. First order convergence of both the contact line and contact angle transport is demonstrated for the Boundary ELVIRA method while the Boundary Youngs method does, as expected, not deliver mesh convergent results.

Directional droplet spreading motion on a slender body is an adaptation found in plants and animals, and can be utilised in micro-scale systems to move droplets. If a droplet, of a size smaller than the capillary length, is placed on a substrate with a conical shape it spontaneously starts to spread in the direction of a growing fibre radius. I will present how we can rationalise this spreading dynamics by developing a lubrication approximation on a cone and a perturbation method of matched asymptotic expansions. Through these theoretical models, I will discuss what are the physical mechanisms that generates this droplet spreading motion, which appear to come from the small scale physics at the contact line and not the pressure capillary pressure gradient from the large scale droplet shape.Our theory predicts that the droplet will move from the cone tip to its base, consistent with experimental observations.

Dynamic wetting problems are fundamental to understanding the interaction between liquids and solids. In addition to the surface physics of the molecular interactions between fluid and substrate, micro-scale roughness may or may not determine the macroscopic spreading flow. Using experiments on spontaneous spreading of droplets on macroscopically smooth surfaces, with well controlled micron-size structures, we investigate how rapid dynamic wetting depends on the actual geometry of the roughness. We explore a range of symmetric and asymmetric substrate structures and are able to quantify how the geometrical characteristics of the roughness elements determine the reduction of spreading speed, along with criteria for when the spreading is insensitive to substrate roughness. We also investigate the influence of electric forces and find that they can “cloak” the micro- structures, that is, deactivate the hindering. We find consistently that the key to understanding the reduction of spreading speed is the contact line friction, together with the kinematics of the motion of the contact line over the microscopic substrate structures.

We study the directional spreading of a viscous droplet on a wetting conical fiber. When the droplet spontaneously moves from the thinner part of the cone to the thicker part due to capillarity, a Landau-Levich film is deposited on the substrate at the tail of the droplet. Remarkably, the thickness of the film $h_f$ scales with the capillary number $Ca$ as $h_f/r_f\sim Ca^{1/2}$, different from the classical scaling of $2/3$. Here $r_f$ is the radius of the cone. We provide a method of asymptotic matching to obtain this $1/2$ power.

A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed, finite-width interface model. The analysis in the sharp-interface limit shows that the singularity of the viscous stress can be balanced by another singularity of the unbalanced surface stress. The dynamic contact angle is determined by surface tension, viscosity, contact-line velocity and a single non-dimensional parameter reflecting the lengthscale ratio between interface width and the thickness of the first molecule layer at the wall surface. Motivated by theoretical research we also present a curvature boundary condition to circumvent the difficulties of previous approaches on explicitly imposing the contact angle and with respect to mass-loss artifacts near the wall boundary. While employing the asymptotic theory of Cox for imposing an effective curvature directly at the wall surface, the method avoids a mismatch between the exact and the numerical contact angles. Validity of the numerical model is demonstrate for a range of benchmark and application cases.

Curtain coating is an important industrial process that poses formidable challenges for models of dynamic wetting. In this work, dynamic wetting failure of Newtonian liquids in a curtain coating geometry is studied using a hydrodynamic model developed in our prior work (Liu et al., J. Fluid Mech. 808, 290-315 (2016)). Here, we use the model to predict the onset of wetting failure using curtain heights consistent with prior experimental setups. In the model, a Navier-slip boundary condition and constant contact angle are used to describe the dynamic contact line (DCL). The governing equations are solved with the Galerkin finite-element method and the critical substrate speed is identified at which wetting failure occurs. A boundary of a coating window is constructed which outlines the critical substrate speed for different flow rates of the liquid curtain. The model predictions are compared with prior experimental observations reported by Blake et al. (1999) and Marston et al. (2009). The model reproduces the phenomenon of "hydrodynamic assist"---the non-monotonic behavior of the critical speed as the liquid flow rate increases. When surfactants are absent, our results suggest that the experimental observations can largely be explained with a model that uses the simplest boundary conditions at the DCL (Navier-slip and constant contact angle) and accounts for the air stresses there to accurately calculate interface shapes. The hydrodynamic pressure generated by the inertia of the impinging curtain leads to a strong capillary-stress gradient that pumps air away from the DCL and thus increases the critical substrate speed for wetting failure. When surfactants are present, our results suggest that a decrease in the equilibrium surface tension may not be the only mechanism responsible for changes in the shape of the coating window. In particular, Marangoni stresses may play an important role. The results of this work mostly resolve decades-old mysteries related to curtain coating, and suggest several additional challenges for future work (Liu et al., Chem. Eng. Sci. 195, 74-82 (2019)).

The dynamic contact line is studied numerically in two cases -curtain coating and Couette flow- using the CFD program Basilisk. In order to solve accurately the three-phase point we implemented a generalized Navier boundary condition by adding the uncompensated Young stress to a previously computed Robin boundary condition. We compared our results on the hydrodynamic assist with the numerical ones from Liu & al. (2016) and the experimental ones from Blake & al. (1994). Some key-results on the onset of wetting failure will be shown. For Couette flow system, we compared our results with the MD and phase field ones obtained by the KTH research group. Moreover, we placed great importance on the agreement of our model with the Cox law on the interface curvature.

Some polymer brushes show the surprising co-nonsolvency effect: They collapse in a mixture of two good solvents at some specific mixing ratio. Recent studies focused previously on the response of brushes which are entirely covered by a liquid. Here, we concentrate on partial wetting of co-nonsolvent polymer brushes, i.e., on the dynamics of a three-phase contact line moving over such brushes. We demonstrate that the wetting behavior depends on the wetting history of the polymer brush. We use Poly(N-isopropylacrylamide) (PNiPAAm) brushes and water and ethanol as good solvents. In water/ethanol mixtures, the brush thickness is a non-monotonous function of the ethanol concentration. The memory of brushes is tested by consecutively depositing drops of increasing size at the same position. Previously deposited drops induce changes in the brush that modifies the wetting behavior (advancing contact angle) of subsequent drops. We believe that the change in the contact angels is induced by adaptation like swelling of or liquid exchange in the brush due to the drop on top. Since the brush is also in contact with the atmosphere, we are controlling humidity of the atmosphere. We show that the memory effect of the water drop does not appear if the drop is deposited in 100% rel. humidity. It was also investigated how the ethanol concentration changes the memory effect generated by subsequent drops.

Capillary driven flows in tubes or channels with corners impact fluid movement in microfluidic devices and porous media. The main meniscus in cornered capillaries with sizes on the order of the capillary length of the fluid are similar to that in cylindrical capillaries. However, if the walls of the pores are sufficiently wettable, the fluid interface must attain a tight radius near the corners, resulting in the formation of rivulets rising in the corners. This study combines experiment, analysis, and simulation, and investigates the spontaneous and forced movement of fluid in square capillaries and open rectangular channels. Co-authors: V. Gurumurthy, I. Roisman, C. Tropea Technische Universität Darmstadt, Germany.

Moving contact-lines (CLs) dissipate. Sessile droplets, mechanically driven into resonance, can exhibit oscillatory CL motions where CL losses dominate bulk dissipation. Conventional practice measures CL dissipation based on the rate of mechanical work of the unbalanced Young's force at the CL. Typical approaches require measurements local to the CL and assumptions about the “equilibrium” contact angle (CA). This paper shows how to use frequency scanning to characterize CL dissipation without any dependence on measurements from the vicinity of the CL. The results are of immediate relevance to an International Space Station (ISS) experiment and of longer-term relevance to Earth-based wettability applications. Experiments reported here use various concentrations of a water-glycerol mixture on a low-hysteresis non-wetting substrate.

I will reconsider first previous experiments on sliding drops made long ago with silicon oils, and later in Snoeijer team with water. There are strong evidence that the silicon oil case is well described by assuming some slip length at naometer scale, while, on the contrary, a very strong additional friction at contact line must be added in the case of water. I will show how the 3D theory developed for the drop tail shape must be modified to include this effect, via some mixed model in the spirit of Petrov ad Petrov work or the one from Mons team (de Ruiter et al). I will then skip to the case of deformable substrates, in which the dissipation is mainly localized in the - viscoelastic - substrate. We were able to generalize a model from Long et al, and solve the case of very thin layers deposited on a rigid substrate. There are specific scaling laws on both the velocity and layer thickness that we have discovered, and which open a way to the control of wetting dynamics via elastic coating deposited on solids. If time remains I will describe some recent perspectives on non-linear 3D effects in elastowetting, or in the case of spreading on a cold solid with liquid solidification, for which the prediction of the contact line arrest condition remains a challenge.

Since James Thomson (1855), Marangoni phenomena have been extensively discussed and applied to a myriad of applications including material migration, mixing, coating and cleaning. In this talk, we would like to specifically focus on the mechanism of the solutal Marangoni stress how it occurs at the interface between two solutions, in particular alcohol and water. This is to answer how alcohol mixes with water at the boundary and alcohol components in water or generate complex flow structures. We observe that the finite timescale and length scale to create the Marangoni flow exit. Using optical measurements, such as time-resolved 2D particle image velocimetry, 3D particle tracking velocimetry based on machine-learning algorithm, and Schlieren methods, we quantitatively measure the Marangoni-driven convective flow speed for a relatively large and small scale. Physical arguments to support the observations will be discussed during the meeting.

Imbibition of volatile liquids on textured surfaces and in porous layers governs heat and mass transport in natural phenomena and in technological applications, including thermal management of electronic devices and ink-jet printing. These processes are responsible for significant improvement of cooling efficiency during drop impact cooling and flow boiling if the surfaces to be cooled are covered by highly porous nanofiber layers. Prediction of imbibition rate in textured substrates and porous coatings, especially in the presence of evaporation and forced wetting or dewetting, is a very complicated task. The existent imbibition theories for porous media rely on the known constant capillary pressure and the permeability and are not applicable as soon as the shape of the liquid-gas interface changes along the direction of imbibition. In this work a framework for modelling the simultaneous imbibition and evaporation on textured substrates and porous coatings is established and illustrated for two typical elements of textured/coated substrates: a triangular groove and a wedge between a flat substrate and a fiber. The scaling for imbibition rate determined by the balance between the capillarity and viscous friction as well as the scaling for maximum imbibition length are obtained and compared with available experimental data.

The motion of wall-bounded drops, films and rivulets, moving on solid substrates driven by an air flow in a wind tunnel, is determined by the aerodynamic forces, viscous stresses as well as the forces associated with the wall wettability. Better understanding and modeling of such flows is required mainly in the field of the car soiling and aircraft icing. In this study two main cases are considered. One case is the drop motion on a smooth solid substrate. The second case is related to the interaction of a single drop with a groove. For the case of drop behaviour on a smooth substrate the criteria for the inseption of the drop motion are determined experimentally and modelled theoretically. The model has been developed for the mimimum air velocity at which drop still propagates. This critical velocity among other parameters is influenced by the contact angle hysteresis. The motion of the drop is influenced by the viscous stresses in the rear tail. The force balance allwas to develop a simple scaling behaviour fo the dependence of the drop propagation velocity on the air speed. Moreover, the maximumdrop speed is measured, which is associated with the maximum velocity of dewetting. Drop motion is also inluenced by the stick-slip motion of theadvancing and receding contact lines. This contact line bahaviour is analysed in the study. An affective dynamic conatct angle is introudced, which is associated with the contact angle fluctuations. Finally, the drop interaction with a thin groove in a substrate is investigated.Vairous outcomes are classified. The conditions for the drop suckshing by the groove are determined from the comparison of the typical times of the drop sucktion and time of the drop transitions. The model prediction agrees well with the experiments.

Despite the idealization of Young’s law, contact line pinning has been a dominating influence in the studies of wetting. It enables droplets to adhere to vertical windows, drives the coffee ring-stain effect and causes hysteresis in electrowetting to name just a few of its consequences. Here I will consider two recent innovations in surfaces – slippery liquid-infused porous surfaces (SLIPS)/lubricant impregnated surfaces and super omniphobic covalently attached liquid-like (SOCAL) surfaces – which retain the ability to support sessile droplets whilst removing contact line pinning. I will show examples of their application to droplet studies including pinning free evaporation, energy invariant transport, hysteresis free electrowetting and surface acoustic wave driven motion. I will argue that a liquid analogue to Young’s law can be used to predict the apparent contact angle of droplets and that, for conformal coatings, surface free energy arguments show this can be used in familiar equations from contact angle theory, such Cassie-Baxter, Wenzel and the electrowetting equation. Finally, I will give an example of droplet transport using these ideas and a gradient surface. Acknowledgements: The financial support of the UK Engineering & Physical Sciences Research Council (EPSRC) is gratefully acknowledged (EP/K014803/1, EP/K015192/1, EP/P026613/1). Collaborators at Durham, Northumbria and Nottingham Trent Universities were instrumental in the work described.

Colloidal forces are known to influence the pattern deposition of nanoparticles off a volatile carrier liquid. Several experimental studies suggest a direct connection between colloidal forces and the morphology of the particulate deposit. Specifically, variations in the zeta potential of the suspended particles and substrate and variations in the ionic strength in the suspension were found to alter the geometry of the deposit. We use theory and experiment to investigate the connection between colloidal forces and the pattern deposition of colloidal particles off a volatile carrier liquid.
We connect between colloidal forces and pattern deposition by considering the adhesion of particles to the solid substrate and the coagulation of particles in the suspension. Our initial theoretical approach is based on an asymptotic – long wave type – model for the deposition process. In this model we employ the interaction–force boundary layer theorem to account for the rate of adhesion of particles to the solid substrate. The theorem allows for manifesting the dynamic process of adhesion in a form that is reminiscent of a first order chemical reaction in a dynamic advection-diffusion equation for the transport of particle mass in the liquid. Similarly, we employ the augmented Smoluchowski theorem to account for particle aggregation. Hence, the rate of aggregation is manifested in a form that is reminiscent of multiple second order chemical reactions. The coefficients of the reaction terms are associated with the energy barriers for adhesion or coagulation. Comparing the predictions of our asymptotic model to experiment, we find that the rate of adhesion, coagulation, and diffusion of particles in the volatile liquid as well as the rate of liquid evaporation govern the deposition of particles. Moreover, fast adhesion of particles to the solid substrate and fast diffusion of particles in the liquid disperse the spatial distribution of the particulate deposit. Fast coagulation and fast evaporation support the deposition of denser patterns of particles of sharper spatial boundaries.

References
1. E. Homede, A. Zigelman, et al. Signatures of van der Waals and electrostatic forces in the deposition of nanoparticle assemblies; J. Phys. Chem. Lett. 9 (5226–5232) 2018
2. A. Zigelman and O Manor. Simulations of the dynamic deposition of colloidal particles from a volatile sessile drop, J. Colloids Interface Sci. 525 (282-290) 2018
3. A. Zigelman and O. Manor. The deposition of colloidal particles from a sessile drop of a volatile suspension subject to particle adsorption and coagulation, J. Colloids Interface Sci. 509 (195) 2018

This contribution will focus on recently developed models and computational techniques for thin films, with focus on nematic liquid crystal films. Models and computations are developed within the framework of long wave approach, augmented by inclusion of liquid-solid interaction forces via disjoining pressure model. Particular aspect that will be discussed includes tractable inclusion of liquid-crystalline nature of the film in the model in a tractable manner. The simulation techniques include algorithms for GPU computing that allow for simulations of large domains and analysis of various instability mechanisms.

In the past 50 years, numerous alternative models have been advanced to describe dynamic wetting in the framework of continuum mechanics. The multitude of models has led to a lively debate between the modellers but, from the practitioner's viewpoint, is rather unhealthy. Experimental tests performed by some groups to validate/invalidate at least some of the theories on the basis of how accurately they describe some standard experiments turned out to be inconclusive - in each case, several theories appear to be able to describe the data with comparable/acceptable accuracy. This situation calls for a qualitative (as opposed to quantitative) experiment which would serve as a 'litmus test' to cast aside models that fail it and single out those modelling approaches that deserve further development. In this presentation, we discuss such a test. We will also discuss the specific aspects brought in by the nanoscale and the modelling issues that have to be addressed.

An overview is given about formulations of mesoscopic hydrodynamics (or thin-film) models in terms of a gradient dynamics on an underlying free energy. First, the approch is reviewed for films of nonvolatile and volatile simple liquids as well as for films of mixtures and suspensions [1]. Particular attention is given to the extraction of wetting energies from microscopic models [2] and their usage, e.g., to describe the terrassed spreading of nanodroplets [3]. Next, we discuss how the developed gradient dynamics form may be employed to develop models for liquids with more complex phase behaviour and intricate cross-couplings [4], e.g., in the case of concentration-dependent wettability [5]. As an outlook we discuss drops on adaptive substrates.

References
[1] U. Thiele, Colloids Surf. A 553, 487-495 (2018).
[2] A. P. Hughes, U. Thiele and A. J. Archer, J. Chem. Phys. 142, 074702 (2015) and J. Chem. Phys. 146, 064705 (2017). [3] H. Yin, D. N. Sibley, U. Thiele and A. J. Archer, Phys. Rev. E 95, 023104 (2017). [4] U. Thiele, A. Archer, L. Pismen, Phys. Rev. Fluids 1, 083903 (2016). [5] U. Thiele, D. Todorova, H. Lopez, Phys. Rev. Lett. 111, 117801 (2013)

We present the scalar auxiliary variable (SAV) approach to deal with nonlinear terms in a large class of complex dissipative/conservative systems. In particular, for gradient flows driven by a free energy, it leads to linear and unconditionally energy stable second-order (extendable to higher-orders) schemes which only require solving decoupled linear equations with constant coefficients. Hence, these schemes are extremely efficient as well as accurate. As a particular application, we consider the Cahn-Hilliard equations with dynamical boundary conditions, which can be used to model certain wetting phenomena when coupled with Navier-Stokes equations.

Phong-Minh Timmy Ly1, Uwe Thiele1, Svetlana V. Gurevich1, Lifeng Chi2
1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
2Institute of Functional Nano & Soft Materials (FUNSOM) and Jiangsu Key Laboratory for Carbon-based Functional Materials & Devices Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University 215123 Suzhou, P. R. China

The Langmuir-Blodgett transfer is a surfactant based dip-coating technique where pattern formation occurs via self-organization. In particular, a solid substrate is pulled out of a liquid bath, covered by a monolayer of surfactants. In this setup the transfer velocity is the main control parameter and leads to deposition of different kinds of patterns depending on its magnitude. The procedure excels in through-put in comparison to traditional lithographic methods as means for pattern creation but lacks in terms of uniformity and ways to control the patterns. Therefore, we investigate the effect of a time-periodically modulated velocity on the pattern formation by means of a generalized Cahn-Hilliard equation [KGFT12]. 1D and 2D direct numerical simulations reveal various synchronization phenomena as well as the deposition of a variety of complex patterns. Interest- ingly, it is also possible to influence the system in the spatial direction which is transversal to the direction of the forcing which can lead to the formation of synchronized patterns in two-spatial dimensions [LTCG19].

References
[KGFT12] M. H. Köpf, S. V. Gurevich, R. Friedrich, and U. Thiele. Substrate-mediated pattern formation in monolayer transfer: a reduced model. New J. Phys., 14:023016, 2012.
[LTCG19] Phong-Minh Timmy Ly, Uwe Thiele, Lifeng Chi, and Svetlana V. Gurevich. Effects of time-periodic forcing in a cahn-hilliard model for langmuir-blodgett transfer. Phys. Rev. E, 99:062212, Jun 2019.

In the slot-die coating process, a thin liquid layer is spread over a substrate, while the fluid is continuously supplied through a slot that moves over the surface at a constant speed. This technique is able to produce homogeneous coating layers, as required by industrial applications, provided that the process parameters lie within specific ranges. Outside this so-called coating window, instabilities lead to defective layers and self-organised patterns, e.g., ripple structures. We present a modeling approach of the meniscus dynamics using a thin-film equation for a simple liquid in one and two spatial dimensions, that reproduces the ripple instability. We discuss the results of FEM-based numerical simulations and compare them to experiments.

During this talk, I will review some very recent results about the dynamics of wetting. We have indeed shown that the thermal fluctuations of the three-phase contact line formed between a liquid and a solid at equilibrium can be used to determine key parameters that control dynamic wetting. To validate this approach, We use large-scale molecular dynamics simulations and Lennard-Jones potentials to model a liquid bridge between two molecularly smooth solid surfaces and study the positional fluctuations of the contact lines so formed as a function of the solid–liquid interaction. Within this approach, we show that the fluctuations have a Gaussian distribution and may be modelled as an overdamped one-dimensional Langevin oscillator. Our results suggest that it should be possible to predict the dynamics of wetting and, in particular, the velocity-dependence of the local, microscopic dynamic contact angle, by experimentally measuring the fluctuations of the contact line of a capillary system at equilibrium. This would circumvent the need to measure the microscopic dynamic contact angle directly.

Despite its wide interest in many applications, modeling accurately the dynamics of two phases (fluid-fluid and fluid-solid) interface still remains quite challenging, even when dealing with simple fluids. This is even more complex when three-phase (fluid-fluid-solid) interface dynamics is dealt with, because of the multi-scale (in time and space) nature of such systems. A possible way to improve our understanding of such systems at the nano-scale is to use molecular dynamics simulations in which the interface dynamics behavior emerges without any a priori. Thus, during the presentation, we will illustrate how molecular dynamics simulations of a nanodroplet moving on a perfectly rigid solid can shed light on some small scales phenomena occurring at interfaces.

For the wetting of a substrate by a liquid to advance, the three-phase contact line needs move along the substrate. When the liquid is water and shows good wetting of the substrate, hydrogen bonds between liquid and substrate do not allow slip. Modeling this with a continuum model requires more physics than only Navier-Stokes, but the question is what. We simulate water wetting different substrates using atomistic molecular dynamic (MD) simulations with a three-site water model to properly capture hydrogen bonding effects. Although we are mainly interested in a nanometer sized region around the contact line, we use droplets with a diameter of up to 100 nm to avoid finite size effects. We identified different mechanisms of contact line advancement and measure and rationalize contact line friction. The contact line friction is lowered by an order of magnitude when an electric field is applied, which is also observed in experiments. This is due to strong electric fields around the contact line that weaken the hydrogen bonding. And finally, we observe activated processes at length scales much larger than the intermolecular distance, depending on the geometry.

In this work, we carry out both molecular dynamics and phase field simulations of a nanoscale sized sheared water droplet between two moving plates. We consider a silicon based substrate, which in principle should have zero-slippage in contact with the fluid. In the phase field, we set the physical parameters (density, viscosity, surface tension) to have the same values as in the molecular dynamics, while numerical or model parameters (phase field mobility, interface thickness, boundary conditions) we vary and observe the agreement between phase field and molecular dynamics. We investigate dynamic evolution of the interface between the water and the water vapour as well as steady conditions of the droplet. Based on these results, we draw conclusions about phase field simulation capabilities in describing a small scale droplet in sheared conditions. In addition, we discuss the required phase field parameters for the best agreement with the molecular dynamics simulations.