Paints and Coatings are ubiquitous with wide ranging applications in architectural and construction, aerospace, automotive, electronic, food, and the pharmaceutical industries. The manufacture and storage of paints, their application on a substrate, and the film formation process all involve fluid flow whose understanding and control is important for achieving the desired finish. Within this context, this special issue presents developments in advanced computational models, experiments, and analysis related to the various stages of paint formulation and their applications.
Coating flows correspond to fluid flows where a thin liquid film is coated on a large area of a substrate. The liquid film is subsequently dried or cured to obtain a homogenous dry film devoid of defects. One of the most common industrial coating processes involves a slot-die coating, which requires a precision liquid delivery system and a die for widthwise distribution.1,2 Kasischke et al.3 focus on the slot-die coating process and show that thin water-based films coated on hydrophobic surfaces become unstable resulting in a range of patterns from parallel to perpendicular stripes to break up of stripes into drops. They show this to be a wettability-driven instability, where decreasing film thickness causes the disjoining pressure to destabilize the film. Detailed numerical simulation reproduces most of the observations. Barreiro-Villaverde et al.4 investigate a related problem applicable to many coating processes, including air-knife and slot-die coating, namely, the stability of a thin liquid film dragged by a vertical substrate moving against gravity. The model incorporates the mechanisms of capillary and nonlinear damping and identifies the instability threshold of the coating processes. The results show that transverse modulations can be beneficial for damping two-dimensional waves, thereby increasing the stability of thin coatings.
While the aforementioned studies focused on Newtonian liquids, Silva et al.5 report a computational study of free surface flows with rheologically complex interfaces in the film formation region of a slot coater. They couple the Boussinesq–Scriven constitutive equation for viscous interfaces with the equations of motion for incompressible Newtonian liquids in the bulk flow to show that the interfacial viscosity plays a critical role in slot coating flows. The interfacial viscosity makes the interfaces stiffer, thereby slowing down the film flow and increasing the development length over the substrate. Cunha et al.6 use the same constitutive relation to investigate the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface. As expected, the surface viscosity reduces the mobility of the free interface considerably, which then reduces the pressure difference between the perturbed region and the fluid extremities. Consequently, the driving force of the drainage process is reduced leading to enhanced stability of those films. Naghshineh et al.7 investigate the effect of the developing boundary layer when laminar liquid films are coated on moving substrates, which has applications in a high speed, curtain-coating method. Here, the boundary-layer length is essential in determining the location of the wetting line. The authors provide an analytical solution to the boundary-layer problem for Ostwald–de Waele power law fluids via a power series expansion. Specifically, they provide a convergent power series solution to the non-Newtonian Sakiadis boundary-layer problem.
How does one model coating flows on complex geometries when a multitude of forces are at play? Duruk et al.8 tackle such a problem by investigating the three-dimensional flow of a thin liquid film distributed on the outer surface of an ellipsoid, rotating around the vertical axis at constant angular velocity. Their model incorporates gravitational, centrifugal, and capillary forces. By employing numerical simulations, they highlight the significance of rotation on a non-constant curvature substrate by comparing the thickness profiles with the static case.
The stability of a thin, Newtonian liquid film flowing down an inclined slope has a rich history with seminal contributions by Kapitza,9 Benjamin,10 and Yih.11 Priyadarshi et al.12 focus on elastic liquids and demonstrate the existence of a new elastic instability in gravity-driven viscoelastic film flow. Using an Oldroyd-B constitutive equation, they show that the film is susceptible to two distinct purely elastic instabilities in the inertialess limit, wherein the first instability originates from the existence of a free surface and second is due to the base-state shear. Interestingly, the surface tension plays a dual role of both stabilizing and destabilizing the flow configuration.
While the aforementioned papers focused on the coating flow process, a significant body of work exists on the drying and the film formation process in coatings.13 In this respect, Mondal et al.14 review the problem of drying of a fluid drop while focusing on the flow field, pattern formation, and desiccation cracks. They provide an overview of the physics of drying pure and binary liquid droplets, followed by drying colloidal droplets. The phenomena of pattern formation and desiccation cracks are reviewed including the impact of evaporation-driven flows on the accumulation of particles that influence deposit patterns and cracks. Pauchard15 investigates the evolution of colloidal coatings due to the wetting and the drying process and shows that the drying process can yield coatings ranging from those with no porosity to uniform porous coatings. In some cases, drying and wetting processes lead to the formation of singularities, such as cracks and blisters. The stresses are caused by the capillary forces while the singularities owe their origin to the excess strain energy arising from the competition between the drying-induced shrinkage of the deposit and its adhesion to the substrate.
The spreading of the droplet is also influenced by the permeability of the substrate. Song et al.16 present a theoretical analysis of the contact line pinning mechanisms of a non-wetting droplet penetrating a permeable substrate. The analysis considers the force balance of volumetric force, capillary force, and pinning and depinning forces in the vertical and radial directions. They propose two dimensionless numbers, namely, the ratio of the volumetric force to the capillary force and the ratio of the depinning force to the pinning force, to establish a phase diagram based on the droplet penetration patterns. These results are confirmed via the lattice Boltzmann simulations. Far et al.17 present a three-dimensional phase-field model that uses the cumulant lattice Boltzmann method based on a new equilibrium distribution function to simulate droplet dynamics in a multicomponent–multiphase system containing soluble surfactants. The methodology results in better computational efficiency and may be used to simulate coating process, where surfactants play a critical role. A variation to the drop spreading problem is presented by Granda et al.,18 who consider the case of a paint drop spreading on wood and its enhancement by an in-plane electric field. A comprehensive study encompassing theory, simulations, and experiments elucidates the effect of an in-plane electric field on a diffusion-like spreading of paint drops resulting in a significant increase in the painted area of balsa wood substrates.
Coating applications with the goal of reducing drag is addressed by Lin et al.19 and Xie et al.20 The former reports on the drag-reducing performance of a water-soluble polymer coating. The coating consists of a film of polyvinyl alcohol with polyethyleneoxide (PEO) incorporated inside it. When the dried coating contacts water, PEO is continuously dispersed into external flow resulting in drag reduction. Interestingly, partial coating of the immersed body induces significant drag reduction compared to full coating of the solid. The optimal length ratio of coated to uncoated surface was related to the polymer characteristics and the speed of the main flow. Xie et al.20 report on a novel drag reduction coating, wherein a gelatin-based coating releases bio-polysaccharides to reduce drag. They tested five different bio-polysaccharides and show that increasing polysaccharide proportion not only promotes the release of polysaccharides but also increases the surface roughness and, therefore, drag, thereby suggesting a competition between these mechanisms.
Liu et al.21 describe a rapid, efficient, and low-cost preparation of large-scale wear-resistant superhydrophobic surface on aluminum alloy using laser-chemical hybrid methods. The process results in an array of micro–nano composite with multi-layer structures and chemical modification, thereby providing both wear-resistant and superhydrophobic properties to the surface. Khadka et al.22 describe the development of eco-friendly cellulose wearable heaters using Korean traditional Han paper coated with graphene nanosheets via binder-free supersonic spraying. The latter embeds graphene flakes firmly inside Hanji, which consists of celloluse fibers. Heaters with thicker graphene layer had the lowest electrical resistance with the highest heating at a fixed voltage.
Finally, the special issue also reports on the emerging area of AI/ML models in fluid mechanics. Pendar et al.23 perform a detailed modeling of the Nitrotherm electrostatic spray-painting method, which finds application in the automotive and aerospace industries. They employ computational fluid dynamic models in deep learning models as input dataset to predict flow with high accuracy. They show that use of novel conductors with special geometries in combination with the Nitrotherm spraying technique during the electrostatic atomizing can significantly reduce material and energy consumptions.
Taken together, the 17 contributions in various areas of Paints and Coatings Physics highlight the advances in computations, analysis, and experiments with significant applications to the industry. It is hoped that the community finds the collection of papers a valuable contribution to the field.
The author would like to thank the editorial board of Physics of Fluids, especially the Editor-in-Chief Professor Alan Jeffrey Giacomin, Journal Manager Mark Paglia, and Editorial Assistant Jaimee-Ian Rodriguez for their kind help and efforts. The author acknowledges the financial support from the Science and Engineering Research Board, Department of Science and Technology, India (Grant No. CRG/2022/004288).
Conflict of Interest
The authors have no conflicts to disclose.
Mahesh S. Tirumkudulu: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.