Contact Line Dynamics and Droplet Spreading

Contact line motion occurs when a liquid encounters a solid surface. The physics of liquid contact line movement and droplet spreading involves interfacial science and fluid dynamics. Contact line dynamics and droplet spreading significantly impact a broad range of scientific fields and technologies, including microfluidics, nanofluidics, printed electronics, nano-printing, 3D bioprinting, coatings, and phase-change heat transfer. The contact line is a three-phase region (gas/liquid/solid or liquid/liquid/solid) with an intricate configuration. Its structure depends on several parameters, namely the solid surface topography, liquid rheology, gas environment, and other physical properties of each phase. In this Special Issue, we aim to explore the recent developments in contact line physics and droplet impact mechanisms, encompassing theory, state-of-the-art experiments, and computations while considering their applications in various scientific and technological fields, including biotechnology, microfluidics, nanofluidics, printings, and coatings, as well as heat transfer.

In spray paintings, Ye et al. [1] computationally explored the mechanism of viscous droplet impact on dry and wetted solid walls, considering air entrapment, film structure, and flake flat pigment orientation using a computational fluid dynamics (CFD) program. The numerical results were compared with observations using high-speed visualization [1]. In printings, Shah and Mohan [2] presented a model for droplet evolution using the volume of fluid (VOF) approach to solve Navier–Stokes and continuity equations for incompressible flow, with various immiscible phases in a finite volume. Their computational model agreed well with observations of the impact, spread, and recoil of droplets on a substrate [2]. In their study, they considered three main non-dimensional parameters, including the Reynolds number, Weber number, and Ohnesorge number [2]. Water droplet impact dynamics on a two-layered pool composed of an ultrathin suspended layer of silicone oil on top of a deep water pool was explored by Dehghanghadikolaei et al. [3]. They found that the viscosity of the suspended oil layer is a major parameter to regulate droplet impact dynamics [3]. In spray coatings, Stober et al. [4] studied the asymmetric crown morphology caused by an oblique impact (α = α = 60°) of a single droplet on a horizontal wetted wall with the same liquid film. They showed that the Weber number variation in the splashing stage causes distinct crown morphologies [4].

Droplet impact and coalescence physics was investigated by Chashechkin and Ilinykh [5] via probing the flow pattern, cavity formation, and distribution of a free-falling droplet onto a liquid pool at rest. They also considered the droplet coalescence based on the observed energy conservation due to the droplet’s kinetic energy and surface potential energy. Beloborodov and Vishnyakov [6] studied the coalescence dynamics of Lennard–Jones nano-droplets as a function of droplet size and temperature using molecular simulations. Comparing the duration of coalescence with the droplet lifespan in a suspension revealed that for dense suspensions and small droplets, the coalescence timescale is enhanced and needs to be taken into account in aggregation theoretical modeling [6].

In organized packings, Croce and Suzzi [7] computationally examined liquid film instability in a falling down motion on a vertical plate with lateral walls, mimicking the structured packing configuration by applying the lubrication assumption. Their numerical findings, based on a linear stability analysis and considering substrate wettability, suggested that the formed rivulets at a wavelength larger than the minimum threshold promote partial dewetting [7]. In the interfacial instability of a complex multi-phase flow, Hasegawa and Kishimoto [8] experimentally explored the contact line and interfacial instability dynamics of a binary droplet (a water and 2-propanol (IPA) mixture) on an immiscible (sunflower oil) pool. Their experimental observations showed that fingering instability is driven by the capillary effect for a liquid–liquid system and Plateau–Rayleigh instability [8].

The impact of biochemically active heterogeneous droplets on a solid surface plays a key role in the food and pharmaceutical industry. In an advanced drug delivery system, suspended therapeutic particles in an aqueous environment (i.e., heterogeneous droplets) are deposited onto a solid surface. It is critical to print uniform drug-loaded droplets on a substrate surface for sustained and regulated drug release in patients upon administration. The bioactive heterogeneous droplet impact mechanism deserves much more attention in future research. In bacterial encapsulation process, motivated by the food and pharmaceutical industry, Mohd Isa et al. [9] studied the encapsulation of bacteria in single water-in-oil (W/O) and double water-in-oil-in-water (W₁/O/W₂) emulsions under cold storage and temperature-regulated release conditions. In their study, storage conditions at freezing temperatures (−20 °C and −80 °C) caused an extensive droplet destabilization with a rapid release of encapsulated bacteria upon thawing, where the temperature-regulated release of encapsulated bacteria was reached [9]. Their study provides an excellent review for utilizing emulsion droplets for temperature-regulated bacterial encapsulation, which is a crucial factor to consider for food and pharmaceutical storage and usage.

The dropwise condensation of steam over a hybrid hydrophobic–hydrophilic surface was numerically explored by Croce and Suzzi [10] through a non-dimensional analysis of the heat transfer model using a Lagrangian approach. Their computational findings agreed well with observations, and they showed that heat flux was enhanced under various operating conditions by the hybrid surface [10]. In the development of energy systems and thermal management processes, Lakew et al. [11] explored a bubble growth mechanism for modeling boiling heat transfer to reach the optimum heat flux needed for its operation. They presented analyses of evaporating ultra-thin (i.e., microlayer) liquid underneath steam bubbles growing at the heated surface in the atmospheric pressure nucleate of boiling water [11].

The contact line dynamics of ionic liquids at the mesoscopic scale was investigated by Carvalho et al. [12]. They examined the effect of the deposition speed and substrate temperature on the nucleation, droplet formation, and droplet spread of the ionic liquid films formed by thermal evaporation [12]. They considered four ionic liquids consisting of an alkylimidazolium cation (C_nC₁im) and either bis(trifluoromethylsulfonyl)imide (NTf₂) or triflate (OTf) as the anion [12]. Each ionic liquid droplet was simultaneously deposited on surfaces of indium tin oxide (ITO) and silver (Ag) [12]. They found that the substrate’s wettability by the ionic liquids was remarkably influenced by changes in the mass flow rate and substrate temperature [12]. Taitelbaum [13] provided a review on the top-view reactive contact line dynamics based on statistical physics, with significant attention on the spread of mercury droplets over metal-on-glass at room temperature, and compared the findings with the case of reactive droplets spreading at high temperatures. Mohammad Karim and Suszynski [14] provided a comprehensive review of the conventional physical models applied for describing the contact line dynamics, using hydrodynamics and molecular kinetics.

Three-dimensional (3D) bioprinting is a rapidly advanced technology in regenerative medicine such as cardiac tissue engineering and 3D cancer modeling [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54]. However, more studies still need to be performed to precisely mimic the complex microstructures and nanostructures of biological tissues and accurately control the distribution of cells, biochemical factors, and biomaterials in a layer-by-layer approach.

With the emerging advancements in technology ranging from machine/deep learning, quantum power, and nanoscience, it is highly recommended to utilize these state-of-the-art tools to conduct research in the field of droplet impact for complex systems due to droplet biochemical heterogeneity and the heterogeneous topography of substrate surfaces. A recent study utilized machine learning along with experimental observation to study the spreading and freezing process of water droplet impact upon a supercooled substrate [55]. There has been significant attention on bioprinting for healthcare and medicine to print live biological cells and be used for artificial organ synthesis and tissue engineering [18,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90]. Over the last decade, a remarkable advancement has been achieved in the field of printed electronics for the application of wearable and stretchable sensors [56].

Finally, we thank the authors and reviewers for their contributions to this Special Issue by sharing their research or their comments in the rigorous review process to provide a highly selective collection of articles in the field of contact line physics and droplet impact dynamics.