We revisit the classical problem of liquid imbibition in a single tube with spatially varying wettability. Starting from the Lucas-Washburn equation, we derive analytical solutions for the imbibition time (crossing time) in systems where wettability alternates between different materials. For ordered arrangements, we demonstrate that the imbibition speed depends non-trivially on the spatial distribution, with the "more hydrophobic-first" configuration being optimal. For disordered systems, where segment lengths follow a Gaussian distribution, we show that the classical Cassie-Baxter contact angle, originally derived for static wetting, fails to predict the dynamics of capillary-driven flow. To address this, we propose a new weighted harmonic averaging method for the contact angle, which accurately describes the viscous crossing time in such heterogeneous systems. Our findings reveal fundamental insights into the role of wettability heterogeneity in capillary-driven flow, offering a basis for understanding imbibition dynamics in complex heterogeneous systems. The research data and the software supporting this study are openly available at DOI:10.5281/zenodo. 14537452.

Wetting phenomena have been studied quantitatively for more than 200 years, but there remain many fundamental questions that are not understood. For example, the speed of a water drop sliding down an inclined plane cannot be predicted. A drop that slides down a surface experiences a resistance. We call this resistance drop friction. It is still debated how and where energy is dissipated in a sliding drop. Particularly for the most common liquid, water, there have been considerable advances in the understanding of wetting, driven by the development of new physical, preparative and theoretical methods. Water is a special liquid, owing to its polar nature, its tendency to form hydrogen bonds, the self-ionization into OH− and H3O+, its low viscosity and its high surface tension. In recent years, water–surface interactions due to adaptation, spontaneous electrostatic charging and deformation on elastomers have been identified as important processes that increase drop friction. They may be responsible for drop friction even on seemingly smooth, homogeneous and rigid surfaces. The dynamic wetting of sliding drops, particularly of water, remains poorly understood. New experimental techniques have shown that, in addition to viscous dissipation, other energy dissipation mechanisms such as adaptation, electrostatic charging and deformation can contribute significantly and affect the motion of the drops.

HYPOTHESIS:Despite the importance of wetting on the processing of polymers and key role of chain entanglements on the mechanical properties of polymer parts, the understanding of the role of chain entanglements during wetting is still rudimentary. It is hypothesized that by progressively changing the molecular weights (Mn) of polymer liquids, different relations between contact-line friction (ζ) and Mn would be obtained without (below the critical entanglement molecular weight, Mc) and with chain entanglements (above Mc). EXPERIMENTS:Forced wetting of polydimethylsiloxane (PDMS) liquids with different Mn around a polyethylene terephthalate (PET) fiber is studied. The dynamics is modelled by the molecular-kinetic theory (MKT) and the influence of chain entanglements on the relation between ζ and Mn is discussed. FINDINGS:Two regimes are indeed observed for the contact line friction versus molecular weight and are modelled by ζ ∼ Mnδ with δ = 2.18 ± 0.27 for Mn < Mc and δ = 3.78 ± 0.51 for Mn > Mc. The solid-liquid interaction activation energy Δgs∗ is small ∼0.013 J/m2 regardless of Mn, as it is mainly controlled by the interfacial interaction between the PDMS chains and the fiber. In contrast, the viscous interaction activation energy Δgvis∗ presents a significant increase when Mn reaches Mc, with Δgvis∗ surpassing Δgs∗ up to 21.6 %. It is proposed that the dominating role of Δgvis∗ regulates the relationship between ζ and Mn when Mn > Mc.

In this note, we revisit the problem of the pressure-driven transport of a meniscus through a narrow cylindrical capillary or pore. This generic process finds many applications in science and technology. As it is known that Direct Numerical Simulations of moving contact line problems are highly demanding in terms of computational costs, simplified models in the form of ordinary differential equations offer an interesting alternative to perform a mathematical optimization of the flow. Blake and De Coninck studied the pressure-driven transport of a meniscus and identified two major competing mechanisms. While a hydrophilic surface is favorable to enhance the spontaneous imbibition into the pore, the friction is known to be significantly reduced on a hydrophobic surface. Blake and De Coninck showed that, depending on the applied pressure difference, there exists an optimal wettability that minimizes the time required to move the meniscus over a certain distance. We revisit this problem and derive analytical solutions in the limiting cases of negligible inertia and negligible contact line friction.

To explore the complicated physics of boiling heat transfer, researchers are increasingly using numerical simulation methods like the Volume of Fluid (VOF) and the Diffuse Interface (DI) approaches. The VOF method, popular for macro-scale simulations (mu m to mm), effectively tracks the bubble growth and detachment. On the other hand, the DI method, which represents the interface as a continuous phase field, is mainly used for mesoscale simulations (nm to mu m). The DI method is precise in resolving microscopic interfacial phenomena, but is computationally expensive for larger domains. Based on the pros and cons of the VOF and DI methods, a multi-scale modeling approach that combines the strengths of both can be utilised in the future. To pursue the goal, an initial attempt is taken to check the scaling capability of VOF in lower spatial and temporal limits. Therefore, an enhanced customised VOF methodology that has been developed within the OpenFOAM tool-box is employed here for various bubble growth scenarios exploring its applicability at progressively lower temporal and spatial scales, scaling down traditional application scales with a factor of 10 and 100, aiming to identify the resulting accuracy. It is shown for the first time, that the enhanced VOF model can accurately and effectively simulate phase-change and boiling behaviour at sub-micron scales that have not been explored in the past.

The advancement of technology has led to a significant increase in thermal loads, thus presenting new challenges in heat dissipation. Traditional single-phase cooling systems are often inadequate to meet these demands. As a result, phase-change technologies utilizing boiling and condensation, which can achieve high heat transfer coefficients, have garnered considerable attention. To delve into the complex physics of boiling heat transfer, researchers are increasingly turning to numerical simulation methods such as the Volume of Fluid (VOF) and the Diffuse Interface (DI) approaches. The VOF method, widely employed for macro-scale simulations ranging from micrometers to millimeters, effectively tracks bubble growth and detachment. Conversely, the DI method represents the interface as a continuous phase field and is primarily used for mesoscale simulations spanning from nanometers to micrometers. While the DI method excels in resolving mesoscale interfacial phenomena, it is computationally expensive for larger domains. Considering the strengths and weaknesses of both the VOF and DI methods, there is a growing interest in developing a multi-scale modeling approach that amalgamates their benefits. To pursue this objective, initial efforts are being made to evaluate the scaling capability of VOF towards lower spatial and temporal limits. Hence, an enhanced and customized VOF methodology has been developed within the OpenFOAM toolbox. This methodology is employed to investigate various bubble growth scenarios, progressively exploring its applicability at lower temporal and spatial scales to identify the lower limits of its application. By taking this first step towards combining the strengths of both the VOF and DI methods through a multi-scale modeling approach, the presented paper paves the way for enhancing the accuracy and efficiency of modelling approaches for boiling heat transfer while tackling a challenge associated with varying spatial and temporal scales. This endeavor not only pushes the boundaries of computational fluid dynamics but also holds promise for addressing real-world thermal management issues in diverse technological applications.

For super-heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro-bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. Until covering a patch, making a pinned macro-bubble, a bubble has a contact angle $\pi-\theta_2$, where $\theta_2$ is the receding contact angle of water on the patch material. This pinned macro-bubble serves as the initial condition of a quasi-static growth process, \`a la Landau, leading to detachment through the formation of a neck, so long as depinning and dewetting of the hydrophilic matrix was avoided during the growth of the pinned bubble: the bubble contact angle should not exceed $\pi-\theta_1$, where $\theta_1$ is the receding contact angle of water on the matrix material. The boiling process may then enter a cycle of macro-bubbles forming and detaching on the patches; the radii of these patches can be optimized for maximizing the heat transfer for a given substrate area. For this analysis to become quantitative, we revisit the Young-Laplace quasi-static evolution of key physical quantities, such as bubble energy, as functions of bubble growing volume, when gravity is either significative or negligible: this concerns both pinned bubbles on a fixed circular footprint (Dirichlet boundary conditions) and free un-pinned bubbles with a fixed contact angle (Neumann boundary conditions).

Dynamic wetting is a ubiquitous phenomenon and frequently observed in our daily life, as exemplified by the famous lotus effect. It is also an interfacial process of upmost importance involving many cutting-edge applications and has hence received significantly increasing academic and industrial attention for several decades. However, we are still far away to completely understand and predict wetting dynamics for a given system due to the complexity of this dynamic process. The physics of moving contact lines is mainly ascribed to the full coupling with the solid surface on which the liquids contact, the atmosphere surrounding the liquids, and the physico-chemical characteristics of the liquids involved (small-molecule liquids, metal liquids, polymer liquids, and simulated liquids). Therefore, to deepen the understanding and efficiently harness wetting dynamics, we propose to review the major advances in the available literature. After an introduction providing a concise and general background on dynamic wetting, the main theories are presented and critically compared. Next, the dynamic wetting of various liquids ranging from small-molecule liquids to simulated liquids are systematically summarized, in which the new physical concepts (such as surface segregation, contact line fluctuations, etc.) are particularly highlighted. Subsequently, the related emerging applications are briefly presented in this review. Finally, some tentative suggestions and challenges are proposed with the aim to guide future developments.

Despite the key to the adhesion between polymers and a plethora of materials, our understanding of reactive wetting is still rudimentary. In the present work, we report the reactive wetting dynamics of molten maleic anhydride-grafted polypropylene (MA-g-PP) liquids modeled by molecular-kinetic theory (MKT). The dependencies of the contact line friction (zeta) and viscosity (eta) were compared for reactive and nonreactive wetting polymer systems. Compared with linear dependencies of zeta and eta for the nonreactive wetting systems, the reactive wetting system presented a nonlinear relationship. In the capillary regime, the chemistry-affected regime is followed by a regime that is nearly not affected by chemical reactions, which is identified by the linear MKT. The formation of a new interface and the resulting entanglements of polymer chains in the chemistry-affected regime contribute to the dependence of zeta on eta in the capillary regime.

Hypothesis: The maximum velocity of dewetting encodes sufficient information on the hydrodynamics of the wetting process to enable the local dynamic contact angle at the molecular scale, 0; to be determined from the apparent contact angle measured experimentally at much larger scales, 0app.Methods: Effective models of wetting dynamics need to account for differing channels of dissipation. One such model was recently verified by large-scale molecular dynamics (MD). It combines the 2-parameter molecular-kinetic theory of dynamic wetting (MKT), which attributes the velocity-dependence of 0 to dissipation at the contact line, with the Cox-Voinov hydrodynamic (HD) model. The latter attributes the difference between 0 and 0appto viscous bending of the interface and contains an additional, nonpredictable, logarithmic parameter. Crucially, the MD simulations indicated that viscous bending may play a minor role during wetting, but dominates dewetting. This observation suggested that by applying the MKT to the advancing contact angle only and combining the results with the maximum velocity of dewetting, it might be possible to extract the value of the logarithmic parameter and so determine 0 and, hence, the relative significance of the two channels of dissipation. A simple iterative procedure has been developed to achieve this.Findings: Data available to test the procedure are sparce, but comparisons with the MD results and those from three experimental studies are encouraging. Near perfect agreement is achieved with the simulations, where both 0 and 0app are known, and plausible results are obtained for the experimental systems. Moreover, the procedure appears to be more effective than simply fitting 0app to the 3-parameter model. (c) 2022 Elsevier Inc. All rights reserved.

The rise of a liquid column inside a thin capillary against the action of gravity is a prototypical example of a dynamic wetting process and plays an important role for applications but also for fundamental research in the area of multiphase fluid dynamics. Since the pioneering work by Lucas and Washburn, many research articles have been published which aim at a simplified description of the capillary rise dynamics using complexity-reduced models formulated as ordinary differential equations. Despite the fact that these models are based on profound simplifications, they may still be able to describe the essential physical mechanisms and their interplay. In this study, we focus on the phenomenon of oscillations of the liquid column. The latter has been observed experimentally for liquids with sufficiently small viscosity leading to comparably small viscous dissipation. Back in 1999, Quéré et al. formulated a condition for the appearance of rise height oscillations for an ODE model introduced by Bosanquet in 1923. This model has later been extended to include further dissipative mechanisms. In this work, we extend the mathematical analysis to a larger class of models including additional channels of dissipation. We show that Quéré’s critical condition is generalized to Ω+β<2, where Ω was introduced earlier and β is an additional non-dimensional parameter describing, e.g., contact line friction. A quantitative prediction of the oscillation dynamics is achieved from a linearization of the governing equations. We apply the theory to experimental data by Quéré et al. and, in particular, reveal the oscillatory behavior of dynamics for the nearly critically damped case of ethanol.

Dynamic wetting processes inherently manifest as multiscale phenomena. While the capillary length is typically millimeters, solid-liquid interactions occur at the nanometer scale. These short-range interactions significantly affect macroscopic behaviors like droplet spreading and menisci dynamics. The Navier slip length, determined by liquid viscosity and solid-liquid friction, plays a crucial role in three-phase contact line dynamics. It varies from nanometers (hydrophilic) to microns (hydrophobic). However, resolving it in computational fluid dynamics (CFD) simulations can be computationally expensive. In this study, we propose simplified ordinary differential equation (ODE) models, leveraging local dissipation rates from Stokes flow solutions near the moving contact line, to bridge the nanoscale physics and macroscopic dynamics. Our ODE model accurately predicts the impact of the slip parameter in fully resolved CFD simulations, focusing on capillary rise dynamics.

In this work, we present a dynamical theory of boiling based on fluctuating hydrodynamics and the diffuse interface approach. The model is able to describe boiling from the stochastic nucleation up to the macroscopic bubble dynamics. It covers, with a modest computational cost, the mesoscale area from nano to micrometers, where most of the controversial observations related to the phenomenon originate. In particular, the role of wettability in the macroscopic observables of boiling is elucidated. In addition, by comparing the ideal case of boiling on ultra-smooth surfaces with a chemically heterogeneous wall, our results will definitively shed light on the puzzling low onset temperatures measured in experiments. Sporadic nanometric spots of hydrophobic wettability will be shown to be enough to trigger the nucleation at low superheat, significantly reducing the temperature of boiling onset, in line with experimental results. The proposed mesoscale approach constitutes the missing link between macroscopic approaches and molecular dynamics simulations and will open a breakthrough pathway toward accurate understanding and prediction.

Wettability is a macroscopic consequence of microscopic phenomena occurring at the fluid-solid interfaces. This functional property is crucial for the formulation of wettable powders in food and non-food sectors. Basically, powder wettability is mostly assessed through the contact angle measurements of solid particles reacting with dispersing media, by either the sessile drop method or the capillary rise technique. Among the most popular bioactive agents nowadays are probiotics and their metabolites, which are receiving a growing interest for their beneficial effects on our ecosystem health. As live functional ingredients, probiotics are mainly available in a powder form that is sensitive to the environmental stress factors during processing and storage steps. It is therefore crucial to understand and control their wettability, regarding their performance, dispersibility, and stability when probiotic particles come into contact with dispersing media and body fluids. The proposal chapter aims to review: (1) the theoretical aspects of powder wettability by considering compact and porous materials; (2) the analytical tools and methodologies of measurement, including sessile drop and capillary rise methods using models Lucas-Washburn equation and Darcy\'s law; and (3) the applications to probiotic powders as functional ingredients in food and agricultural sectors.

Inspired by the stenocara beetle, we study an ideal flat surface composed of a regular array of hydrophilic circular patches in a hydrophobic matrix on an incline of tilt α with respect to the horizontal. Based on an exact solution of the Laplace-Young equation at first order in the Bond number, the liquid storage capacity of the surface is maximized as function of the patch radius, for suitable ranges of hydrophilic and hydrophobic contact angles, for tilt angles such as 45◦ or 90◦. It is found that the optimal radius equally prevents dewetting from the top of the patches and overflow at the bottom. These theoretical considerations are validated by several experiments for the glass/octadecyltrichlorosilane (OTS) system involving different patch sizes and different inclinations. In a simple dynamical model, taking into account the flux of fog onto the surface or condensation on a suitably cooled surface, we find that the conditions for maximum harvest agree with the ones of maximum static storage. The method could be developed for drop storage and drop transport applications such as water-harvesting systems.

Hypothesis: Molecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (theta(m) and theta(app)). Methods: We use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F-0. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle theta(0). Protocols are devised to measure theta(m) and theta(app) as a function of contact-line velocity U-cl. Findings: For all theta(0), theta(m) is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, theta(app) diverges from theta(m) as F-0 is increased, especially at the receding meniscus. The behavior of theta(app) follows that predicted by Voinov: (theta(app))(3) = (theta(m))(3) + 9Ca center dot ln(L/L-m), where Ca is the capillary number and L and L-m are suitably-chosen macroscopic and microscopic length scales. For each theta(0), there is a critical velocity U-crit and contact angle theta(crit) at which theta(app) -> 0 and the receding meniscus deposits a liquid film. Setting theta(app) = 0, theta(m) = theta(crit) and U-cl = U-crit in the Voinov equation yields the value of L/L-m. The predicted values of theta(app) then agree well with those measured from the simulations. Since theta(m) obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov. (C) 2020 Elsevier Inc. All rights reserved.

For a pendent drop whose contact line is a circle of radius r0, we derive the Furmidge-like relation mgsinα=π2γr0(cosθmin−cosθmax) at first order in the Bond number, where θmin and θmax are the contact angles at the back (uphill) and at the front (downhill), m is the mass of the drop and γ the surface tension of the liquid. The Bond (or Eötvös) number is taken as Bo=mg∕(2r0γ). The tilt angle α may increase from α=0 (sessile drop) to α=π∕2 (drop pinned on vertical wall) to α=π (drop pendent from ceiling). The focus will be on pendent drops with α=π∕2 and α=3π∕4, while α=π∕4 is also included for comparison. The drop profile is computed exactly, in the same approximation. Results are compared with Surface Evolver simulations, showing good agreement up to about Bo=1.2, corresponding for example to hemispherical water droplets of volume up to about 50μL. An explicit formula for each contact angle θmin and θmax is also given and compared with the almost exact Surface Evolver values.

The analytical expressions of liquid–vapor equilibrium contact angles are analyzed in the thermodynamic limit for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of wetting when the substrate is completely wet, the Cassie–Baxter state when the liquid hangs over the substrate, but also intermediate states of wetting which are shown to be relevant and in competition with the two other ones. Under a separation of scales hypothesis, a composition rule of contact angles is developed whose interest is illustrated in a close packing setup of raspberry-like particles.

Most probiotic-based products are available in powder particles under different solid-state forms. Such diversity can affect the probiotic stability, viability, and performance at different stages of processing, storage, and use. Here, we apply complementary physical chemistry techniques to characterize the bulk and surface properties of probiotic powder particles under different forms and report quantitative results of a highly concentrated multistrain reference product. The solid particle morphology, size/shape distribution, and the powder surface wettability in the compressed disc and porous packed bed forms are successively measured by sessile drop and capillary rise techniques. A complete wettability of the disc surface is observed through equilibrium contact angle measurements for various solvents, whereas the associated capillary rise data exhibit two regimes: a power law regime for the first few moments followed by a second regime, which can be described using Darcy's law. The use of this modeling approach shows the possibility of assessing the particle-packed bed permeability and porosity. These results open a new route of the structure-activity relationship study on the impact of probiotic solid particles on their functionalities and performance in promoting health benefits, related particularly to the human and animal gut permeability. This statement also strengthens the idea of using the compressed disc technique for easily performing probiotic wettability measurements.