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Using experiments and numerical simulations, we investigate the spontaneous spreading of droplets of aqueous glycerol (Newtonian) and aqueous polymer (shear-thinning) solutions on smooth surfaces. We find that in the first millisecond the spreading of the shear-thinning solutions is identical to the spreading of water, regardless of the polymer concentration. In contrast, aqueous glycerol solutions show a different behavior, namely, significantly slower spreading rate than water. In the initial rapid spreading phase, the dominating forces that can resist the wetting are inertial forces and contact-line friction. For the glycerol solutions, an increase in glycerol concentration effectively increases the contact-line friction, resulting in increased resistance to wetting. For the polymeric solutions, however, an increase in polymer concentration does not modify contact-line friction. As a consequence, the energy dissipation at the contact line can not be controlled by varying the amount of additives for shear-thinning fluids. The reduction of the spreading rate of shear-thinning fluids on smooth surfaces in the rapid wetting regime can only be achieved by increasing solvent viscosity. Our results have implications for phase-change applications where the control of the rapid spreading rate is central, such as anti-icing and soldering

Structures that are periodic on a microscale in three dimensions are abundant in nature, for example, in the cellular arrays that make up living tissue. Such structures can also be engineered, appearing in smart materials1–4, photonic crystals5, chemical reactors6, and medical7 and biomimetic8 technologies. Here we report that fluid–fluid interfacial energy drives three-dimensional (3D) structure emergence in a micropillar scaffold. This finding offers a rapid and scalable way of transforming a simple pillar scaffold into an intricate 3D structure that is periodic on a microscale, comprising a solid microscaffold, a dispersed fluid and a continuous fluid. Structures generated with this technique exhibit a set of unique features, including a stationary internal liquid–liquid interface. Using this approach, we create structures with an internal liquid surface in a regime of interest for liquid–liquid catalysis. We also synthesize soft composites in solid, liquid and gas combinations that have previously not been shown, including actuator materials with temperature-tunable microscale pores. We further demonstrate the potential of this method for constructing 3D materials that mimic tissue with an unprecedented level of control, and for microencapsulating human cells at densities that address an unresolved challenge in cell therapy. The revelation that fluid–fluid interfacial energy can drive structure formation in micropillar scaffolds offers a scalable way of synthesizing soft composites, which may have applications in building materials that mimic biological tissue.

The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn–Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase-field mobility parameter and the local slip length in accurately modelling the moving contact line.

Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and anti-icing. However, droplet impact on such surfaces is not fully understood. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be a useful for designing structured surfaces for controlling droplet mobility., Comment: 24 pages, 9 figures

The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular phenomena close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics (MD) simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended (SPC/E) water model with particle-mesh Ewald electrostatics treatment. This model provides a very small slip and a more realistic representation of the molecular physics than Lennards-Jones models. The Cahn-Hilliard phase-field model and the Volume-of-Fluid model are calibrated against the drop displacement from MD reference data. It is demonstrated that the calibrated continuum models can accurately capture droplet displacement and droplet breakup for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behavior, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight of the line friction experienced by the advancing and receding contact lines and evidence of large-scale temporal "stick-slip" like oscillations. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics., 45 pages, 23 figures, 4 tables, 1 supplementary PDF, 2 supplementary movies, 1 supplementary archive, accepted for publication in "Journal of Fluid Mechanics"

Liquid-infused surfaces (LIS) can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. For the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the grooves must be sufficiently strong (P\'eclet number larger than 1). The ratio of the surface cavity to the system height is an upper limit of the direct contribution from the recirculation. While this ratio can be significant for laminar flows in microchannels, it is limited for turbulent flows, where the system scale (e.g. channel height) usually is much larger than the texture height. However, heat transfer enhancement on the order of $10\%$ is observed (with a net drag reduction) in a turbulent channel flow at a friction Reynolds number $Re_\tau \approx 180$. It is shown that the turbulent convection in the bulk can be enhanced indirectly from the recirculation in the grooves., Comment: 23 pages, 14 figures

Multiscale homogenization represents a powerful tool to treat certain fluid-structure interaction problems involving porous, elastic, fibrous media. This is shown here for the case of the interacti ...

Surfaces with filamentous structures are ubiquitous in nature on many different scales, ranging from forests to micrometre-sized cilia in organs. Hairy surfaces are elastic and porous, and it is not fully understood how they modify turbulence near a wall. The interaction between hairy surfaces and turbulent flows is here investigated numerically in a turbulent channel flow configuration at friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\approx 180$. We show that a filamentous bed of a given geometry can modify a turbulent flow very differently depending on the resonance frequency of the surface, which is determined by the elasticity and mass of the filaments. Filaments having resonance frequencies lower than the main frequency content of the turbulent wall-shear stress conform to slowly travelling elongated streaky structures, since they are too slow to adapt to fluid forces of higher frequencies. On the other hand, a bed consisting of stiff and low-mass filaments has a high resonance frequency and shows local regions of increased permeability, which results in large entrainment and a vast increase in drag.

A set of boundary conditions called the transpiration-resistance model (TRM) is investigated in altering near-wall turbulence. The TRM was proposed by Lacis et al. (J. Fluid Mech., vol. 884, 2020, p. A21) as a means of representing the net effect of surface micro-textures on their overlying bulk flows. It encompasses conventional Navier-slip boundary conditions relating the streamwise and spanwise velocities to their respective shears through the slip lengths $\ell _x$ and $\ell _z$ . In addition, it features a transpiration condition accounting for the changes induced in the wall-normal velocity by expressing it in terms of variations of the wall-parallel velocity shears through the transpiration lengths $m_x$ and $m_z$ . Greater levels of drag increase occur when more transpiration takes place at the boundary plane, with turbulent transpiration being predominately coupled to the spanwise shear component for canonical near-wall turbulence. The TRM reproduces the effect of a homogeneous and structured roughness up to $k^{+}\approx 18$ , encompassing the regime of smooth-wall-like turbulence described using virtual origins (Luchini, 1996 Reducing the turbulent skin friction. In Computational Methods in Applied Sciences’ 96 (Paris, 9–13 Sept. 1996), pp. 465–470. Wiley; Ibrahim et al., J. Fluid Mech., vol. 915, 2021, p. A56) and slightly beyond it. The transpiration factor is defined as the product of the slip and transpiration lengths, i.e. $(m\ell )_{x,z}$ . This factor contains the compound effect of the wall-parallel velocity occurring at the boundary plane and increased permeability, both of which lead to the transport of momentum in the wall-normal direction. A linear relation between the transpiration factor and the roughness function is observed for regularly textured surfaces in the transitionally rough regime of turbulence. This shows that such effective flow quantities can be suitable measures for characterizing rough surfaces in this flow regime.

Recent developments in neural networks have shown the potential of estimating drag on irregular rough surfaces. Nevertheless, the difficulty of obtaining a large high-fidelity dataset to train neural networks is deterring their use in practical applications. In this study, we propose a transfer learning framework to model the drag on irregular rough surfaces even with a limited amount of direct numerical simulations. We show that transfer learning of empirical correlations, reported in the literature, can significantly improve the performance of neural networks for drag prediction. This is because empirical correlations include ‘approximate knowledge’ of the drag dependency in high-fidelity physics. The ‘approximate knowledge’ allows neural networks to learn the surface statistics known to affect drag more efficiently. The developed framework can be applied to applications where acquiring a large dataset is difficult but empirical correlations have been reported.

The impact of liquid drops on a rigid surface is central in cleaning, cooling and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drop impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We define the line-friction capillary number $Ca_f={\mu_f V_0}/{\sigma}$ (where $\mu_f$, $V_0$ and $\sigma$ are the line friction, impact velocity and surface tension, respectively) as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when $Ca_f \ll 1$, the contact line speed in the direction against the inclination of the ridges is set by line-friction, whereas in the direction with inclination the contact line is pinned at acute corners of the ridge. When $Ca_f \sim 1$, the pinning is only temporary until the liquid-vapor interface reaches to the next ridge where a new contact line is formed. Finally, when $Ca_f\gg 1$, the geometric details of non-smooth surfaces play little role., Comment: 12 pages, 7 figures, under consideration for Physical Review Fluids. Revised February 04 2021

Microstructured surfaces that control the direction of liquid transport are not only ubiquitous in nature, but they are also central to technological processes such as fog/water harvesting, oil-water separation, and surface lubrication. However, a fundamental understanding of the initial wetting dynamics of liquids spreading on such surfaces is lacking. Here, we show that three regimes govern microstructured surface wetting on short time scales: spread, stick, and contact line leaping. The latter involves establishing a new contact line downstream of the wetting front as the liquid leaps over specific sections of the solid surface. Experimental and numerical investigations reveal how different regimes emerge in different flow directions during wetting of periodic asymmetrically microstructured surfaces. These insights improve our understanding of rapid wetting in droplet impact, splashing, and wetting of vibrating surfaces and may contribute to advances in designing structured surfaces for the mentioned applications., 9 pages, 5 figures, under consideration for Soft Matter

We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous domain. Boundary conditions that accurately capture mass and momentum transport at the contact surface between these two domains are derived using the multiscale homogenization technique. In addition to obtaining the generalized version of the widely used Beavers-Joseph slip condition for tangential velocities, the present work provides an accurate formulation for the transpiration velocity and pressure jump at fluid-porous interfaces; these two conditions are essential for handling two- and three-dimensional flows over porous media. All the constitutive parameters appearing in the interface conditions are computed by solving a set of Stokes problems on a much smaller computational domain, making the formulations free of empirical parameters. The tensorial form of the proposed interface conditions makes it possible to handle flows over isotropic, orthotropic, and anisotropic media. A subset of interface conditions, derived for porous media, can be used to model flows over rough walls. The accuracy of the proposed macroscopic model is numerically quantified for flows over porous and rough walls by comparing the results from our homogenized model with those obtained from geometry-resolved microscopic simulations., 47 pages, 19 figures, 8 tables, Under consideration for publication in "Transport in porous media"

A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes.

The surface texture of materials plays a critical role in wettability, turbulence and transport phenomena. In order to design surfaces for these applications, it is desirable to characterise non-smooth and porous materials by their ability to exchange mass and momentum with flowing fluids. While the underlying physics of the tangential (slip) velocity at a fluid-solid interface is well understood, the importance and treatment of normal (transpiration) velocity and normal stress is unclear. We show that, when slip velocity varies at an interface above the texture, a non-zero transpiration velocity arises from mass conservation. The ability of a given surface texture to accommodate for a normal velocity of this kind is quantified by a transpiration length. We further demonstrate that normal momentum transfer gives rise to a pressure jump. For a porous material, the pressure jump can be characterised by so called resistance coefficients. By solving five Stokes problems, the introduced measures of slip, transpiration and resistance can be determined for any anisotropic non-smooth surface consisting of regularly repeating geometric patterns. The proposed conditions are a subset of effective boundary conditions derived from formal multi-scale expansion. We validate and demonstrate the physical significance of the effective conditions on two canonical problems -- a lid-driven cavity and a turbulent channel flow, both with non-smooth bottom surfaces., Comment: 31 page, 12 figures, 5 tables, under consideration for publication in Journal of Fluid Mechanics

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface imperfections or appendages that serve a function -- are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow., 16 pages, 13 figures, 2 tables, under consideration for publication in Phys. Rev. Fluids; revision

This manuscript demonstrates the first successful application of the delayed-x-LMS (dxLMS) control algorithm for TS-wave cancelation. Active wave cancelation of two-dimensional broad-band Tollmien- ...

Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as $10^{-4}$. We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method., Article has undergone final revision stage, minor adjustments in text, fixed citations

This experimental study reports on the behavior of a filament attached to the rear of a three-dimensional cylinder. The axis of the cylinder is placed normal to a uniform incoming flow, and the fil ...

In boundary-layer flows, one may reduce skin-friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien–Schlichting (TS) waves. In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for. However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based LQG controller in wind-tunnel experiments. In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics., Main paper: 28 pages, 14 figures; Supplementary appendicies: 7 pages; under consideration for publication in Roy. Soc. Proc. A