Effective hydrodynamic boundary conditions for microtextured surfaces

An experimental study on the role of inter-particle friction in the shear-thinning behavior of non-Brownian suspensions

This paper focuses on shear-thinning in non-Brownian suspensions. In particular, it proposes a quantitative experimental validation of the model proposed by Lobry et al. [J. Fluid Mech., 2019, 860, 682-710] that links viscosity to microscopic friction between particles and, in particular, shear-thinning to load-dependent friction coefficient. To this aim, Atomic Force Microscopy (AFM) is used to measure the pairwise friction coefficient of polystyrene particles (40 μm in diameter), immersed in a Newtonian liquid, for different normal loads ranging from 10 to 1000 nN. It is shown that the inter-particle friction coefficient decreases with the load, contrarily to what is expected for macroscopic contacting bodies. The experimental friction law is then introduced into the viscosity model proposed by Lobry et al. and the results are compared to the viscosity of suspensions made of the same particles dispersed in the same liquid as those used for AFM measurements. The very good agreement between the measured viscosity values and those predicted by the model of Lobry et al. with the friction coefficient measured by AFM as input data shows the relevance of the scenario proposed by Lobry et al. and highlights the close links between the microscopic friction properties of the particles and the macroscopic rheological behavior of suspensions.

Anisotropic electrokinetic transport in channels modified with patterned polymer brushes

Molecular dynamics simulations have been used to predict the transport dynamics of fluids through nanochannels with polymer patterning surfaces. The effects of different parameters, such as separation between polymer stripes, solvent quality, and direction and strength of the electric field, were explored in terms of electroosmotic flow transport characteristics, conformational dynamics of the polymer brush and ion distribution. Anisotropic electrokinetic transport becomes significant due to the surface patterning of polymers when the direction of the electric field is changed. At the separation between adjacent polymer stripes comparable to the chain length, local strong flow close to the bare surfaces weakens dramatically under the electric field along the stripe direction. However, when the electric field is switched to the direction perpendicular to the stripes, the flow is enhanced considerably. The coupling of the polymer solvent quality further richens and complicates the transport behaviors. We explain the physical mechanism of the electroosmotic flow in complex polymer patterning channels by analyzing the interrelationship among various properties.

Promoting rotation, friction, and mixed lubrication for particles rolling on microstructured surfaces

We investigate how the aspect ratio of micropillar or microwell arrays patterned on a surface affects the rolling and slipping motion of spheres under flooded conditions at low Reynolds numbers. We study arrays of rigid microstructures with aspect ratios varying over two orders of magnitude for surface coverages ranging from 0.04 to 0.96. We investigate how the surface features (dimensions, surface coverage, and geometry) individually impact the motion of the sphere. We find that increasing microstructure height results in higher rotational velocities on all studied surfaces. We then model the motion of the spheres using two physical parameters: an effective separation and a coefficient of friction between the sphere and the incline. We find that a simple superposition of resistance functions, previously shown to accurately predict the motion of spheres for different surface coverages and geometries, indeed shows good agreement with experimental outcomes for all microstructure heights studied. We also perform separate sliding friction measurements via a force microscope to measure the coefficient of friction between the sphere and incline, under identically flooded conditions. A comparison of the sliding friction measurements at different Hersey numbers suggests that the effect of the microstructure on the coefficient of friction becomes more important as the Hersey number increases.

Morphology of soft and rough contact via fluid drainage

The dynamic of contact formation between soft materials immersed in a fluid is accompanied by fluid drainage and elastic deformation. As a result, controlling the coupling between lubrication pressure and elasticity provides strategies to design materials with reversible and dynamic adhesion to wet or flooded surfaces. We characterize the elastic deformation of a soft coating with nanometer-scale roughness as it approaches and contacts a rigid surface in a fluid environment. The lubrication pressure during the approach causes elastic deformation and prevents contact formation. We observe deformation profiles that are drastically different from those observed for elastic half-space when the thickness of the soft coating is comparable to the hydrodynamic radius. In contrast, we show that surface roughness favors fluid drainage without altering the elastic deformation. As a result, the coupling between elasticity and slip (caused by surface roughness) can lead to trapped fluid pockets in the contact region.

A micropatterned elastomeric surface with enhanced frictional properties under wet conditions and its application

Engineered surfaces that have high friction under wet or lubricated conditions are important in many practical applications. However, it is not easy to achieve stable high friction under wet conditions because a layer of fluid prevents direct solid-solid contact. Here, we report a micropatterned elastomeric surface with superior wet friction. The surface has unique arch-shaped microstructures arrayed in a circle on the surface to provide high friction on wet or flooded surfaces. The arch-shaped micropatterned surface exhibits remarkably enhanced and stable friction under wet conditions, surpassing even the performance of the hexagonal patterns of tree frogs, owing to the large contact surface and the optimal shape of drainage channels. Robotic substrate transportation systems equipped with the micropatterned surfaces can manipulate a delicate wet substrate without any sliding in a highly stable and reproducible manner, demonstrating the superior frictional capabilities of the surface under wet conditions.

Rolling Spheres on Bioinspired Microstructured Surfaces

Microstructured surfaces, such as those inspired by nature, mediate surface interactions and are actively sought after to control wetting, adhesion, and friction. In particular, the rolling motion of spheres on microstructured surfaces in fluid environments is important for the transport of particles in microfluidic devices or in tribology. Here, we characterize the motion of smooth silicon nitride spheres (diameters 3-5 mm) as they roll down inclined planes decorated with hexagonal arrays of microwells and micropillars. For both types of patterned surfaces, we vary the area fraction of the micropatterned features from 0.04 to 0.96. We measure directly and independently the rotational and translational velocities of the spheres as they roll down planes with inclination angles that vary between 5 and 30°. For a given area fraction, we find that spheres have a higher translational and rotational velocity on surfaces with microwells than on micropillars. We rely on the model of Smart and Leighton [Phys. Fluids A 5, 13 (1993)] to obtain an effective gap width and coefficient of friction for all microstructured surfaces investigated. We find that the coefficient of friction is significantly higher for a surface with micropillars than that for one with microwells, likely due to the presence of interconnected drainage channels that provide additional paths for the fluid flow and favor solid-solid contact on the surface with micropillars. We find that while the effective gap width at a very low solid fraction is equal to the height of the patterned features, the effective separation decreases exponentially as the surface coverage of microstructures increases, with little measured differences between the two geometries. Superposition of resistance functions is used to relate the rapid decrease in the effective gap height with increase in the surface coverage observed in experiments.

Probing effective slippage on superhydrophobic stripes by atomic force microscopy

While the effective slippage of water past superhydrophobic surfaces has been studied over a decade, theoretical predictions have never been properly confirmed by experiments. Here we measure a drag force on a sphere approaching a plane decorated by superhydrophobic grooves and compare the results with the predictions of semi-analytical theory developed here, which employs the gas cushion model to calculate the local slip length at the gas sectors. We demonstrate that at intermediate and large (compared to a texture period) separations the half-sum of longitudinal and transverse effective slip lengths can be deduced from the force-distance curve by using the known analytical theory of hydrodynamic interaction of a sphere with a homogeneous slipping plane. This half-sum is shown to depend on the fraction of gas sectors and its value is in excellent agreement with theoretical predictions. At small distances the half-sum of effective longitudinal and transverse slip lengths becomes separation-dependent, and is in quantitative agreement with the predictions of our semi-analytical theory.

Scaling Hydrodynamic Boundary Conditions of Microstructured Surfaces in the Thin Channel Limit

Despite its importance in many applications and processes, a complete and unified view on how nano- and microscale asperities influence hydrodynamic interactions has yet to be reached. In particular, the effects of surface structure can be expected to become more dominant when the length scale of the asperities or textures becomes comparable to that of the fluid flow. Here we analyze the hydrodynamic drainage of a viscous silicone oil squeezed between a smooth plane and a surface decorated with hexagonal arrays of lyophilic microsized cylindrical posts. For all micropost arrays studied, the periodicity of the structures was much larger than the separation range of our measurements. In this thin channel geometry, we find the hydrodynamic drainage and separation forces for the micropost arrays cannot be fully described by existing boundary condition models for interfacial slip or a no-slip shifted plane. Instead, our results show that the influence of the microposts on the hydrodynamic drag exhibits three distinct regimes as a function of separation. For large separations, a no slip boundary condition (Reynolds theory) is observed for all surfaces until a critical (intermediate) separation, below which the position of the no-slip plane scales with surface separation until reaching a maximum, just before contact. Below this separation, a sharp decrease in the no-slip plane position then suggests that a boundary condition of a smooth surface is recovered at contact.

Interfacial slip on rough, patterned and soft surfaces: a review of experiments and simulations

Advancements in the fabrication of microfluidic and nanofluidic devices and the study of liquids in confined geometries rely on understanding the boundary conditions for the flow of liquids at solid surfaces. Over the past ten years, a large number of research groups have turned to investigating flow boundary conditions, and the occurrence of interfacial slip has become increasingly well-accepted and understood. While the dependence of slip on surface wettability is fairly well understood, the effect of other surface modifications that affect surface roughness, structure and compliance, on interfacial slip is still under intense investigation. In this paper we review investigations published in the past ten years on boundary conditions for flow on complex surfaces, by which we mean rough and structured surfaces, surfaces decorated with chemical patterns, grafted with polymer layers, with adsorbed nanobubbles, and superhydrophobic surfaces. The review is divided in two interconnected parts, the first dedicated to physical experiments and the second to computational experiments on interfacial slip of simple (Newtonian) liquids on these complex surfaces. Our work is intended as an entry-level review for researchers moving into the field of interfacial slip, and as an indication of outstanding problems that need to be addressed for the field to reach full maturity.

Effective slip-length tensor for a flow over weakly slipping stripes

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has steplike jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of max[b(y)/L] becomes comparable to the leading-order term, but anisotropic, even at very small b(y)/L. This leads to an anisotropy of the effective slip and to its significant reduction compared to the surface-averaged value. The asymptotic formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.