Hydrodynamic drag-force measurement and slip length on microstructured surfaces

Surface Tension and Viscosity Dependence of Slip Length over Irregularly Structured Superhydrophobic Surfaces

A comprehensive understanding of the slip phenomenon on liquid/solid interfaces is essential for multiple real-world applications of superhydrophobic materials, especially those involving drag reduction. In the current contribution, the so-called "slip-length" on an irregularly structured superhydrophobic surface was systematically evaluated, with respect to varying liquid surface tension and viscosity. The superhydrophobic polymer-nanoparticle composite (SPNC) material used exhibits a dual-scale surface roughness and was fabricated via coating a surface with a mixture of polydimethylsiloxane solution and functionalized silica particles. A cone-and-plate rheometric device was employed to quantify the slip length. To independently study the impact of surface tension and viscosity, three types of aqueous solutions were used: sodium dodecyl sulfate, ethanol, and polyethylene glycol. Our experimental results demonstrate that a decreasing surface tension results in a decreasing slip length when the fluid viscosity is held constant. Meanwhile, the slip length is shown to increase with increasing viscosity when the surface tension of the various liquids is matched to isolate effects. The study reveals a linear relationship between slip length and both capillary length and viscosity providing a reference to potentially predict the degree of achievable drag reduction for differing fluids on SPNC surfaces.

Influence of Surface Texture on the Variation of Electrokinetic Streaming Potentials

The electrokinetic streaming potential (V_s) obtained through electrolyte flow in a microchannel is shown to be related to the underlying surface pattern. Pillar, mesh, and groove patterns were studied for comparing the relative magnitudes of the V_s with air-/liquid-filled surfaces. A record value of the related figure of merit, in terms of the developed V_s per-unit applied pressure, of ∼0.127 mV/Pa, was observed in a mesh texture liquid-filled surface (LFS) impregnated with an electrolyte-immiscible oil. The study indicated that increasing the solid fraction of the pattern surface decreases the effective slip length while enhancing the overall channel ζ potential. Consequently, maximizing the obtained V_s implies a balancing of the slip with the surface potential, with plausibly more significance of the latter. The work has implications for higher-efficiency electrical voltage sources.

Establishment of a Standard Method for Boundary Slip Measurement on Smooth Surfaces Based on AFM

Typically, it is difficult to analyze and design a micro/nanofluid system, and the design process cannot follow the traditional law of hydrodynamics. The boundary condition is very important in the applications of a micro/nanofluid system. The existence of boundary slip can reduce the hydrodynamic resistance and enhance fluid flow. How to accurately determine the dynamic boundary conditions is increasingly concerned by researchers. Atomic force microscope (AFM) is proven to be the most advanced experimental instrument for studying the characteristics of the surface and the interaction interface. Most studies on the application of atomic force microscopy to the measurement of the boundary slip do not describe a systematic standard process, leading to many differences in the measurement results. In this paper, a standard process of measuring slip on smooth and flat surfaces is developed, including the data processing methods that minimize the interference factors in the original data as well as simplify the data expression. Thus, the boundary slip can be obtained more easily and accurately.

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.

Study of the Relationship between Boundary Slip and Nanobubbles on a Smooth Hydrophobic Surface

Surface nanobubbles, which are nanoscopic or microscopic gaseous domains forming at the solid/liquid interface, have a strong impact on the interface by changing the two-phase contact to a three-phase contact. Therefore, they are believed to affect the boundary condition and liquid flow. However, there are still disputes in the theoretical studies as to whether the nanobubbles can increase the slip length effectively. Furthermore, there are still no direct experimental studies to support either side. Therefore, an intensive study on the effective slip length for flows over bare surfaces with nanobubbles is essential for establishing the relation between nanobubbles and slip length. Here, we study the effect of nanobubbles on the slippage experimentally and theoretically. Our experimental results reveal an increase from 8 to 512 nm in slip length by increasing the surface coverage of nanobubbles from 1.7 to 50.8% and by decreasing the contact angle of nanobubbles from 42.8 to 16.6°. This is in good agreement with theoretical results. Our results indicate that nanobubbles could always act as a lubricant and significantly increase the slip length. The surface coverage, height, and contact angle are key factors for nanobubbles to reduce wall friction.

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.

Drag reduction on laser-patterned hierarchical superhydrophobic surfaces

Hierarchical laser-patterned surfaces were tested for their drag reduction abilities. A tertiary level of surface roughness which supports stable Cassie wetting was achieved on the patterned copper samples by laser-scanning multiple times. The laser-fabricated micro/nano structures sustained the shear stress in liquid flow. A rheometer setup was used to measure the drag reduction abilities in term of slip lengths on eight different samples. A considerable increase in slip length (111% on a grate sample) was observed on these surfaces compared to the slip length predictions from the theoretical and the experimental models for the non-hierarchical surfaces. The increase in slip lengths was correlated to the secondary level of roughness observed on the patterned samples. The drag reduction abilities of three different arrangements of the surface features were also compared: posts in a square lattice, parallel grates, and posts in a hexagonal lattice. Although the latter facilitates a stable Cassie state, it nevertheless resulted in a lower normalized slip length compared to the other two arrangements at a similar solid fraction. Furthermore, we coated the laser-patterned surfaces with a silane to test the effect of surface chemistry on drag reduction. While the contact angles were surprisingly similar for both the non-silanized and the silanized samples, we observed higher slip lengths on the latter, which we were able to explain by measuring the respective penetration depths of the liquid-vapour interface between surface features.

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.

Hydrodynamic force between a sphere and a soft, elastic surface

The hydrodynamic drainage force between a spherical silica particle and a soft, elastic polydimethylsiloxane surface was measured using the colloidal probe technique. The experimental force curves were compared to finite element simulations and an analytical model. The hydrodynamic repulsion decreased when the particle approached the soft surface as compared to a hard substrate. In contrast, when the particle was pulled away from the surface again, the attractive hydrodynamic force was increased. The hydrodynamic attraction increased because the effective area of the narrow gap between sphere and the plane on soft surfaces is larger than on rigid ones.

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.

Functionalized AFM probes for force spectroscopy: eigenmode shapes and stiffness calibration through thermal noise measurements

The functionalization of an atomic force microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response? And more importantly for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques?In this paper, the influence of the colloidal mass loading on the eigenmode shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without beads attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode is almost unchanged by mass loading. However the oscillation behavior of higher resonances presents a marked difference: with a particle glued at its extremity, the nodes of the modes are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and inertial moment of the load in an Euler-Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.

Nanobubbles and their role in slip and drag

Atomic force microscope images of flat solid surfaces in water reveal that very soft objects can be formed on the surfaces. These objects are nanobubbles of gas with sizes ranging from 10 nm to several micrometers. The bubbles are stable to dissolution, lasting for several hours. In this paper we review some of the methods that allow their generation and observation using the atomic force microscope. Next, we describe the influence of the bubbles on liquid slip close to a hydrophobic surface. The influence of liquid-gas menisci, formed as a result of nanobubbles being present on the surface, on drag reduction is also discussed. Finally, data of liquid flow probed on bubbles entrapped on microstructured surfaces are presented.

Measurement and scaling of hydrodynamic interactions in the presence of draining channels

Central to the adhesion and locomotion of tree frogs are their structured toe pads, which consist of an array of 10 μm hexagonal epithelial cells separated by interconnected channels that are 1 μm wide and 10 μm deep. It has been proposed that the channels facilitate the drainage of excess fluid trapped between the toe pads and the contacting surface, and thus reduce the hydrodynamic repulsion during approach. We performed direct force measurement of the normal hydrodynamic interactions during the drainage of fluid from the gap between a structured and a smooth surface using surface force apparatus. The structured surface consisted of a hexagonal array of cylindrical posts to represent the network of interconnected channels. The measured hydrodynamic drainage forces agree with the predictions from Reynolds' theory for smooth surfaces at large separations. Deviations from theory, characterized by a reduction in the hydrodynamic repulsion, are observed below some critical separation (h(c)), which is independent of drive velocity. We employ a scaling analysis to establish the relationship between structural features (channel depth, width, and post diameter) and the critical separation for the onset of deviations. We find agreement between our experiments and the scaling analysis, which allows us to estimate a characteristic length scale that corresponds to the transition from the fluid being radially squeezed out of the nominal contact area to being squeezed out through the network of interconnected channels.