Inelastic non-Newtonian flow over heterogeneously slippery surfaces

Modeling of Shear Flows over Superhydrophobic Surfaces: From Newtonian to Non-Newtonian Fluids

The design and use of superhydrophobic surfaces have gained special attentions due to their superior performances and advantages in many flow systems, e.g., in achieving specific goals including drag reduction and flow/droplet handling and manipulation. In this work, we conduct a brief review of shear flows over superhydrophobic surfaces, covering the classic and recent studies/trends for both Newtonian and non-Newtonian fluids. The aim is to mainly review the relevant mathematical and numerical modeling approaches developed during the past 20 years. Considering the wide ranges of applications of superhydrophobic surfaces in Newtonian fluid flows, we attempt to show how the developed studies for the Newtonian shear flows over superhydrophobic surfaces have been evolved, through highlighting the major breakthroughs. Despite the fact that, in many practical applications, flows over superhydrophobic surfaces may show complex non-Newtonian rheology, interactions between the non-Newtonian rheology and superhydrophobicity have not yet been well understood. Therefore, in this Review, we also highlight emerging recent studies addressing the shear flows of shear-thinning and yield stress fluids in superhydrophobic channels. We focus on reviewing the models developed to handle the intricate interaction between the formed liquid/air interface on superhydrophobic surfaces and the overlying flow. Such an intricate interaction will be more complex when the overlying flow shows nonlinear non-Newtonian rheology. We conclude that, although our understanding on the Newtonian shear flows over superhydrophobic surfaces has been well expanded via analyzing various aspects of such flows, the non-Newtonian counterpart is in its early stages. This could be associated with either the early applications mainly concerning Newtonian fluids or new complexities added to an already complex problem by the nonlinear non-Newtonian rheology. Finally, we discuss the possible directions for development of models that can address complex non-Newtonian shear flows over superhydrophobic surfaces.

Effects of vertical confinement on the flow of polymer solutions in planar constriction microchannels

The flow of polymer solutions under extensional conditions is frequently encountered in numerous engineering fields. Planar contraction and/or expansion microchannels have been a subject of interest for many studies in that regard, which, however, have mostly focused on shallow channel structures. We investigate here the effect of changing the depth of contraction-expansion microchannels on the flow responses of three types of polymer solutions and water. The flow of viscoelastic polyethylene oxide (PEO) solution is found to become more stable with suppressed vortex formation and growth in the contraction part while being less stable in the expansion part with the increase of the channel depth. These opposing trends in the contraction and expansion flows are noted to have similarities with our recent findings of constriction length-dependent instabilities in the same PEO solution (M. K. Raihan, S. Wu, Y. Song and X. Xuan, Soft Matter, 2021, 17, 9198-9209), where the contraction flow gets stabilized while the expansion flow becomes destabilized with the increase of the constriction length. In contrast, the entire flow becomes less stable in deeper channels for the shear-thinning xanthan gum (XG) solution as well as the shear thinning and viscoelastic polyacrylamide (PAA) solution. This observation aligns with that of water flow, which is attributed to the reduced top/bottom wall stabilizing effects.

Flow of Non-Newtonian Fluids in a Single-Cavity Microchannel

Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion-contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction-expansion microchannel of similar dimensions.

Flow Structure and Mixing Efficiency of Viscous Fluids in Microchannel with a Striped Superhydrophobic Wall

The peculiarities of a Newtonian fluid flow structure in microchannels with a striped superhydrophobic lower wall texture are studied by means of numerical modeling. In the Cassie-Baxter state, an oblique orientation of such a texture induces helicoidal streamlines with micro spirals. Such a flow structure favors the enhancement of fluid mixing efficiency, which can be quantified using the total root-mean-square deviation of streamlines from the microchannel axis. This characteristic was shown to be a nonmonotonic function of the striped texture tilt angle and to depend strongly on microchannel thickness. The mechanisms of micro and macro helicoidal flow structure formation are investigated, and the mixing quality of miscible fluids is estimated for various Peclet numbers and texture tilt angles. It was found that the striped superhydrophobic wall leads to a notable enhancement in the microchannel mixing efficiency at sufficiently large Peclet numbers.

Taylor-vortex flow in shear-thinning fluids

This paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding of the influence of the viscosity stratification and the nonlinear variation of the effective viscosity μ with the shear rate γ[over ̇] on the flow structure in the Taylor-vortex flow regime. A wide gap configuration (η=0.4) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order, is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns is shifted axially toward the radial outflow boundaries (z=0,z/λ_{z}=1). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes stronger than the inflow and the extent of the inflow zone where the vorticity is low increases acoordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.

Oil-Impregnated Hydrocarbon-Based Polymer Films

Porous surfaces impregnated with a liquid lubricant exhibit minimal contact angle hysteresis with immiscible test liquids, rendering them ideal as self-cleaning materials. Rather than roughening a solid substrate, an increasingly popular choice is to use an absorbent polymer as the "porous" material. However, to date the polymer choices have been limited to expensive silicone-based polymers or complex assemblies of polymer multilayers on functionalized surfaces. In this paper, we show that hydrocarbon-based polymer films such as polyethylene can be stably impregnated with chemically compatible vegetable oils, without requiring any surface treatment. These oil-impregnated hydrocarbon-based films exhibit minimal contact angle hysteresis for a wide variety of test products including water, ketchup, and yogurt. Our oil-impregnated films remain slippery even after several weeks of being submerged in ketchup, illustrating their extreme durability. We expect that the simple and cost-effective nature of our slippery hydrocarbon-based films will make them useful for industrial packaging applications.

Wall slip for complex liquids - Phenomenon and its causes

In this review, we tried to qualify different types and mechanisms of wall slip phenomenon, paying particular attention to the most recent publications and issues. The review covers all type of fluids - homogeneous low molecular weight liquids, polymer solution, multi-component dispersed media, and polymer melts. We focused on two basic concepts - fluid-solid wall interaction and shear-induced fluid-to-solid transitions - which are the dominant mechanisms of wall slip. In the first part of the review, the theoretical and numerical studies of correlation of wetting properties and wall slip of low molecular weight liquids and polymeric fluids are reviewed along with some basic experimental results. The influence of nanobubbles and microcavities on the effectiveness of wall slip is illuminated with regard to the bubble dynamics, as well as their stability at smooth and rough interfaces, including superhydrophobic surfaces. Flow of multi-component matter (microgel pastes, concentrated suspensions of solid particles, compressed emulsions, and colloidal systems) is accompanied by wall slip in two cases. The first one is typical of viscoplastic media which can exist in two different physical states, as solid-like below the yield point and liquid-like at the applied stresses exceeding this threshold. Slip takes place at low stresses. The second case is related to the transition from fluid to solid states at high deformation rates or large deformations caused by the strain-induced glass transition of concentrated dispersions. In the latter case, the wall effects consist of apparent slip due to the formation of a low viscous thin layer of fluid at the wall. The liquid-to-solid transition is also a dominant mechanism in wall slip of polymer melts because liquid polymers are elastic fluids which can be in two relaxation states depending on the strain rate. The realization of these mechanisms is determined by polymer melt interaction with the solid wall.

Apparent slip of shear thinning fluid in a microchannel with a superhydrophobic wall

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonian fluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.