Effective Slip Research Articles

The investigation of the height effect of a slit microchannel with a textured wall on its hydrodynamic drag

The numerical investigation of the fluid flow in a slit microchannel with a textured wall was carried out. The effect of the channel height on the hydrodynamic drag coefficient, as well as on the pressure drop in such channel and the effective slip length on the wall for various Reynolds numbers, are presented in the paper. The channel length was 100 µm, and its height was varied from 25 µm to 500 µm. The Reynolds number was varied from 0.1 to 100. The main studied characteristics were compared to the similar ones obtained for a channel with normal walls (no-slip conditions). It was found that the pressure drop in such textured microchannel was lower as compared to a conventional channel for any of its heights and for any Reynolds numbers. The dependences of the relative pressure drop, effective slip length, and drag coefficient on the Reynolds number were obtained for different channel heights. The drag coefficient was described as 20/Re for the average values of the channel height. A correlation that describes the dependence of the friction factor on the Reynolds number for small and large heights of the channel was proposed. The accuracy of the proposed correlation was about 90%.

A review on slip boundary conditions at the nanoscale: recent development and applications.

The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed.

Flow and Drop Transport Along Liquid-Infused Surfaces

Liquid-infused surfaces (LISs) are composite solid–liquid surfaces with remarkable features such as liquid repellency, self-healing, and the suppression of fouling. This review focuses on the fluid mechanics on LISs, that is, the interaction of surfaces with a flow field and the behavior of drops on such surfaces. LISs can be characterized by an effective slip length that is closely related to their drag reduction property, which makes them suitable for several applications, especially for turbulent flows. Drag reduction, however, is compromised by failure mechanisms such as the drainage of lubricant from surface textures. The flow field can also sculpt the lubricant layer in a coupled self-organization process. For drops, the lubricant reduces drop pinning and increases drop mobility, but also results in a wetting ridge and the associated concept of an apparent contact angle. Design of LIS wettability and topography can induce low-friction drop motion, and drops can dynamically shape the lubricant ridges and film thickness.

Effect of microstructure on low-cycle fatigue property of Ti6321 alloy

The low-cycle-fatigue behavior of Ti6321 alloy with bimodal and lamellar microstructure have been investigated by analyzing of strain-cycles curve under different stress amplitudes. The results show that under the stress amplitude of 600 MPa, the fatigue life of lamellar microstructure is 6644 times, and the fatigue life of bimodal microstructure is 16252, which is more than twice that of the former. What’s more, two dislocation models of initiation and growth of cracks were demonstrated by analysis of fatigue fracture. The bimodal microstructure have the higher dislocation density and the shorter effective dislocation slip distance, which could hinder the initiation and propagation of fatigue cracks. The findings of low-cycle-fatigue property can provide data support and theoretical guidence for the safety assessment of titanium alloy pressure structures.

Effect of α texture on the anisotropy of yield strength in Ti–6Al–2Zr–1Mo–1V alloy fabricated by laser directed energy deposition technique

Near α titanium alloys fabricated by laser directed energy deposition (LDED) technique always display strong anisotropies of mechanical properties even they only contain a small amount of strong-textured β phase. This work gives a detailed investigation on the effect of α texture on the anisotropy of yield strength of a laser directed energy deposited (LDEDed) Ti–6Al–2Zr–1Mo–1V (TA15) alloy by consideration of the solid phase transformation. Results indicate that the yield strength of LDEDed TA15 alloy along three directions, the building direction (VD), the horizontal direction (HD) and 45° direction (OD), shows dramatically differences of 899.7 MPa, 937.3 MPa and 1016.7 MPa. The α texture is transformed from strong β texture respected to Burgers orientation relationship with weak variant selection. The crystallographic orientation and spatial orientation of textured α phase are the key factors to dominate the yield strength of LDEDed TA15 alloy at different loading directions. Along the VD direction, strong intensity of texture is found in the easily-activated <101¯1> and <112¯0> orientation of α phase, resulting in the largest Schmid factor. However, strong intensity along the OD direction in the hardly-activated <0001> orientation for basal and prismatic slip system of α phase leads to the lowest Schmid factor. The spatial orientation of textured α phase also affects the effective slip distance, which leads to the difference of resolved shear stress in different loading directions. The coupled effect of Schimd factor and effective slip distance controlled by transformed α texture mainly results in the anisotropy of yield strength.

Effect of pH on Effective Slip Length and Surface Charge at Solid-Oil Interfaces of Roughness-Induced Surfaces.

Featured Application Drag reduction in many applications of micro-/nano-fluidic channel. In the development of micro/nano fluid control systems, fluid resistance has always been one of the key factors restricting its development. According to previous studies, it is found that the boundary slip effect of the solid-liquid interface can effectively reduce the resistance of the microfluid and improve the transport efficiency of the microfluid. The boundary slip length is mainly affected by surface wettability, roughness, and surface charge density. Among them, the influence mechanism of surface charge density on the boundary slip is the most complicated, and there is a lack of relevant research, and further investigation is needed. In this paper, we present research on quantification of effective slip length and surface charge density, where the roughness effect is considered. The electrostatic and hydrodynamic force data obtained from atomic force microscopy (AFM) measurements were fitted and processed for comparative analysis. We obtained the variation of surface charge density and effective slip length when different oleophobic surface samples were immersed in ethylene glycol with different pH values. The effect of pH on the surface charge density and effective slip length was investigated by their variations. The mechanism of the effect of pH on the surface charge density was discussed. The experimental results show that in the ethylene glycol solution, no matter whether the pH value of the solution increases or decreases, the charge density of the surface with the same properties decreases, and the effective boundary slip length also shows a downward trend. In deionized water, the surface charge density and effective boundary slip length decreases with the decrease of PH value.

Nonequilibrium characteristics and spatiotemporal long-range correlations in dense gas-solid suspensions

The nonequilibrium properties and strong spatiotemporal long-range correlations in gas-solid suspensions were analyzed systematically by discrete particle simulation in periodic domains. The effective interphase slip velocity is significantly larger than the particle terminal velocity, the particle velocity distribution function is non-Maxwellian with a high-energy tail and the solid concentration distribution function is far from the discrete Poisson distribution, all of which manifest strong deviation from the equilibrium or homogeneous state in gas-solid flow. The solid concentration, gas and solid velocities are spatiotemporally correlated and show a clear scale-dependence. More importantly, all characteristic correlation lengths scale linearly with the size of simulation domain, although the correlation length of solid concentration is much smaller than those of gas and solid velocities. On the other hand, the characteristic correlation times at first increase with increasing domain size and then seem to approach to asymptotic values. Those results indicate that the heterogeneity and spatiotemporal long-range correlations should be considered properly in continuum theory of heterogeneous gas-solid flow.

Effect of Surface Nanopatterning on Slip: The Case of Couette Flow of Long-Chain Polyethylene Melt Flowing Past Gold Surfaces.

The manifestation of slip during flow of a polymer melt past a solid surface depends on several parameters, such as film thickness, the strength of polymer-solid interactions compared to the cohesive energy of the polymer, and the roughness of the surface. Understanding the role of these molecular aspects for slip is crucial in microfluidics, friction-tuning, polymer extrusion, and nanocomposites applications. The present article investigates the effect of surface nanopatterning on slip, via Couette-flow simulations of long chain polyethylene melts past nanopatterned gold surfaces. Slip is quantified in terms of the true and effective slip velocity, and the slip length. When polymer chains are adsorbed to surfaces with periodic features (e.g., crystal planes), they develop preferential ordering in a way that enables them to minimize their free energy. The orientation of a chain is affected by that of its neighbors; thus, when several chains come together, they are prone to form regions with crystal-like orientation. We show that, in some cases, the introduction of nanopatterns on the surface can perturb and induce reorganization of these regions, and in turn affect slip. The nanopatterns are realized as periodic defect stripes of variable width, depth, areal density, and orientation angle. In situations in which the width of the defects becomes comparable to the diameter of individual chain backbones, slip is minimized (stick conditions). Cutting the nanopatterns in low symmetry directions can affect the quality of their edges and lead to enhanced friction. To characterize these edges we have devised a scheme for the quantification of the mean square roughness and mean position of the surface, which is general and applicable in 2 and 3 dimensions for any kind of material, either crystalline of amorphous. Applying the patterns on the opposing solid surfaces in a symmetric or antisymmetric manner has a profound effect on flow. We show that the application of nanopatterns in symmetric configurations generates zero net flow and induces additional shear along directions normal to the direction of the flow. The application of symmetry-breaking configurations can guide flow toward preferential directions, a result with possible applications in microfluidic devices.

Coarsening behavior of the Ti2Cu phase of a Ti-14Cu alloy during isothermal thermal exposure

The static coarsening behavior of a Ti-14Cu alloy relative to the Ti2Cu phase after long-term isothermal thermal exposure was comprehensively investigated. The growth of the precipitated phase is shown to be controlled by the diffusion mechanism characterized by morphological variation during thermal exposure. The static coarsening process is composed of a rapid coarsening stage and stable coarsening stage, and it is primarily governed by volume diffusion of the Lifshitz-Slyozov-Wagner (LSW) model. The rapid coarsening stage is mainly dominated by the terminal migration mechanism, while the stable coarsening stage is governed by the Ostwald ripening mechanism. The rapid coarsening of the Ti2Cu phase enhances the effects of precipitation strengthening significantly and simultaneously improves the plasticity of the alloy. However, with stable coarsening, the presence of the high-volume Ti2Cu phase in a Ti-14Cu alloy increases the effective slip length during deformation and reduces plasticity.

Unraveling dislocation mediated plasticity and strengthening in crack-resistant ZnAlMg coatings

Mg-alloyed zinc coatings suffer from early cracking during deformation due to the combined influences of detrimental constituents (e.g., Zn/MgZn2 binary eutectic), unfavorable crystal orientations and incompatible local plastic deformation. This study addresses the crack resistance and deformation mechanisms of a ZnAlMg coating, in the absence of binary eutectic, by using correlative in-situ scanning electron microscopy tensile tests, electron backscatter diffraction, scanning transmission electron microscopy and micro digital image correlation methods. The plasticity and strengthening mechanisms of the binary eutectic-free ZnAlMg coating are thoroughly unravelled via theoretical and experimental approaches including dislocation slip trace analysis, Taylor factor calculations, quantitative dislocation density determination and slip/strain transfer across the grain boundaries. It has been found that the microstructure of the coating, comprising of primary zinc and ternary eutectic, effectively accommodates the applied strain without cracking till fracture of steel substrate. The absence of binary eutectic and the activation of abundant deformation mechanisms in the coating microstructure, promote local compatible plastic deformation and inhibit early damage. Effective slip transfer is unveiled by activation of pyramidal <c+a> slip in addition to primary dislocation slip systems. The present findings deliver significant insights and solution for improvement in the formability of Mg-alloyed zinc coatings on steel sheets by tailoring the microstructure.

Analysis of strain hardening behavior in a ductile Mg–Yb based alloy

A ductile Mg–Yb based alloy shows a larger strain hardening exponent of 0.45 than those of high-formable Mg alloys, suggesting better strain hardening ability and formability at room temperature. Hence we investigated the strain hardening behavior of the studied alloy under tensile mode. The studied alloy exhibits four strain hardening stages labeled as stage I, II, III, and IV from small to large strain, different from the majority of Mg alloys. Specifically, stage II is characterized by an increased strain hardening rate rather than plateau or decrease, which is principally attributed to the combined results of reducing effective slip length by twin boundaries, increasing the hardness of twinned regions by Basinski mechanism, and the interactions of dislocation-stacking faults. Moreover, the dropping strain hardening rate suddenly slows in a strain of ~15% in stage III, which associates with basal-dissociated sessile dislocation structures that can hinder mobile dislocation so as to enhance hardening rate. Finally, we concluded that strong strain hardening ability in studied alloy essentially ascribes the alloying effect of Yb, which decreases stacking fault energy so that facilitate the formation of twins and stacking faults.

Influence of Surface Texture on the Variation of Electrokinetic Streaming Potentials.

The electrokinetic streaming potential (Vs) 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 Vs with air-/liquid-filled surfaces. A record value of the related figure of merit, in terms of the developed Vs 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 Vs 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.

Upstream events dictate interfacial slip in geometrically converging nanopores.

Continuum computations of fluid flow in conduits approaching molecular scales are often executed with a certain level of abstractions via the imposition of a pre-defined slip condition at the wall. However, in reality, the interfacial slip may not be affixed a priori as a direct one-to-one mapping with the surface wettability and charge but is implicitly interconnected with the concomitant dynamical events that may be effectively captured only under flow conditions. The flow in nanofluidic channels with axially varying cross sections hallmarks such situations in which the effective slip at the wall gets dynamically modulated by upstream flow conditions and cannot be trivially stamped as guided by localized intermolecular interactions over interfacial scales alone. In an effort to capture such flows without resorting to full-domain molecular dynamics simulations, here we bring out advancements on hybrid molecular-continuum simulations and report predictions that closely capture molecular dynamics based predictions of water transport through converging nanopores. Our results turn out to be of significant implications toward designing of emerging nanoscale devices of multifarious applications ranging from miniaturized reactors to highly targeted drug delivery systems.

Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles

Abstract A common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope $\sigma _T$, we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width $2c$ is small compared with the array period $2l$. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation $$\begin{align*}&amp; \pi \frac{G\sigma_T c^2}{\mu l} I(\alpha), \end{align*}$$wherein $G$ is the applied-gradient magnitude, $\mu $ is the liquid viscosity and $I(\alpha )$, a non-monotonic function of the protrusion angle $\alpha $, is provided by the quadrature, $$\begin{align*}&amp; I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s. \end{align*}$$

Fatigue crack growth microstructural mechanisms and texture-sensitive predictive modeling of lightweight structural metals

Long and small fatigue crack growth (FCG) mechanisms of various light structural aluminum and titanium alloys were studied with respect to microstructure, stress ratio, and initial flaw size and related to the effective slip length (grain and phase boundaries). Damage mechanism maps were developed to provide design tools to improve material selection for safety-critical structural components. A predictive model for grain size-controlled microstructurally small FCG was developed with consideration of crack size, grain orientation, and the stochastic effects of discrete microstructural interactions. The model allows for rapid estimation of small FCG behavior and agrees well with experimental data.

Effect of surface nanocrystallization on fatigue properties of Ti–6Al–4V alloys with bimodal and lamellar structure

High-energy shot peening (HESP) was employed to obtain a nanocrystalline surface layer in Ti–6Al–4V alloy with bimodal and lamellar structure. The microstructure and residual stress after HESP treatment were characterized by transmission electron microscope (TEM) and X-ray diffractometer (XRD), respectively. The fracture morphology of fatigue was analyzed by scanning electron microscope (SEM). The results showed that the average grain sizes of Ti–6Al–4V alloy with bimodal and lamellar structure were 18.9 nm and 17.1 nm at the topmost surface layer, respectively. The maximum compressive residual stress of the bimodal structure was −906MPa, which was higher than that of the lamellar structure (−859 MPa). The fatigue limits of the HESP-treated Ti–6Al–4V alloy with the bimodal and lamellar structure were increased by 13.5% and 32.8%, respectively. Finally, a Goodman equation was employed to calculate the local fatigue strength and analyze the residual stress-fatigue strength correlation. Highly defected substructure, reduced effective slip length and improved yield strength were important factors for the improvement of fatigue strength. The synergy effect of surface gradient nanostructure and compressive residual stress improved the fatigue limit of the HESP-treated Ti–6Al–4V alloy with bimodal and lamellar structure.

Non-Einstein Rheology in Segmented Polyurethane Nanocomposites

To provide a fundamental understanding regarding the potential of nanoparticle-induced viscosity reduction in segmented block copolymer-based nanocomposites, the shear rheological behavior of segmented polyurethane/C₆₀ nanocomposites (NPUs) was studied up to 2 wt % C₆₀, and the results were complemented by several dynamic and structural probes. The same microstructural features and dynamical relaxations were revealed for each matrix (PU) and its corresponding NPUs in the absence of deformation, representing the lack of difference in their dynamical behaviors at all studied C₆₀ content. Under shear, however, interesting changes in the terminal rheological properties of PUs were observed in the presence of a C₆₀ nanofiller. An anomalous terminal shear viscosity (η₀) reduction was found for microphase-mixed PUs at a low C₆₀ content of up to 0.5 wt %. However, the microphase-mixed NPUs containing a higher C₆₀ content as well as the microphase-separated NPUs showed a higher η₀ than their matrices. Slippage at the polymer/C₆₀ interfaces was suggested as a possible mechanism behind the viscosity reduction, which appeared controllable by the degree of microphase separation, the ratio of slip length to the nanoparticle size, and the stiffness of segments. Accordingly, an effective slip length, bₑff, was considered as the key factor in controlling the observed noncontinuum effects regarding the nanoparticle-induced viscosity reduction in the microphase-mixed PUs. When most C₆₀ nanoparticles of radius r are positioned on the hard segments (HSs) of microphase-mixed PUs, bₑff/r > 1 can lead to viscosity reduction, while the localization of C₆₀ in the vicinity of soft segments (SSs) increased the matrix’s η₀. A semiuniversal curve was also found to roughly estimate the η₀ values of various NPUs.

Motion of an active particle in a linear concentration gradient

Janus particles self-propel by generating local tangential concentration gradients along their surface. These gradients are present in a layer whose thickness is small compared to the particle size. Chemical asymmetry along the surface is a prerequisite to generate tangential chemical gradients, which gives rise to diffusio-osmotic flows in a thin region around the particle. This results in an effective slip on the particle surface. This slip results in the observed “swimming” motion of a freely suspended particle even in the absence of externally imposed concentration gradients. Motivated by the chemotactic behavior of their biological counterparts (such as sperm cells, neutrophils, macrophages, bacteria, etc.), which sense and respond to external chemical gradients, the current work aims at developing a theoretical framework to study the motion of a Janus particle in an externally imposed linear concentration gradient. The external gradient along with the self-generated concentration gradient determines the swimming velocity and orientation of the particle. The dominance of each of these effects is characterized by a non-dimensional activity number A (ratio of applied gradient to self-generated gradient). The surface of Janus particle is modeled as having a different activity and mobility coefficient on the two halves. Using the Lorentz reciprocal theorem, an analytical expression for the rotational and translational velocity is obtained. The analytical framework helps us divide the parameter space of surface activity and mobility into four regions where the particle exhibits different trajectories.

Viscoplastic fingers and fractures in a Hele-Shaw cell

Abstract A study is presented of the instabilities that may arise in radial displacement flows of yield-stress fluid in a Hele-Shaw cell. Theoretically, the viscoplastic version of the Saffman–Taylor interfacial instability is predicted to arise when the yield-stress fluid is displaced by a Newtonian one. The interface is expected to remain stable, however, if the yield-stress fluid displaces the Newtonian one. A variety of experiments are then performed using an aqueous suspension of Carbopol. As predicted theoretically, the Saffman–Taylor instability is observed when the Carbopol is displaced by either air or an immiscible oil, and no instabilities are observed when the displacement is the other way around. However, when water is used in the displacement experiments, other instabilities appear that take the form of localized fractures of the Carbopol over the sections of the interface that are under tension. The fractures arise in both the stable and unstable Saffman–Taylor configurations, leading to a rich range of patterns within the Hele-Shaw cell. We argue that this pattern formation cannot be explained by a recently proposed instability of shear-thinning extensional flow, whatever the degree of effective slip over the plates of the cell. Instead, we attribute the fractures to a reduction in the fracture energy of the suspension when placed in contact with water.

Tear-film breakup: The role of membrane-associated mucin polymers.

Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to elucidate the hydrodynamic mechanisms by which loss of membrane-associated mucins causes premature tear-film rupture. We model the bulk of the tear film as a Newtonian fluid in a two-dimensional periodic domain, and the lipid layer at the air-tear interface as insoluble surfactants. Gradual loss of membrane-associated mucins produces growing areas of exposed cornea in direct contact with the tear fluid. We represent the hydrodynamic consequences of this morphological change through two mechanisms: an increased van der Waals attraction due to loss of wettability on the exposed area, and a change of boundary condition from an effective negative slip on the mucin-covered areas to the no-slip condition on exposed cornea. Finite-element computations, with an arbitrary Lagrangian-Eulerian scheme to handle the moving interface, demonstrate a strong effect of the elevated van der Waals attraction on precipitating tear-film breakup. The change in boundary condition on the cornea has a relatively minor role. Using realistic parameters, our heterogeneous mucin model is able to predict quantitatively the shortening of tear-film breakup time observed in diseased eyes.