Effective Slip Length Research Articles

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.

Effect of Deformation Reduction on Microstructure, Texture, and Mechanical Properties of Forged Ti-6Al-4V

In this work, the effects of nominal reductions during forging experiments on microstructures, tensile and fatigue properties of Ti-6Al-4V have been investigated. The microstructure of the starting material was a combination of equiaxed and lamellar α phases. With further deformation and annealing heat treatment, the volume fraction of globular primary α increased by about 20% as the nominal reduction increased from 10 to 50%. More notably, the ultimate tensile stress and yield stress were increased by approximately 50 MPa, and the ductility remained constant, with the nominal reduction from 10 up to 50%. Further detailed characterization revealed that the improvement in tensile and fatigue properties could be attributed to the reduction in the effective slip length, increase in the interface density, and realignment of the (0002) planes with the tensile axis.

Molecular insight of flow property for gas-water mixture (CO2/CH4-H2O) in shale organic matrix

Gas-water two-phase flow mechanism of CO2/CH4 in moist nanoporous media is significant in carbon capture and storage (CCS) and enhanced oil and gas recovery (EOR) technology. However, in untraditional oil and gas exploitation, the flow property of CO2/CH4-H2O mixtures are neglected in shale organic nanopores under reservoir conditions. In this work, molecular dynamic simulation combined with a theoretical model is performed to investigate two-phase flow characteristics of CH4/CO2-H2O mixtures in shale organic nano-slits. From the density profile of gas-water mixtures in shale organic nano-slits, we find that water molecules prefer to form water clusters at the surface and center region to replace CH4 molecules of the adsorption layer (AL) and CO2 molecules of the bulk-free layer (BL), respectively. Based on the results of MD simulations, an analytical theoretical slip model is established to quantitatively characterize the effective viscosity and slip length of CH4/CO2-H2O binary mixtures systems, which can be integrated into the macro framework to mimic the flow property of gas-water two-phase in shale and predict the apparent gas permeability in moist shale. Particularly, although the viscous flux of CO2 decreased with the increase of gas water mole percent (GWP) values and the slippage flux appears largely unaffected, the variation of total flux for CO2 has been small. Taking into account the influence mechanisms of H2O molecule among the gas-water (CH4/CO2-H2O) two-phase mixtures in shale organic nano-slits, CO2 displacement and fracturing technology may provide a productivity improvement avenue for shale gas.

Reassessing water slippage in hydrophobic nanostructures.

Reported data of measured slip lengths in nanostructures span several orders of magnitude, from a few nanometers to tens of micrometers. Small roughness on surfaces caused by structural defects or thermal fluctuations dramatically reduces slippage. Tiny bubbles entrapped on rough surfaces can also affect slippage. We used an asymptotic solution and a high density-ratio pseudopotential lattice Boltzmann model to systematically study the drag resistance of a rough surface with attached bubbles. As bubbles nucleate and grow, drag resistance is slightly reduced until the tri-phase contact line reaches the edges of roughness, where bubbles with small angles substantially reduce drag resistance. As bubbles grow to become a continuous gas layer on the surface, the drag resistance greatly decreases. However, the interface deformation from flat to curved shape greatly hinders liquid flow, and the vortex structures cause a wave-like fluctuation in the effective slip length. This finding sheds light on the controversies of reported large variations in the slip length of super-hydrophobic surfaces in nanostructures, e.g., carbon nanotubes.

Influence of insoluble surfactants on shear flow over a surface in Cassie state at large Péclet numbers

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Superhydrophobic annular pipes: a theoretical study

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Quantifying Frictional Drag Reduction Properties of Superhydrophobic Metal Oxide Nanostructures.

We measure the frictional drag-reducing property of various superhydrophobic metal oxide nanostructures by quantifying their effective slip length. Scalable chemical methods tailored to each metal substrate are applied to grow oxide nanostructures on copper (Cu), aluminum (Al), and titanium (Ti), respectively. In particular, three different types of oxide nanostructures are grown on the titanium substrate by changing the chemical composition to investigate the morphological influence on the slip length. Microchannels containing metal oxide nanostructures are fabricated based on the microfluidic sticker method, while the slip length is unambiguously determined by measuring the ratio of the volume flow rate over the superhydrophobic surface to that over the flat surface simultaneously. The slip length is measured to be 6.8 ± 1.4 μm on Cu nanostructures, while it is measured to be 2.5 ± 0.6 μm on Al nanostructures. For Ti nanostructures, the measured slip lengths range from 1 to 2.5 ± 0.5 μm, where they increase proportionally with the structural pitch of the nanostructures, agreeing with the theoretical predictions. We believe that our results will be useful in applying scalable low-cost metal oxide nanostructures to underwater applications by providing their frictional characteristics.

General criteria for the estimation of effective slip length over corrugated surfaces

In this work, we aim to develop an effective hydrodynamic boundary condition over patterned surfaces for the application to microfluidics. Four different criteria to estimate the effective Navier-slip length and their performance are investigated for flows over corrugated surfaces, such as patterned surfaces or porous interfaces, which can be applied for efficient flow simulations. Four distinctive methods were discussed in the estimation of slip length, namely: mass conservation, balance of energy dissipation rate, force balance, and interfacial slip velocity averaging. Expressions of slip length were derived analytically for each criterion in a pressure-driven flat channel flow and the slip length was determined using a combination of analytic and numerical methods. We report that (i) the slip length from force balance appears to be the most accurate and exactly the same as that from interfacial slip velocity averaging, (ii) the slip length from mass conservation deviates from that of force balance, though minor, particularly for a small relative channel height to the length scale of patterns or pores, and (iii) the energy balance yields significantly different slip lengths. The slip length reduces to a single value for a sufficiently large relative channel height, which indicates that it can be considered as a surface property in general, when the pattern dimension is much smaller than the length scale of flow.

Liquid slippage on rough hydrophobic surfaces with and without entrapped bubbles

The process of liquid slip on rough-walled hydrophobic surfaces with and without entrapped gas bubbles is modeled. Here, starting with the Navier–Stokes equations, a set of partial differential equations (PDE) and boundary conditions for the general effective slip tensor of a rough hydrophobic surface are constructed by an asymptotic analysis. The intrinsic slip and surface roughness are considered as the characteristics of the surface. The solution is based on a weak variation form that fully recovers the set of PDE and Navier slip boundary. For the surface with entrapped bubbles, a semi-analytical model based on eigenfunction expansion is developed. In addition to the surface characteristics, the size and contact angle of the bubbles are considered in the semi-analytical solution. Both models are validated with the published data as well as direct numerical simulation. Based on the model results, we present correlations of effective slip length with surface characteristics and entrapped bubbles. We found that surface roughness reduces liquid slippage on a surface. However, if the asperities on a surface are filled with gas bubbles, the effective slip length can significantly increase as long as the bubble contact angle is small. Interestingly, bubbles with a larger contact angle could act inversely and change a hydrophobic surface with a large intrinsic slip to a no-slip or even a sticky surface. These results shed light on the controversy over the order of magnitude of the actual slip length of water flow in carbon-based nanotubes and nanochannels. The model results also help understand the anomalies of high water production and high amounts of hydraulic fracturing fluid leak-off observed in tight oil and shale gas reservoirs.

Rate of capillary rise in quartz nanochannels considering the dynamic contact angle by using molecular dynamics

As a universal phenomenon in nature, capillary rise not only strongly influences the physical properties and industrial processes of powder materials but can also be applied as an important technique to measure their wettability. In this paper, molecular dynamics (MD) was implemented to investigate the capillary transport behavior of water flow through α-quartz nanochannels considering the channel height. The results showed that the Capillary rise method (CRM) with the classical Lucas-Washburn (L-W) equation may obtain an overestimated equilibrium contact angle, and the value decreases with increasing channel height. Through the introduction of the concepts of effective viscosity, slip length and dynamic contact angle, a modified L-W equation was proposed. The equilibrium contact angle calculated by the equation was more accurate and independent of channel size. Additionally, the pore-water can be divided into absorption water and capillary water. The upper bound of the absorption water density was determined to be 1.14 g/cm3.

On the flow separation mechanism in the inverse Leidenfrost regime

The inverse Leidenfrost regime occurs when a heated object in relative motion with a liquid is surrounded by a stable vapour layer, drastically reducing the hydrodynamic drag at large Reynolds numbers due to a delayed separation of the flow. To elucidate the physical mechanisms that control separation, here we report a numerical study of the boundary-layer equations describing the liquid-vapour flow around a solid sphere whose surface temperature is above the Leidenfrost point. Our analysis reveals that the dynamics of the thin layer of vaporised liquid controls the downstream evolution of the flow, which cannot be properly described substituting the vapour layer by an effective slip length. In particular, the dominant mechanism responsible for the separation of the flow is the onset of vapour recirculation caused by the adverse pressure gradient in the rearward half of the sphere, leading to an explosive growth of the vapour-layer thickness due to the accumulation of vapour mass. Buoyancy forces are shown to have an important effect on the onset of recirculation, and thus on the separation angle. Our results compare favourably with previous experiments.

Large Effective Slip on Lubricated Surfaces Measured with Colloidal Probe AFM.

In this work, we study the interfacial boundary conditions at the interface between two immiscible liquids under a laminar flow. We measure the hydrodynamic drainage forces acting on a colloid probe as it approaches a flat and smooth Teflon film coated with silicone oil films, submerged in a sucrose solution using atomic force microscopy. On Teflon substrates, silicone oil films of thickness several hundred nanometers could be stabilized, and we found the effective slip length over these to be of the order of several hundred nanometers which increases with increasing silicone oil film thickness, as expected. The fitted slip length values weakly increased with increasing shear rates. The high values of effective slip length indicate that lubricant-infused surfaces are likely to reduce drag on length scales that approach the macroscopic scales.

Analytical spontaneous imbibition model for confined nanofractures

Abstract The capillary spontaneous imbibition length of slick water in confined rectangular cross-sectional nanofractures is investigated in this paper. In the established model, the effective slip length, effective viscosity, wettability and nanofracture size are incorporated into the modified Hagen–Poiseuille equation. The calculated spontaneous imbibition length as a function of time, viscosity, wettability and pore size is qualitatively validated by experimental and previous theoretical Hagen–Poiseuille flow results. Our model calculation results agree well with the published experimental data. The ratio of the effective and bulk water viscosities is higher than one, and increases with an increase in the ratio of the nanofracture width to height and decreasing contact angle. The spontaneous imbibition capacity of confined water is enhanced ∼0.67–1.28 times, as determined by the Hagen–Poiseuille equation without the slip effect for various contact angles and nanofracture dimensions.

Prediction of Shale Apparent Liquid Permeability Based on Fractal Theory

In this paper, we investigate the apparent liquid permeability (ALP) of shale composed of inorganic matter (IOM) and organic matter (OM). An ALP model for porous media is developed based on water transport through a single nanopore, which is upscaled with the aid of fractal theory, taking the total organic carbon (TOC) content and structural parameters into account by considering a varying viscosity that depends on nanopore size. The proposed model results are effectively validated with data from previous research. The results show that (1) the confined water transport capacity increases with the contact angle and decreases with the maximum pore size, (2) the ALP increases with the TOC content for a given effective slip length and varying viscosity and the viscosity effect cannot be ignored, (3) and the fluid transport capacity is strongly dependent on the structural parameters of the pores, increasing with the pore size but decreasing with the pore fractal dimension.

On the Interfacial Flow Over Porous Media Composed of Packed Spheres: Part 1-Identification of the Effective Slip Length

The effective slip length at the interface between pure fluid flow and porous media composed of packed spheres has been accurately characterized. In this study, as the first part of a two-part series, the slip length is obtained by matching the flow rate over the actual packed spheres from a direct simulation with that over an effective smooth surface using the Navier-slip boundary condition from analytic solution. Three classical packing structures, e.g., simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC), are employed. The accuracy of the slip length is validated by comparing the velocity field of flow over the actual porous architecture and over the effective smooth surface. We report that the slip length is best described as a function of the free slip area, rather than conventional variables such as solid volume fraction and packing structure, with the error less than 7.5%. Then, the effective smooth surface with the slip length is applied to describe two flow problems: a stick–slip–stick flow and channel flow. The slip velocity as well as its slope at the interface and the velocity profile within the pure fluid channel is accurately reproduced. In Part 2, effective slip length will be employed to characterize optimal effective viscosity and stress jump coefficient in the Stokes–Brinkman approach, which can be applied for industrial and natural flows in dual-scale porous media in predicting flow solutions inside and outside the porous media.

Capillary imbibition of confined water in nanopores

The spontaneous capillary imbibition of confined nanopores is investigated using an analytical model that includes the slip effect, wettability and effective viscosity at the water surface interface. The results show that the effective viscosity of confined water is larger than that of bulk water and decreases with diameter and wettability. The effective slip length is negative for a contact angle of 0◦, and the effective slip length is positive and increases with diameter. The results of the presented model show that the capillary imbibition length for nanoconfined water can vary up to 0.389-1.033 times that determined by the Lucas-Washburn equation with no-slip boundary conditions for nanopores due to the effective viscosity and slippage with various dimensions and contact angles. The enhancement increases with diameter and contact angle. These results elucidate the confined movement through nanopores, which can be used to understand fracturing-fluid flow in the nanopores of shale reservoir formations. Cited as : Zeng, F., Zhang, Q., Guo, J., Meng, Y., Shao, X., Zheng, Y. Capillary imbibition of confined water in nanopores. Capillarity, 2020, 3(1): 8-15, doi: 10.26804/capi.2020.01.02

The local slip length and flow fields over nanostructured superhydrophobic surfaces

The local slip behavior and flow fields near the gas-liquid interface (GLI) of a Newtonian liquid flowing past a superhydrophobic surface with periodic rectangular grooves are investigated using molecular dynamics (MD) simulations. The saturated vapor of the liquid fills the groove to form the GLI. A flat GLI is introduced by carefully adjusting the channel height to make the liquid bulk pressure equal to the coexistence pressure. The setup with the flat GLI allows for an accurate determination of the local slip velocity, shear rate and slip length. We find that the local slip velocity and shear rate at the GLI are well described by the elliptical and exponential functions, respectively. By directly computing the local slip length from the local flow fields, we propose a novel distribution function for the slip length along the GLI for both transverse and longitudinal flows. Moreover, we demonstrate that the relationship between the local and the effective slip lengths in the transverse and longitudinal cases deviates from the continuum assumptions as the groove width is reduced to the nanoscale dimensions. The functional form for the local slip length can be potentially used as a boundary condition in the continuum analysis without considering the explicitly gas flow in the grooves of superhydrophobic surfaces.

Analysis of microstructural facet fatigue failure in ultra-fine grained powder metallurgy Ti-6Al-4V produced through hydrogen sintering

The hydrogen sintering and phase transformation (HSPT) process is a powder metallurgy method that produces Ti-6Al-4V with fatigue properties rivaling wrought processed Ti-6Al-4V. Previous fatigue work on HSPT Ti-6Al-4V has shown failure to be frequently caused by microstructural facets, which were believed to be grain boundary (GB) α phase. This belief conflicts with other reports as fatigue failure typically occurs across α colonies or primary α grains, not GB α. In this work, electron backscattered diffraction is used to identify these facets as GB α. Furthermore, a simple geometric model predicting the effective slip length of GB α is presented.

Influence of texture shape and arrangement on thermo-hydraulic performance of the textured microchannels

Textured superhydrophobic surfaces (TSS) are purported to reduce flow friction in microchannels due to velocity slip at liquid-gas interface. At the same time, the liquid-gas interface inhibits heat transfer in textured microchannels due to the low thermal conductivity of entrapped gas phase. Despite significant understanding on fluid flow and thermal transport on the TSS, the interplay of texture shape and arrangement on thermo-hydraulic performance has not been investigated in detail hitherto. To this end, we have numerically investigated the pressure-driven flow through textured microchannels with an aim to enhance the thermo-hydraulic performance. The effective slip length and temperature jump length were estimated as a function of flow and geometry parameters for three types of micropillar shapes viz., square, triangular and herringbone, decorated in microchannels in regular and staggered manner. Scaling relations for the effective slip length and temperature jump length have been shown to be valid for triangular and herringbone shaped micropillars at different flow and geometry related parameters. Herringbone shaped micropillars exhibit more flow friction and allow a significant heat transfer in microchannels within the parameter range investigated, followed by triangular and square shaped micropillars. Although the arrangement of textures in microchannels was found to affect the flow friction substantially, its effect on heat transfer was found to be marginal. Subsequently, the overall thermo-hydraulic performance was observed to be superior in regularly arranged herringbone shaped micropillars, at moderate to high constriction ratios (a ratio of texture pitch to half channel height) and high Peclet numbers over the other texture shapes. The results presented in this work would serve as a useful guide to attain maximum thermo-hydraulic performance in textured microchannels.