Apparent Slip Velocity Research Articles

Numerical approach to pipe flow of fresh concrete based on MPS method

As a fundamental study of concrete pumping, this study developed a numerical method to simulate the flow and segregation of fresh concrete in pipes, based on the improved MPS (Moving Particle Semi-implicit) that has complete implicit algorithm, hereafter called I-MPS. The slip layer (LL) near the pipe inner wall was treated by the macroscopic approach, which estimates the slip resistance and the volumetric flow rate of LL from the apparent slip velocity of LL. Two constituent models were used to describe fresh concrete, called single-phase & mono-particle (SPMP) model and double-phase & multi-particle (DPMP) model, respectively. In the former, fresh concrete is considered as a single-phase granular fluid, but in the latter, fresh concrete is regarded as two-phase granular fluid with different particle shapes and sizes of coarse aggregate and matrix mortar. By comparing the numerical and theoretical pumping pressures of three concretes having slump from 13 cm to 21 cm, it was found that by using the macroscopic approach of LL and either of the constituent models, the numerical approach can predict properly the pumping pressure and velocity profile of fresh concrete in pipes. Moreover, if using the DPMP model, the segregation behavior of coarse aggregate particles during the pipe flow can also be simulated.

Yield stress and wall slip of kaolinite networks

In this work, the nonlinear rheological properties of kaolinite suspensions as a model fluid were studied. Three kaolinites with different average particle, aspect ratio and asperity were used to gain a deeper understanding of the effects of particle's geometry on yielding, rheology, and apparent slip velocity over a wide range of concentrations in the semi-concentrated to concentrated regime. To reveal the impact of geometry on kaolinite suspension's rheology, atomic force microscopy was employed, thus revealing unique information about the particle's structural differences. The apparent slip velocity was studied through the application of the Mooney technique using experimental data from parallel-plate geometry at various gap spacings. Sandpaper of varying grit was used to eliminate slip and estimate the true rheological parameters including the yield stress of these materials. Kaolinite suspensions were found to follow a Herschel–Bulkley model with yield stress that increases with concentration irrespective of the type of kaolinite particles. The aspect ratio and asperity of particles were found to alter their slip behavior by enabling the kaolinite network to have a tunable yield stress. It was also determined that the existence of resilient larger clusters at higher shear rates often induce higher slip effects.

Apparent wall slip effects on rheometric measurements of waxy gels

The effects of apparent wall slip on rheometric measurements of waxy gels are quantified for gels consisting of a macrocrystalline wax added in mineral oil in concentrations of 3.0 and 7.5 wt. %. The waxy gels are formed in situ in a stress-controlled rheometer, and rheological properties are then obtained. Seven different geometry configurations, including parallel plates, concentric cylinders, and vane, are employed. The surface roughness of the different geometries and wax crystals size are assessed to provide insight into the apparent wall slip phenomenon. In the presence of smooth surfaces, a decrease in approximately 80% in the measured yield stress value is observed in oscillatory tests, regardless of system composition. In addition, the storage modulus measurements are substantially different when obtained from smooth or grooved geometries. In creep experiments, the yield stress measurements decrease by 68%. As expected, apparent wall slip markedly affects the shape of the flow curves obtained, causing the appearance of kinks for smooth Couette geometry. Apparent slip velocities are calculated in the regime just above the yield stress, and it is found that for low concentrations apparent slip increases with concentration and decreases with the ratio between the shear stress and dynamic yield stress. The gathered results also demonstrate that the reproducibility of rheological measurements is improved by using geometries with grooved parts. By quantifying the effects of apparent wall slip on rheological measurements of waxy gels for different geometries, this work can provide useful information for the design of pipelines and oil transportation processes.

Axial flow structure of solids holdup in an 18-m high-density CFB riser based on pressure measurements

The axial flow structure in a high-density CFB riser having a height of 18m is investigated on the basis of pressure measurements. Solids circulation rates reach 1400kg/(m2s) at superficial gas velocities of 5–9m/s and the apparent solids holdup exceeds 0.2, indicating high-density operations have been achieved. The apparent solids holdup increases with the solids circulation rate increasing and/or superficial gas velocity decreasing. Axial distributions of the apparent solids holdup have exponential shapes with denser regions at the bottom and more dilute regions in the upper part. The apparent slip velocity increases with the increasing solids holdup and reaches 14m/s, showing that there are more opportunities of cluster formation in high-density operation. Furthermore, the apparent slip velocity has a power relation with the apparent solids holdup under a wide range of operating conditions.

Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: Effect of fluid relaxation and retardation time

We investigate the electroosmotic flow of a quasi-linear viscoelastic fluid over a surface having charge modulation in narrow confinements. We obtain analytical solutions using a combination of regular and matched asymptotic expansions in order to describe the viscoelastic flow field and apparent slip velocity besides pinpointing variations of the flow rate and ionic currents due to the surface charge modulation. We demonstrate excellent agreement between the asymptotic analytical solution for the flow field and the full numerical solution in the limiting condition of a thin electrical double layer and weakly viscoelastic fluid. For a wide range of flow governing parameters, we analyze the flow velocity, vortex dynamics, flow rates, and streaming current. We demonstrate that the magnitude of the observed electroosmotic slip velocity is more sensitive to the thickness of the electrical double layer rather than the viscoelasticity of the fluid. We have observed that the contribution of fluid elasticity is prominent in breaking the axial symmetry in the electroosmotic flow with the presence of periodic charge distributions, which is in contrast to the symmetric electroosmotic flow field of a Newtonian fluid over the same charge modulated walls. The results hold the key toward understanding the flow of biological fluids in microfluidic flows by leveraging electrokinetic transport over charge modulated surfaces. We believe that the results of net throughput, streaming current, and vortex dynamics will aid our understanding of the complex fluid behavior and microfluidic mixers.

Thermal transport due to liquid jet impingement on superhydrophobic surfaces with isotropic slip: Isoflux wall

Thermal transport due to a liquid water jet impinging an isoflux superhydrophobic surface with isotropic slip was modeled analytically. An integral analysis of the transport equations resulting in a system of ordinary differential equations was solved numerically. Impingement on superhydrophobic surfaces greatly reduces the heat transfer that occurs relative to a smooth surface due to gas trapped in cavities on the surface. This results in an apparent slip velocity and temperature jump at the surface. Local and average Nusselt numbers are presented as a function of radial position (0 to 45 jet radii), jet Reynolds number (3×103 to 1.5×104), liquid Prandtl number (2 to 11), normalized slip length (0 to 0.2), and normalized temperature jump length (0 to 0.2). All results are compared to classical (no-slip, no temperature jump) behavior on a smooth surface. Although local Nusselt numbers for the isoflux scenario are greater than the corresponding isothermal case, the difference in Nusselt number between these two heating conditions becomes negligible as the temperature jump length increases to quantities realizable on superhydrophobic surfaces. These results may be utilized to explore heat transfer degradation in applications where smooth surfaces are replaced by superhydrophobic surfaces to avoid fouling.

Unsteady electrophoresis of a dielectric cylindrical particle suspended in porous medium

The starting electrophoresis of a dielectric cylindrical particle in an electrolyte solution saturated in a charged porous medium after the sudden application of an external electric field is investigated semi-theoretically. For the case of a thin electric double layer, the apparent slip velocity caused by the time-dependent electroosmotic flow of the electrolyte solution in the Brinkman medium along a charged plane is used as the boundary condition at the particle surface to drive the dynamic electrophoretic motion. Analytical formulas, for the time-dependent electrophoretic velocity of the cylindrical particle in the Laplace transform, have been obtained for both axially and transversely when the uniform electric fields are imposed. They can also be linearly superimposed for an arbitrarily oriented relative to the electric field. Results for the electrophoresis mobility and acceleration are presented as functions of the dimensionless elapsed time, the particle-to-medium density ratio, the electrokinetic particle radius, and the permeability parameter of the porous medium. In general, the electrophoretic velocity with the dimensionless time for a cylindrical particle is weaker than for a spherical one due to its smaller specific surface area. The growth of the electrophoretic mobility with the time scale is more slower for high permeability, and the effect of the relaxation time for unsteady electrophoresis is found to be negligible, regardless of the thickness of the double layer, the relative mass density or the permeability of the medium.

Driven spheres, ellipsoids and rods in explicitly modeled polymer solutions

Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results.

On the influence of forced homogeneous-isotropic turbulence on the settling and clustering of finite-size particles

We investigate the motion of heavy particles with a diameter of several multiples of the Kolmogorov length scale in the presence of forced turbulence and gravity, resorting to interface-resolved direct numerical simulation based on an immersed boundary method. The values of the particles’ relative density (1.5) and of the Galileo number (180) are such that strong wake-induced particle clustering would occur in the absence of turbulence (Uhlmann and Doychev in J Fluid Mech 752:310–348, 2014. https://doi.org/10.1017/jfm.2014.330 ). The forced turbulence in the two present cases (with Taylor-scale Reynolds number 95 and 140) would lead to mild levels of clustering in the absence of gravity (Uhlmann and Chouippe in J Fluid Mech 812:991–1023, 2017. https://doi.org/10.1017/jfm.2016.826 ). Here we detect a tendency to cluster with an intensity (quantified via the standard deviation of the distribution of Voronoi cell volumes) which is intermediate between these two limiting cases, meaning that forced background turbulence decreases the level of clustering otherwise observed under ambient settling. However, the clustering strength does not monotonically decay with the relative turbulence intensity. Various mechanisms by which coherent structures can affect particle motion are discussed. It is argued that the reduced interaction time due to particle settling through the surrounding eddy (crossing trajectories) has the effect of shifting upward the range of eddies with a time-scale matching the characteristic time-scale of the particle. In the present cases this shift might bring the particles into resonance with the energetic eddies of the turbulent spectrum. Concerning the average particle settling velocity, we find very small deviations (of the order of one percent) from the value obtained for an isolated particle in ambient fluid when defining the relative velocity as an apparent slip velocity (i.e., as the difference between the averages computed separately for the velocities of each phase). This is consistent with simple estimates of the nonlinear drag effect. However, the relative velocity based upon the fluid velocity seen by each particle (computed via local averaging over a particle-attached sphere) has on average a smaller magnitude (by 5–7%) than the ambient single-particle value.

Abnormal Behaviors in the Capillary Rheometry of Plastisol Formulations

Abstract The rheology of plastisol formulations for flooring applications using knife-over-roll coating process is studied using both Couette and capillary rheometers. The behavior is similar in many aspects to the rheology of suspensions: Shear thinning behavior at low shear rate, then a Newtonian plateau at intermediate shear rates followed by a dilatancy peak. However several abnormal phenomena may be observed in capillary experiments. At very high shear rates, a second shear thinning behavior is observed which depends on the flow geometry. Due to the non-monotonous behavior of the plastisol viscosity, this is analysed using a dedicated numerical method. An apparent slip velocity has been determined. Otherwise capillary experiments point out the existence of important entrance pressure loss. These measures are interpreted using a modified Cogswell method as an important elongationnal viscosity, around hundred times the shear viscosity.

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

We use interface-resolved numerical simulations to study finite-size effects in turbulent channel flow of neutrally buoyant spheres. Two cases with particle sizes differing by a factor of two, at the same solid volume fraction of 20 % and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501), a particle–wall layer is responsible for deviations of the mesoscale-averaged statistics from what is observed in the continuum limit where the suspension is modelled as a Newtonian fluid with (higher) effective viscosity. Here we investigate in detail the fluid and particle dynamics inside this layer and in the bulk. In the particle–wall layer, the near-wall inhomogeneity has an influence on the suspension microstructure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the scaling laws in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501) to second-order Eulerian statistics in the homogeneous suspension region away from the wall. The results show that finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that single-point dispersion is dominated by particle–turbulence (and not particle–particle) interactions, while differences in two-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.

Hydrodynamics of countercurrent bubble column: Experiments and predictions

Experiments were conducted to study the hydrodynamics of a countercurrent bubble column equipped with porous plate distributor. Four flow regimes – purely homogeneous bubbling regime, discrete bubbling regime, helical flow regime and churn-turbulent regime are identified based on the bubble swarm velocity plot. Regime maps are presented showing the effect of liquid velocity on transition gas velocity and gas holdup along all three transition boundaries. The liquid velocity advances the onset of discrete bubbling regime, helical flow regime and churn-turbulent regime. Gas holdup increases with an increase in gas and liquid velocities. A methodology for predicting the gas holdup for both the homogeneous and heterogeneous regimes and the transition gas velocity and holdup is developed by extending existing models for homogeneous and heterogeneous regime. Bubble diameter, the model parameter in homogeneous regime, decreases with an increase in liquid velocity. Apparent slip velocity between gas and liquid phase, the model parameter in heterogeneous regime, increases with both gas and liquid velocity. The method predicts the data of the present work and literature satisfactorily. The effect of gas and liquid velocities on the radial profile of liquid velocity and its properties are simulated using the validated model.

A multiscale approach to interpret and predict the apparent slip velocity at liquid-liquid interfaces

The classical boundary conditions at flat liquid-liquid interfaces are continuity of the velocity and of the tangential component of stress; for curved interfaces, one also demands that the jump in the normal stress at the interface is balanced by the product of the interfacial tension and curvature. While these conditions are widely accepted, and are often used at the macro scale, the recent interest in micro and nano-fluidics challenges their validity. At molten polymer-polymer interfaces, for instance, it has been consistently shown by direct and indirect measurements that, apparent, velocity jumps exist and can be modelled effectively via a Navier slip condition (NSC). Here, we discuss that if a viscosity, which accounts for the density and mole fraction distributions, is included in the Navier-Stokes equations, we can describe, naturally, and without recourse to ad-hoc models such as the NSC, the velocity profile in the interfacial region separating two fluids. This approach is supported by the observation that there is a relation between apparent slip and density distribution across the interface.

Rheological effect on screen-printed morphology of thick film silver paste metallization

Up to now the topography of thick film silver paste metallization is still a great challenge to the crystalline silicon solar cell manufacturers due to lack of overall understanding about the dependence of screen-printed morphology on paste rheology. In this article, we demonstrate that both the shear thixotropy and wall slip are primary rheological behaviors of pastes affecting screen-printed morphology. By comparison among three different commercial pastes, the association of screen-printed morphology with apparent viscosity and slip velocity of pastes were investigated. The results from printing finger lines with designed width of 45 μm show clearly that the widening degree of lines is associated with the paste viscosity, and the height and cross-sectional profile of lines mainly rely on the wall slip velocity of paste passing through screen meshes. Briefly, the lower the apparent viscosity, the wider the lines; and the greater the wall slip velocity, the less the line height and more likely the formation of trapezoidal cross-sectional profile with larger area. Our study shows for the first time that the wall slip of pastes may produce significant influence on cell efficiency, since its influence on screen-printed morphology is considerably remarkable and vital.

Near-field laser Doppler velocimetry measures near-wall velocities

A new near-wall velocimetry technique is proposed, based on evanescent wave dynamic light scattering, which allows for the measurement of near-wall velocity profile (characterized by an apparent slip velocity and a shear rate) with a resolution of tens of nanometers. A full theoretical expression of the correlation function is derived for the case of linear flow with negligible Brownian motion. The technique is demonstrated for latex spheres dispersed in water-glycerol mixtures.

Apparent wall slip velocity measurements in free surface flow of concentrated suspensions

In this work we have experimentally measured the apparent wall slip velocity in open channel flow of neutrally buoyant suspension of non-colloidal particles. The free surface velocity profile was measured using the tool of particle imaging velocimetry (PIV) for two different channels made of plane and rough walls. The rough walled channel prevents wall slip, whereas the plane wall showed significant wall slip due to formation of slip layer. By comparing the velocity profiles from these two cases we were able to determine the apparent wall slip velocity. This method allows characterization of wall slip in suspension of large sized particles which cannot be performed in conventional rheometers. Experiments were carried out for concentrated suspensions of various particle volume concentrations and for two different sizes of particles. It was observed that wall slip velocity increases with particle size and concentration but decreases with increase in the viscosity of suspending fluid. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements. The effect of wall slip on free surface corrugation was also studied by analyzing the power spectral density (PSD) of the refracted light from the free surface. Our results indicate that free surface corrugation is a bulk flow response and it does not arise from boundary problem such as development of slip layer.

Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples

As originally realized by Nyborg (J. Acoust. Soc. Am., vol. 30, 1958, p. 329), the problem of the inner acoustic/steady streaming can be analysed in quite general terms. The inner streaming is the one that develops in the high-frequency limit in a thin Stokes (shear-wave) layer at a boundary, in contrast to the outer streaming in the main bulk of the fluid. The analysis provides relevant inner-streaming characteristics through a given distribution of the acoustic amplitude along the boundary. Here such a generalized treatment is revisited for a motionless boundary. By working in terms of surface vectors, though in elementary notations, new compact and easy-to-use expressions are obtained. The most important ones are those for the effective (apparent) slip velocity at the boundary as seen from a perspective of the main bulk of the fluid, which is often the sole driving factor behind the outer streaming, and for the induced (acoustic) steady tangential stress on the boundary. As another novel development, non-adiabatic effects in the Stokes layer are taken into account, which become apparent through the fluctuating density and viscosity perturbations, and whose contribution into the streaming is often ignored in the literature. Some important particular cases, such as the axisymmetric case and the incompressible case, are emphasized. As far as the application of the derived general inner-streaming expressions is concerned, a few examples provided here involve a plane acoustic standing wave, which either grazes a wall parallel to its direction (convenient for the estimation of the non-adiabatic effects), or into which a small (compared to the acoustic wavelength) rigid sphere is placed. If there are simultaneously two such waves, out-of-phase and, say, in mutually orthogonal directions, a disk placed coplanarly with them will undergo a steady torque, which is calculated here as another example. Two further examples deal with translational high-frequency harmonic vibrations of particles relative to an incompressible fluid medium, viz. of a rigid oblate spheroid (along its axis) and of a sphere (arbitrary three dimensional). The latter can be a fixed rigid sphere, one free to rotate or even a (viscous) spherical drop, for which the outer streaming and the internal circulation are also considered.

Study of slip velocity and application of drift-flux model to slip velocity in a liquid–solid circulating fluidized bed

The increasing applications of liquid–solid circulating fluidized bed in chemical/biochemical industries require a better understanding of hydrodynamics of such system. This work aims to experimentally investigate the slip between the phases in a LSCFB. The variation of slip velocity with superficial liquid velocity, solids velocity, bed voidage and particle size and density is discussed. The apparent slip velocity of the phases is higher than the particle terminal velocity of a single particle. The R–Z equation developed based on the homogenous flow characteristics underpredicts the slip velocity in a LSCFB. The drift-flux model which considers the radial non-uniformity and slip between the phases was applied to the data of the present study. The predicted value by the model agreed with the apparent slip velocity well. The study also proposed an empirical correlation to predict the slip velocity. The empirical correlations aggress well with the experimental data.

Prediction of turbulent channel flow with superhydrophobic walls consisting of micro-ribs and cavities oriented parallel to the flow direction

Turbulent flow in a parallel-plate micro-channel with superhydrophobic walls has been explored numerically. The k-ω turbulence model is used for closure to the turbulent Reynolds-averaged Navier-Stokes equations and the Reynolds number was varied from 4 × 10 3 to 10 4. Results show that as the shear-free region increases the apparent velocity slip increases, and the Darcy friction factor decreases. The observed reduction in fraction factor was found to be significantly greater for turbulent flow conditions than for laminar flow scenarios under the same geometric channel conditions. Expressions that correlate the friction factor and apparent slip velocity as functions of the relevant parameters are also presented.

Laminar Drag Reduction in Hydrophobic Microchannels

AbstractThe apparent slip effects of laminar water flow in smooth hydrophobic microchannels and patterned hydrophobic microchannels were investigated. A series of experiments were performed to demonstrate the drag reductions for laminar water flow in hydrophobic microchannels. These microchannels were fabricated from silicon wafers using photolithography and were coated with hydrophobic octadecyltrichlorosilane (OTS). To generate a larger drag reduction, the patterned hydrophobic microchannels were fabricated to allow the liquid to flow over a region of trapped air in the cavity between the microridges. With the geometrical dimensions used, pressure drop reductions ranging from 10 to 30 % were found in the smooth microchannels and patterned microchannels. The pressure drop reduction was shown to increase with increasing microridge spacing and decreasing microchannel width. Using micro‐particle image velocimetry (PIV), we measured an apparent slip velocity at the wall of approximately 8 % of the centerline velocity, yielding a slip length of approximately 2 μm in the smooth hydrophobic microchannel. Theoretically, the analytical solution derived for three‐dimensional flow in a rectangular duct is presented to predict the slip velocity and slip length at the wall based on the pressure drop measurement. These results are in agreement with the experimental data obtained using micro‐PIV.