Viscous Shear Effects Research Articles

Viscous shear is a key force in Drosophila ventral furrow morphogenesis.

Ventral furrow (VF) formation in Drosophila melanogaster is an important model of epithelial folding. Previous models of VF formation require cell volume conservation to convert apically localized constriction forces into lateral cell elongation and tissue folding. Here, we investigated embryonic morphogenesis in anillin knockdown (scra RNAi) embryos, where basal cell membranes fail to form and therefore cells can lose cytoplasmic volume through their basal side. Surprisingly, the mesoderm elongation and subsequent folding that comprise VF formation occurred essentially normally. We hypothesized that the effects of viscous shear may be sufficient to drive membrane elongation, providing effective volume conservation, and thus driving tissue folding. Since this hypothesis may not be possible to test experimentally, we turned to a computational approach. To test whether viscous shear is a dominant force for morphogenesis in vivo, we developed a 3D computational model incorporating both accurate cell and tissue geometry and experimentally measured material parameters. Results from this model demonstrate that viscous shear generates sufficient force to drive cell elongation and tissue folding in vivo.

Experimental and numerical investigation on the bubble breakup and coalescence characteristics in the highly efficient static mixers

CFD-PBM and experiment methods were applied to study the bubble dispersion characteristics in the static mixers with three twisted blades (TKSM). The gas-liquid velocity ratio was selected as drag correction factors. The simulation data was compared with experimental values at different superficial gas velocity and the results revealed that the modified model could effectively enhance the calculation accuracy of gas holdup. Furthermore, bubble size distribution (BSD) was well predicted by Luo-Prince model and the mean relative error (MRE) of axial d32 between the prediction of Luo-Prince model and experimental value was 2.86 %. Meanwhile, the influences of bubble collision mechanisms and coalescence correctors on the numerical prediction were quantitatively analyzed. The effects of turbulent fluctuation, viscous shear, wake entrainment and buoyancy driven were considered for the prediction of bubble collision frequency in TKSM. The prediction precision of cumulative probability distribution (CPD) was promoted by 17.26 % when the correctors obtained from Energy-Minimization Multi-Scale (EMMS) method were used. In addition, empirical parameter CDas was evaluated and the results showed that the Das coalescence model could accurately describe the BSD when CDas was 0.01–0.1. The backmixing performance of the gas phase in the TKSM exceeds that of the liquid phase, which is distinct from that in vortex unit.

Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

Propagation of pore pressure and stress in water-saturated elastic porous media is theoretically investigated when considering the Darcy-Brinkman law. The wave mode, phase velocity, phase lag, damping factor, and characteristic frequency are found from the updated mathematic model. The Brinkman term describes the fluid viscous shear effects and importantly contributes to the dispersion relation and wave damping. The coincidence of the properties of Biot waves of the first and second kinds occurs at a characteristic frequency, which is remarkably influenced by the Brinkman term. A key finding is that, compared to the Darcy-Brinkman law, Darcy’s law overestimates the phase velocity, damping, and phase lag of the first wave, while underestimates the phase velocity, damping, and phase difference of the second wave. The introduction of the Darcy-Brinkman law yields an improved description of the damping of the compressional wave modes in saturated porous media.

Laminar spread of a circular liquid jet impinging axially on a rotating disc

The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number,$Ro$. The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by$Ro$. Its numerical solutions are discussed for a wide range of values of$Ro$. The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases$Ro\gg 1$and$Ro\ll 1$. The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.

Viscous shear effect in non-Newtonian lubrication of finite porous elastic bearings

PurposeThe purpose of this study is to investigate the viscous shear effect on finite porous elastic journal bearings lubricated with non-Newtonian couple stress fluid.Design/methodology/approachBased on Stokes micro-continuum mechanics, the modified Reynolds equation including bearing deformation was derived. The porous flow was modeled by the complete Darcy–Brinkman equation. To show the viscous shear effects, bearing characteristics including load capacity and friction factor are compared to those obtained from Darcy model with Beavers–Joseph slip conditions (slip flow model [SFM]) by developing a computer program and discussed for different couple stress values, permeabilities and elastic deformation parameters.FindingsIt is found that the viscous shearing forces effects of the Brinkman model increase the load capacity and friction factor compared to those derived using SFM. Moreover, the couple stresses increase the load capacity while decreasing the friction factor for both models.Originality/valueThis study introduces for the first time the viscous effect on finite porous elastic journal bearings lubricated with couple stress fluid.

CFD study on the effects of viscous shear in a hot cascade Ranque–Hilsch vortex tube

The objective of this paper is to carry out an extensive Computational Fluid Dynamics (CFD) study on work transfer due to viscous shear in a hot cascade Ranque–Hilsch vortex tube. The commercial CFD code ANSYS FLUENT 14.0 has been employed to carry out the numerical analysis using RANS standard k-epsilon turbulence model. A two-dimensional axisymmetric geometrical domain has been generated with structured mesh and air has been taken as the working fluid. The CFD results reveal that work transfer due to the action of viscous shear along the tangential direction increases considerably with hot cascading. However, the work transfer due to viscous shear along the axial direction degrades the performance of the device as the heat transfer takes place from cold zone to the hot zone. The effect of radial shear stress is negligible due to low value of radial velocity gradient.

Combined Non-Newtonian and Viscous Shear Effects on Porous Squeeze Film Behavior

On the basis of the Stokes microcontinuum theory, a numerical study of the combined effects of non-Newtonian couple stress and viscous shear forces on porous squeeze film behavior for parallel circular plates is presented in this article. A modified Reynolds equation governing the film pressure is derived using the Stokes constitutive equations to account for lubricant couple stress effects due to the presence of additives or suspended particles. The Darcy-Brinkman equations describing the fluid flow within the porous plate are used to account for viscous shearing forces. Numerical solutions for the squeeze film characteristics including film pressure, radial velocity, squeeze velocity, and response time are calculated for various values of the couple stress and viscous shear parameters. The simulation results indicate that the combined effects of couple stresses and viscous shearing forces are considerable.

A numerical simulation of viscous shear effects on porous squeeze-film using the Darcy-Brinkman model

In recent decades, problems related to the squeeze of fluid films in the presence of a porous medium draw attention of researchers and are the subject of many applied studies for industry and biomechanics. Our concerns in this paper are the numerical simulation of the viscous shear stresses effects on the fluid film characteristics between two discs with one porous. This study is based on the coupling, at the fluid film-porous disc interface, of the Darcy-Brinkman equations in the porous medium and the modified Reynolds equation describing the flow in the fluid film. The system of equations obtained is discretized by the means of finite differences method and solved numerically using the technique of Successive Over-Relaxation (SOR). The results show that the viscous shear effects increase the radial and the axial fluid film velocities as well as the squeeze film velocity but decrease the response time. Moreover, these effects are enlarged for smaller viscous shear parameter and for smaller fluid film thickness.

Numerical model for predicting thermodynamic cycle and thermal efficiency of a beta-type Stirling engine with rhombic-drive mechanism

This study is aimed at development of a numerical model for a beta-type Stirling engine with rhombic-drive mechanism. By taking into account the non-isothermal effects, the effectiveness of the regenerative channel, and the thermal resistance of the heating head, the energy equations for the control volumes in the expansion chamber, the compression chamber, and the regenerative channel can be derived and solved. Meanwhile, a fully developed flow velocity profile in the regenerative channel, in terms of the reciprocating velocity of the displacer and the instantaneous pressure difference between the expansion and the compression chambers, is derived for calculation of the mass flow rate through the regenerative channel. In this manner, the internal irreversibility caused by pressure difference in the two chambers and the viscous shear effects due to the motion of the reciprocating displacer on the fluid flow in the regenerative channel gap are included. Periodic variation of pressures, volumes, temperatures, masses, and heat transfers in the expansion and the compression chambers are predicted. A parametric study of the dependence of the power output and thermal efficiency on the geometrical and physical parameters, involving regenerative gap, distance between two gears, offset distance from the crank to the center of gear, and the heat source temperature, has been performed.

Derivation of Modified Reynolds Equation: A Porous Media Model With Effects of Electrokinetics

A lubrication theory that includes the effects of electrokinetics and surface microstructure is developed. A porous layer attached to the impermeable substrate is used to model the microstructure on a bearing surface. The Brinkman-extended Darcy equations and Stokes equations are modified by considering the electrical body force and utilized to model the flow in porous media and fluid film, respectively. The stress jump boundary conditions on the porous media/fluid film interface and the effects of viscous shear and electric double layer (EDL) are also considered when deriving the modified Reynolds equation. Under the usual assumptions of lubrication and Debye–Hückel approximation for low surface potential, the velocity distributions, the apparent viscosity, and the modified Reynolds equation are then derived. The apparent viscosity is expressed explicitly as functions of the Debye length, the electroviscosity, the charge density, the stress jump parameter, and the porous parameters (permeability, porosity, and porous film thickness). The considerations of EDL near the interface and the charge density of the flow in the porous media increase the apparent viscosity. The existence of porous film also increases the apparent viscosity as well. Both effects are important for flow within microspacing and lubrication problems. The apparent viscosity and the performance of 1D slider bearings are analyzed and discussed. The results show that the apparent viscosity and the load capacity increase as the permeability decreases, the stress jump parameter decreases, the charge density increases, the inverse Debye length decreases, or the porosity decreases.

Modified Reynolds equation for coupled stress fluids ? a porous media model

In this paper, the rheological effects of coupled stress fluids on thin film lubrication modeling are developed. Thin porous layers attached to the impermeable substrate are utilized to model the microstructure of bearing surfaces. In the fluid film region, the constitutive equations for coupled stress fluids proposed by Stokes [1] as well as the continuity and momentum equations are applied to model the flow. In the porous region, the Brinkman-extended Darcy equations are applied to model the flow. Under the usual assumption of hydrodynamic lubrication applicable to thin films, the effects of viscous shear and the stress jump boundary condition at the porous media/fluid film interface are included in deriving the modified Reynolds equation. The effects of material properties such as coupled stress parameter Open image in new window viscosity ratio (αi2), thickness of porous layer (Δi), permeability (Ki), and stress jump parameter (βi), on the velocity distributions and load capacities of one-dimensional converging wedge problems are discussed.

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.

Performance characteristics of finite porous slider bearings: Brinkman model

On the basis of the Brinkman model (BM), the present paper is mainly concerned with the viscous shear effects on the performance characteristics of finite porous slider bearings. The modified Reynolds equation is obtained by using the Brinkman equations to account for the effects of viscous shearing stresses. The film pressure is evaluated by a finite difference technique employing the Conjugate Gradient method of iteration, and applied to calculate the bearing performance. According to the results, the BM predicts quite different characteristics to those derived using either the slip-flow model or Darcy model. In particular, a higher load-carrying capacity and a lower friction parameter are predicted using the BM for porous slider bearings with with low permeability parameters and/or large width–length ratios. For engineering applications, a design example is also illustrated.

Derivation of Modified Reynolds Equation—A Porous Media Model

In this study, a porous media model is developed which can be applied to thin film lubrication problems. The microstructure of bearing surfaces is modeled as porous layers attached to the impermeable substrate. The Brinkman-extended Darcy equations and Stokes’ equations are utilized to model the flow in the porous region and fluid film region, respectively. The stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included in deriving the modified Reynolds equation. The present model can correct and modify a previous study based on the Darcy model with slip-fiow effects or another based on the Brinkman-extended Darcy model with stress continuity at the porous media/fluid film interface. In the results, the effects of material properties: viscosity ratio (αi2), thickness of porous layer (Δi), permeability (Ki), stress jump parameter (βi), on the velocity distributions, and performance of one-dimensional converging wedge problems are discussed.

Hydrodynamic lubrication of long, flexible, porous journal bearings using the Brinkman model

Considering the flexibility of porous bearings, this paper applies the Brinkman model (BM) to study the influences of viscous shear stresses on the lubrication performance of long, flexible, porous journal bearings. It is found that the viscous shear effects of the BM signify an improvement in the steady characteristics of the system. A comparison with the Darcy model (DM) shows that the viscous shear effects provide a significant reduction in the eccentricity ratio and ensure a noticeable reduction in the friction parameter at high loads.

Viscous shear effects on the squeeze-film behavior in porous circular disks

On the basis of the Brinkman model (BM), the main objective of this paper is to predict the viscous shear effects on the squeeze-film characteristics between porous circular disks. According to the results obtained, the influences of viscous shear stresses on the squeeze-film behavior are significant and not negligible. It is found that the BM predicts quite different squeeze-film action to those derived by using the Slip-flow model (SFM) and Darcy model (DM). When comparing with that of the SFM, the viscous shear effects of the BM provide an enhancement in the load-carrying capacity and, then, increase the response time of the squeeze-film behavior; but these trends are reversed as compared to that derived by using the DM.

Squeeze Film Behavior in a Hemispherical Porous Bearing Using the Brinkman Model

On the basis of the Brinkman model, the main objective of this paper is to theoretically predict the effects of viscous shear stresses on the pure squeeze film behavior in a hemispherical porous bearing under a constant load. The modified Reynolds equation is derived by using the Brinkman equations to account for the viscous shear effects. According to the results, the influence of viscous shear stresses on the squeeze film characteristics is significant and not negligible. It is also found that the Brinkman model predicts a quite different squeeze film action than those derived by the Darcy model and the slip-flow model. Compared with that derived by the Darcy model for thin-walled porous bearings, the viscous shear effects of the Brinkman model reduce the load capacity and the response time of the squeeze film, but the viscous shear effects increase the load capacity and lengthen the response lime of the squeeze film action for rotor-bearing contact to occur as compared to that of the slip-flow model. Moreover, by considering the viscous shear effects and the bearing thickness ratio, the Brinkman model provides an appropriate prediction of the squeeze film characteristics for a wide range of the porous bearing thickness.

Lubrication of Long Porous Slider Bearings. (Use of the Brinkman-Extended Darcy Model).

We apply the Brinkman-extended Darcy model to analyze the hydrodynamic lubrication of long porous slider bearings. The solutions are obtained and compared with those based on the Darcy model. The results show that the effects of viscous shear given by the Brinkman-extended Darcy model lead to a higher load capacity and a lower friction parameter. It is found that a thicker porous bearing gives a greater effect of viscous shear on load capacity and friction parameter.

Dynamic behaviour of pure squeeze films in short porous journal bearings using the Brinkman model

On the basis of the Brinkman model (BM), the main objective of this paper is to predict theoretically the effects of viscous shear stresses on the dynamical behaviour of pure squeeze films in short porous journal bearings under cyclic loads. The results obtained from the BM, as the value of permeability parameter Phi approaches zero, show good agreement with that of a solid bearing and, hence, provide support to the present prediction. Comparing with that derived by the Darcy model (DM), the influence of viscous shear stresses of the BM on the squeeze-film performance is slight for the thin-walled bearings. But for the thick-walled bearings, the effects of viscous shear stresses provide a significant increase in the load-carrying capacity. Under dynamic loading, the viscous shear effects reduce the eccentricity ratio and, thus, provide a longer time to prevent the journal-bearing contact. Hence, the viscous shear effects of the BM improve the squeeze-film characteristics for a system with thick-walled bearings.

Linear Stability Analysis of Short Porous Journal Bearings—Use of the Brinkman Model

On the basis of a Brinkman model (BM), this paper predicts that the effects of viscous shear stresses on the linear stability of short porous journal bearings are apparent and not negligible. Compared with those of the slip-flow model (SFM) and the Darcy model (DM), the viscous shear effects provide a significant increase in the stability threshold speeds of short porous journal bearings.