scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

scholarly journals Macroscopic rheology of non-Brownian suspensions at high shear rates: the influence of solid volume fraction and non-Newtonian behaviour of the liquid phase

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jörg Hinrichs ◽  
Reinhard Kohlus
Keyword(s):  
Liquid Phase ◽  
Shear Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Shear Thinning ◽  
High Shear ◽  
Rate Dependency ◽  
Shear Rates ◽  
Liquid Phases ◽  
High Shear Rates

AbstractModelling the macroscopic rheology of non-Brownian suspensions is complicated by the non-linear behaviour that originates from the interaction between solid particles and the liquid phase. In this contribution, a model is presented that describes suspension rheology as a function of solid volume fraction and shear rate dependency of both the liquid phase, as well as the suspension as a whole. It is experimentally validated using rotational rheometry ($$\varphi$$ φ ≤ 0.40) and capillary rheometry (0.55 ≤ $$\varphi$$ φ  ≤ 0.60) at shear rates > 50 s−1. A modified Krieger-Dougherty relation was used to describe the influence of solid volume fraction on the consistency coefficient, $$K$$ K , and was fitted to suspensions with a shear thinning liquid phase, i.e. having a flow index, $$n$$ n , of 0.50. With the calculated fit parameters, it was possible to predict the consistency coefficients of suspensions with a large variation in the shear rate dependency of the liquid phase ($$n$$ n = 0.20–1.00). With increasing solid volume fraction, the flow indices of the suspensions were found to decrease for Newtonian and mildly shear thinning liquid phases ($$n$$ n ≥0.50), whereas they were found to increase for strongly shear thinning liquid phases ($$n$$ n ≤0.27). It is hypothesized that this is related to interparticle friction and the relative contribution of friction forces to the viscosity of the suspension. The proposed model is a step towards the prediction of the flow curves of concentrated suspensions with non-Newtonian liquid phases at high shear rates.

scholarly journals Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and– rheology

2019 ◽  
Vol 864 ◽  
pp. 1125-1176 ◽  
Author(s):  
Koshiro Suzuki ◽  
Hisao Hayakawa
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Stress Ratio ◽  
Volume Fraction ◽  
Microscopic Theory ◽  
Critical Behaviour

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\unicode[STIX]{x1D711}$ is developed. The theory successfully derives the critical behaviour in the vicinity of the jamming point (volume fraction $\unicode[STIX]{x1D711}_{J}$), for both the pressure $P$ and the shear stress $\unicode[STIX]{x1D70E}_{xy}$, i.e. $P\sim \unicode[STIX]{x1D70E}_{xy}\sim \dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}^{-2}$, where $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate, $\unicode[STIX]{x1D702}_{0}$ is the shear viscosity of the solvent and $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}=\unicode[STIX]{x1D711}_{J}-\unicode[STIX]{x1D711}>0$ is the distance from the jamming point. It also successfully describes the behaviour of the stress ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D70E}_{xy}/P$ with respect to the viscous number $J=\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}/P$.

Numerical Analysis of Wall Slip Effects on Flow of Newtonian and Non-Newtonian Fluids in Macro and Micro Contraction Channels

2006 ◽  
Vol 129 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Alfeus Sunarso ◽  
Takehiro Yamamoto ◽  
Noriyasu Mori
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Wall Shear Stress ◽  
Newtonian Fluid ◽  
Stress Function ◽  
Slip Velocity ◽  
Wall Slip ◽  
Average Shear ◽  
Wall Shear ◽  
Shear Stress Function

We performed numerical simulation to investigate the effects of wall slip on flow behaviors of Newtonian and non-Newtonian fluids in macro and micro contraction channels. The results show that the wall slip introduces different vortex growth for the flow in micro channel as compared to that in macro channel, which are qualitatively in agreement with experimental results. The effects of slip on bulk flow behaviors depend on rheological property of the fluid. For Newtonian fluid, the wall slip always reduces the vortex length, while for non-Newtonian fluid, the strength of the slip determines whether the vortex length is reduced or increased. Analyses on the velocity and stress fields confirm the channel size dependent phenomena, such as the reduction of wall shear stress with the decrease in channel size. With the increase in average shear rate, the Newtonian fluid shows the reduction of wall shear stress that increases in the same trend with slip velocity-wall shear stress function, while for non-Newtonian fluid, the effect of the slip is suppressed by shear thinning effect and, therefore, the reduction of wall shear stress is less sensitive to the change in average shear rate and slip velocity-wall shear stress function.

scholarly journals Confined flow of suspensions modelled by a frictional rheology

2014 ◽  
Vol 759 ◽  
pp. 197-235 ◽  
Author(s):  
Brice Lecampion ◽  
Dmitry I. Garagash
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Normal Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Numerical Predictions ◽  
Dry Granular Flow ◽  
Neutrally Buoyant ◽  
Constitutive Parameters ◽  
Axial Development

AbstractWe investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al. (Phys. Rev. Lett., vol. 107 (18), 2011, 188301). The friction coefficient (shear stress over particle normal stress) and solid volume fraction are taken as functions of the dimensionless viscous number $I$ defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive framework from the flowing regime (bounded by the maximum flowing solid volume fraction) to the fully jammed state (the random close packing limit). We obtain an analytical solution of the fully developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number $I$. The predictions are in excellent agreement with available experimental results for neutrally buoyant suspensions, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We also numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully developed state. The available experimental data are in good agreement with our numerical predictions, when using an accepted phenomenological description of the relative phase slip obtained independently from batch-settlement experiments. The solution of the axial development of the flow notably provides a quantitative estimation of the entrance length effect in a pipe for suspensions when the continuum assumption is valid. Practically, the latter requires that the predicted width of the central (jammed) plug is wider than one particle diameter. A simple analytical expression for development length, inversely proportional to the gap-averaged diffusivity of a frictional suspension, is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.

scholarly journals Integral Solution of Two-Region Solid–Liquid Phase Change in Annular Geometries and Application to Phase Change Materials–Air Heat Exchangers

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4474 ◽  
Author(s):  
Hamidreza Shabgard ◽  
Weiwei Zhu ◽  
Amir Faghri
Keyword(s):  
Liquid Phase ◽  
Boundary Conditions ◽  
Phase Change ◽  
Phase Change Materials ◽  
Volume Fraction ◽  
Control Volume ◽  
Solid Volume Fraction ◽  
Solidification Time ◽  
Design And Optimization ◽  
Solid Liquid

A mathematical model based on the integral method is developed to solve the problem of conduction-controlled solid–liquid phase change in annular geometries with temperature gradients in both phases. The inner and outer boundaries of the annulus were subject to convective, constant temperature or adiabatic boundary conditions. The developed model was validated by comparison with control volume-based computational results using the temperature-transforming phase change model, and an excellent agreement was achieved. The model was used to conduct parametric studies on the effect of annuli geometry, thermophysical properties of the phase change materials (PCM), and thermal boundary conditions on the dynamics of phase change. For an initially liquid PCM, it was found that increasing the radii ratio increased the total solidification time. Also, increasing the Biot number at the cooled (heated) boundary and Stefan number of the solid (liquid) PCM, decreased (increased) the solidification time and resulted in a greater (smaller) solid volume fraction at steady state. The application of the developed method was demonstrated by design and analysis of a PCM–air heat exchanger for HVAC systems. The model can also be easily employed for design and optimization of annular PCM systems for all associated applications in a fraction of time needed for computational simulations.

Rheological Behavior of Semisolid Al-6.5wt%Si Alloy under Cyclic Shear Deformation

2011 ◽  
Vol 306-307 ◽  
pp. 104-107
Author(s):  
Hong Chao Luo ◽  
Jun Mei Yang ◽  
Li Yuan Sun ◽  
Li Ping Ju
Keyword(s):  
Experimental Data ◽  
Shear Rate ◽  
Hysteresis Loop ◽  
Shear Deformation ◽  
Rheological Behavior ◽  
Qualitative Agreement ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Cyclic Shear ◽  
The Difference

In the present work, the MCF model for semisolid metal slurries (SSMS) is applied to investigate the thixotropy of the Al-6.5wt%Si alloy under cyclic shear deformation. The study shows that the semisolid Al-6.5wt%Si alloy has the behavior of thixotropy. The area of the hysteresis loop increases with decreasing the up-time, the initial shear rate and increasing resting time, solid volume fraction and maximum shear rate, respectively. These results have qualitative agreement with the experimental data. The origin of the hysteresis loop is atrributed to the difference between the deagglomeration rate and the agglomeration rate.

True Sedimentation and Particle Packing Rearrangement during Liquid Phase Sintering

2007 ◽  
Vol 534-536 ◽  
pp. 609-612
Author(s):  
Jong K. Lee ◽  
Lei Xu ◽  
Shu Zu Lu
Keyword(s):  
Liquid Phase ◽  
Concentration Gradient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Liquid Phase Sintering ◽  
Particle Packing ◽  
Sintering Process ◽  
Second Stage ◽  
Packing Efficiency ◽  
Two Stages

When an alloy such as Ni-W is liquid phase sintered, heavy solid W particles sedimentate to the bottom of the container, provided that their volume fraction is less than a critical value. The sintering process evolves typically in two stages, diffusion-driven macrosegregation sedimentation followed by true sedimentation. During sedimentation, the overall solid volume fraction decreases concurrently with elimination of liquid concentration gradient. However, in the second stage of true sedimentation, the average solid volume fraction in the mushy zone increases with time, and oddly, no concentration gradient is necessary in the liquid zone. In this work, we propose that the true sedimentation results from particle rearrangement for higher packing efficiency.

Experimental study and molecular dynamics simulation of wall slip in a micro-extrusion flowing process

2011 ◽  
Vol 225 (5) ◽  
pp. 1175-1190 ◽  
Author(s):  
D Zhao ◽  
Y Jin ◽  
M Wang ◽  
M Song
Keyword(s):  
Molecular Dynamics ◽  
Shear Stress ◽  
Molecular Dynamics Simulation ◽  
Slip Velocity ◽  
Polymer Melts ◽  
Critical Shear Stress ◽  
Wall Slip ◽  
Dynamics Simulation ◽  
Desorption Mechanism ◽  
Adsorption Desorption

Wall slip is one of the most important characteristics of polymer melts’ elasticity behaviours as well as the most significant factor which affects the flow of polymer melts. Based on the traditional Mooney method, through a double-barrel capillary rheometer, the relationship between velocities of wall slip, shear stress, shear rate, diameters of dies, and temperature of polypropylene (PP), high-density polyethylene (HDPE), polystyrene (PS), and polymethylmethacrylate (PMMA) is explored. The results indicate that the velocities of the wall slip of PP and HDPE increase apparently with shear stress and slightly with temperature. Meanwhile, the rise of temperature results in the decrease of critical shear stress. The wall-slip velocities of PS and PMMA are negative which means that the Mooney method based on the adsorption–desorption mechanism has determinate limitation to calculate the wall-slip velocity. Based on the entanglement–disentanglement mechanism, a new wall-slip model is built. With the new model, the calculation values of velocity of PP and HDPE correspond to the experimental values very well and the velocities of PS and PMMA are positive. The velocities of PS and PMMA increase obviously with the rise of shear stress. The rise of temperature results in the increase of velocity and decrease of critical shear stress. Then, the molecular dynamics simulation is used to investigate the combining energy between four polymer melts and the inside wall. The results show that at the given temperature and pressure, the molecules of PS and PMMA combine with atoms of the wall more tightly than those of PP and HDPE which means when wall slip occurs, the molecules of PS and PMMA near the wall will adsorb to the surface of the wall. However, those of PP and HDPE will be easy to slip. Therefore, the wall-slip mechanism of PP and HDPE is the adsorption–desorption mechanism, and that of PS and PMMA is the entanglement–disentanglement mechanism. According to the different wall-slip mechanisms of four polymers, an all-sided calculation method of wall-slip velocity is raised which consummates the theory of wall slip of polymer melts.

Flow at the interface of a model fibrous porous medium

2001 ◽  
Vol 426 ◽  
pp. 47-72 ◽  
Author(s):  
DAVID F. JAMES ◽  
ANTHONY M. J. DAVIS
Keyword(s):  
Porous Medium ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Circular Cylinders ◽  
Interfacial Region ◽  
Filling Fraction ◽  
Apparent Slip ◽  
Square Array ◽  
Pressure Driven Flow

Planar flow in the interfacial region of an open porous medium is investigated by finding solutions for Stokes flow in a channel partially filled with an array of circular cylinders beside one wall. The cylinders are in a square array oriented across the flow and are widely spaced, so that the solid volume fraction ϕ is 0.1 or less. For this spacing, singularity methods are appropriate and so they are used to find solutions for both planar Couette flow and Poiseuille flow in the open portion of the channel. The solutions, accurate to O(ϕ), are used to calculate the apparent slip velocity at the interface, Us, and results obtained for Us are presented in terms of a dimensionless slip velocity. For shear-driven flow, this dimensionless quantity is found to depend only weakly on ϕ and to be independent of the height of the array relative to the height of the channel and independent of the cylinder size relative to the height of the channel. For pressure-driven flow, Us is found to be less than that under comparable shear-flow conditions, and dependent on cylinder size and filling fraction in this case. Calculations also show that the external flow penetrates the porous medium very little, even for sparse arrays, and that Us is about one quarter of the velocity predicted by the Brinkman model.

The Steady State Rheological Behavior of Semisolid AlSi6Mg2 Alloy

2011 ◽  
Vol 339 ◽  
pp. 257-260 ◽  
Author(s):  
Hong Chao Luo ◽  
Shi Pu Chen ◽  
Qin Nie ◽  
En Sheng Xu ◽  
Li Ping Ju
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Experimental Results ◽  
Present System ◽  
Flow Conditions ◽  
Good Agreement

In the present work, basing on the rheological model of Chen and Fan (CF) [1] of semisolid metal slurries (SSMS), the rheological behavior at steady state of AlSi6Mg2 alloy is investigated. Experimental results on steady state viscosity of the present system in the literature are used to determine the parameters of the CF model by fitting. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The theoretical prediction of the CF model is in good agreement with the experimental results in the literatures quantitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. Specifically, the external flow conditions such as shear rate influences the viscosity by changing the agglomeration degree of the solid particles, that is, the effective solid volume fraction and then changing the viscosity.

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