Semiclassical approach to electrorheological fluids. Influence of solid volume fraction on the suspension yield stress

Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.

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Experimental study on the rheological behaviour of coal ash slurries

Journal of Hydrology and Hydromechanics ◽

10.1515/johh-2015-0029 ◽

2015 ◽

Vol 63 (4) ◽

pp. 303-310 ◽

Cited By ~ 13

Author(s):

K.M. Assefa ◽

D.R. Kaushal

Keyword(s):

Yield Stress ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Substantial Reduction ◽

Relative Viscosity ◽

Rheological Behaviour ◽

Experimental Investigations ◽

Solid Mass ◽

Mixing Proportion ◽

Mass Concentrations

Abstract Extensive experimental investigations were carried out to evaluate the rheological behaviour of fly ash (FA) slurry without and with the addition of bottom ash (BA) and BA slurry without and with the addition of FA. The FA slurries exhibited Bingham behaviour at solid mass concentrations ranging from 60–65% and mixing proportions from 10– 40%. A substantial reduction in yield stress was observed except for mixing proportion of 40% on which the yield stress and viscosity were increased drastically for all solid concentrations. Hence, it can be concluded that the yield stress and viscosity of FA slurry were very much influenced by adding BA up to the mixing proportion of 30%. The rheological behaviour of BA slurries with and without the addition of FA in proportions of 10–50% was investigated and exhibited Newtonian behaviours for solid mass concentrations ranging from 30–50% without and with the addition of FA. The viscosity increases with increasing the solid concentrations and proportion of FA. Based on these experimental data, a correlation was developed to predict the relative viscosity of BA slurries as a function of solid volume fraction and FA mass proportion of 0–50% and the RMSE and R2 values showed good agreement between the experimental and the predicted data.

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L-Box Form Filling of Thixotropic Cementitious Paste and Mortar

Materials ◽

10.3390/ma13071760 ◽

2020 ◽

Vol 13 (7) ◽

pp. 1760

Author(s):

Mareike Thiedeitz ◽

Nasime Habib ◽

Thomas Kränkel ◽

Christoph Gehlen

Keyword(s):

Yield Stress ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Rheological Parameters ◽

Empirical Equations ◽

Dynamic Yield Stress ◽

Shear Rates ◽

Flow Length ◽

Dynamic Yield ◽

Fast Flow

Rheological properties of cementitious pastes and mortar affect the casting, placement, and setting properties of fresh concrete. Fundamental rheological knowledge thus helps in predicting concrete flowability and workability. Empirical equations correlate actual rheological parameters based on physical material characteristics to workability tests. Still, these equations generally only take the dynamic yield stress of the material into account. This is not sufficient for thixotropic cementitious pastes or mortars, which possess structural buildup at rest. Workability predictions regarding the flow of concrete are thus more complicated with thixotropic materials. During form-filling in L-shaped formworks, the flow velocity of concrete slows down, wherefore rheological parameters change with time. At initial fast flow, high shear rates without structural buildup can be assumed. Dynamic yield stress and a steady state viscosity thus are proper parameters for empirical equations describing concrete flowability. During low shear rates, partial structural buildup takes place. Viscosity and yield stress increase due to agglomeration and affect the flowability of concrete tremendously. Rheological parameters of various cementitious pastes and mortars varying in their solid volume fraction and flowability were investigated in a vane-in-cup rheometer. The workability of the same mixtures was investigated by measuring the flow length in an L-shaped formwork. The effect of yield stress, viscosity, and thixotropic structural buildup on flow length was investigated. Subsequently correlations and discrepancies between flowability parameters and workability equations were analyzed.

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YIELD STRESS OF FRACTAL AGGREGATES

Fractals ◽

10.1142/s0218348x15500280 ◽

2015 ◽

Vol 23 (03) ◽

pp. 1550028 ◽

Cited By ~ 3

Author(s):

YUE XI ◽

JINJIAN CHEN ◽

YONGFU XU ◽

FEIFEI CHU ◽

CHUANXIN LIU

Keyword(s):

Fractal Dimension ◽

Yield Stress ◽

Power Law ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Published Data ◽

Proposed Model ◽

Wide Range ◽

The Relationship ◽

Theory And Experiments

A model for the yield stress of aggregates is presented that incorporates fractal dimension taking into account the solid volume fraction and the aggregate diameter. The model shows the yield stress (σy) of aggregates increases with the solid volume fraction (ϕs) as a power law, and is given by [Formula: see text], where the exponent (m) is related to fractal dimension (D), and σy0 is a referenced parameter. The relationship between exponent (m) and fractal dimension is validated by published data of aggregates and represents the measured data very well, over a wide range of the solid volume fractions. The referenced parameter (σy0) is calibrated from experiments of yield stress using power law fittings. The agreement between theory and experiments supports the idea that yielding is ultimately caused by the rupture of a few interparticle bonds within aggregates. In addition, the proposed model for the yield stress of aggregates is found to match better with experiments by comparing with all models in literature.

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Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

Current Nanoscience ◽

10.2174/1573413716999201015090335 ◽

2020 ◽

Vol 16 ◽

Author(s):

Adel Alblawi ◽

Saba Keyani ◽

S. Nadeem ◽

Alibek Issakhov ◽

Ibrahim M. Alarifi

Keyword(s):

Carbon Nanotubes ◽

Velocity Profile ◽

Pressure Gradient ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Pressure Rise ◽

Shear Stresses ◽

Left Wall ◽

Coupled Equations ◽

The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

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Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids

Scientific Reports ◽

10.1038/s41598-021-84018-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Benoit Tallon ◽

Artem Kovalenko ◽

Olivier Poncelet ◽

Christophe Aristégui ◽

Olivier Mondain-Monval ◽

...

Keyword(s):

Experimental Data ◽

Yield Stress ◽

Multiple Scattering ◽

Silicone Rubber ◽

Acoustic Waves ◽

Scattering Theory ◽

Negative Refraction ◽

Volume Fraction ◽

Experimental Demonstration ◽

Acoustic Beam

AbstractNegative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction $$\Phi$$ Φ of the resonant micro-beads. For diluted metafluid ($$\Phi =3\%$$ Φ = 3 % ), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid ($$\Phi =17\%$$ Φ = 17 % ).

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

Rheologica Acta ◽

10.1007/s00397-021-01281-5 ◽

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.

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Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0258 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Subramanian Muthukumar ◽

Selvaraj Sureshkumar ◽

Arthanari Malleswaran ◽

Murugan Muthtamilselvan ◽

Eswari Prem

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Transfer Rate ◽

Hartmann Number ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Darcy Number ◽

Bottom Wall ◽

Uniform Heating ◽

The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

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A sensitivity study on carbon nanotubes significance in Darcy–Forchheimer flow towards a rotating disk by response surface methodology

Scientific Reports ◽

10.1038/s41598-021-87956-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Anum Shafiq ◽

Tabassum Naz Sindhu ◽

Qasem M. Al-Mdallal

Keyword(s):

Heat Transfer ◽

Carbon Nanotubes ◽

Ethylene Glycol ◽

Biot Number ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Rotating Disk ◽

Sensitivity Study ◽

Basic Fluid ◽

Walled Cnts

AbstractThe current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy–Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes’ constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge–Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

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Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/0954408917732759 ◽

2017 ◽

Vol 232 (5) ◽

pp. 622-631 ◽

Cited By ~ 15

Author(s):

R Tabassum ◽

Rashid Mehmood ◽

O Pourmehran ◽

NS Akbar ◽

M Gorji-Bandpy

Keyword(s):

Heat Flux ◽

Friction Coefficient ◽

Skin Friction ◽

Volume Fraction ◽

Variable Viscosity ◽

Solid Volume Fraction ◽

Local Heat ◽

Skin Friction Coefficient ◽

Viscosity Parameter ◽

Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

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