Shear Rate Dependence Of Viscosity Research Articles

Insight into the bidirectional dynamics of hyperbolic tangent hybrid nanomaterial subject to Nield’s conditions using numerical approach

A hyperbolic tangent fluid model characterized by shear rate dependent viscosity together with the effects of hybrid nanoparticles, Brownian motion, thermo-diffusion, and Nield’s conditions, is utilized for thermal enhancement purpose. Five percent copper nanoparticles and twenty percent alumina nanoparticles are submerged into ethylene glycol with the parametric influence of tangent hyperbolic fluid to obtain the tangent hyperbolic hybrid nano suspension. Numerical solutions of the nondimensionalized conservation laws are found by the Keller-box method. The influence of various parametric factors on velocity, temperature, concentration, Nusselt number, and Sherwood number has been discussed. A constant Nusselt number is noted with the influence of Nield’s constraints. A 90% increase in thermal conductivity is achieved by dispersing 5% copper and 20% alumina nanoparticles into the ethylene glycol with the influence of hyperbolic tangent fluid. The error and convergence analysis of the numerical solution have been discussed, along with the validation of the obtained numerical results.

Optimization of the temperature profile of cake batter in an ohmic heating – assisted printing nozzle for 3D food printing applications

Abstract 3D printing of food has great potential for applications such as the design of customised food or the creation of innovative textures. However, printed products often do not retain their structure due to the composition of the material, especially in the case of cereal products. Cooking such products with a nozzle could be an alternative to meet this challenge. The objective of this work was to develop, with the help of a numerical model, a 3D cake batter printing nozzle in which ohmic heating is used for baking. The use of a temperature and shear rate dependent viscosity allowed the solidification of the batter during baking due to starch gelatinization. The numerical model made it possible to predict heterogeneity in temperature distribution. Optimization procedures were used to reach desired temperature profiles at the outlet of the nozzle, reducing by 17 % the electrical power used for heating and by 78 % the energy evacuated during cooling.

Entropy production in the flow of Bingham-Papanastasiou fluid having temperature and shear rate-dependent viscosity

This article comprehensively examines entropy production in a peristaltic flow of Bingham-Papanastasiou fluid in an asymmetric wavy wall channel. The viscosity of the fluid is selected to depend on the temperature in addition to the shear rate. Furthermore, viscous dissipation is considered. The equations governing momentum and energy are adjusted to incorporate the existence of a nonlinear correlation between stress and strain rate. The energy dissipation caused by viscosity in the energy equation exhibits variation between Newtonian and non-Newtonian fluids due to their distinct rheological behaviors and response to shear forces. Newton’s law of viscosity states that the viscous dissipation term for Newtonian fluids follows a simple linear relationship between shear stress and shear rate. In contrast, non-Newtonian fluids exhibit more complex rheological behaviors, with the correlation between shear stress and shear rate described by various constitutive equations, depending on the specific type of non-Newtonian behavior. Consequently, the energy equation for non-Newtonian fluid flow problems becomes more intricate and nonlinear compared to the energy equation for Newtonian fluids, resulting in a more challenging analysis. Modeling of the equations is traditionally obtained using all steps involved in analyzing peristaltic flow. Using MATLAB's bvp5c solver, the obtained coupled set of differential equations is numerically solved. The research explores how the Bingham number and stress growth exponent parameters affect different dimensionless variables, including velocity, streamlines, temperature, axial pressure gradient, entropy production, and the Bejan number.

Numerical study on generalized heat and mass transfer in cross-rheological fluid in the presence of multi-nanoscale particles: A Galerkin finite element approach

Thermal and concentration memory effects on the transport of heat and mass subjected to magnetic field and non-uniform free stream velocity are studied in this article. A cross-rheological model is used with governing laws that are solved numerically using the finite element method (FEM). A computer program is developed. The convergent and grid-independent solutions are computed, which are further used to analyse the impact of related parameters on flow fields. Influence of ternary, di-, and mono-nanoparticles on generalized transport of heat and mass in non-Newtonian fluids with cross-rheology. The dynamics of wall shear stress, wall heat, and mass fluxes are studied. Cross-fluid is a non-Newtonian fluid. It has shear rate-dependent viscosity. The behavior of cross-fluid rheology on velocity can be seen through a variation of the cross-fluid parameter called the Weissenberg number, and it has an increasing behavior on velocity. Cross-nanofluid is highly influenced by the magnetic field in comparison with cross-tri-nanofluid and cross-di-nanofluid.

Rheology of edible soft glassy materials

In this paper we investigate the rheology of three different classes of edible yield stress fluids: a) cookie doughs, b) vegetable/fruit purees, and c) protein-rich doughs as used in meat analogs and 3D food printing. Strains sweeps of different formulations within one class can be mapped to a (partial) master curve, with at least the same strain softening index, and a similar crossover point. For classes showing only a partial master curve, the formulation differs in the response of the loss modulus in the linear viscoelastic (LVE) regime, and the transition regime between LVE and strain softening regimes, where several formulations also show a weak strain overshoot. Amongst different classes, different behaviour in strain softening has been observed. Meat analogs and fruit purees show a ratio of 2 between strain softening indices of elastic and loss modulus, while for cookie doughs and protein-rich inks, the ratio is near unity. A constitutive model using a configurational tensor with shear rate-dependent viscosity and strain-dependent elastic modulus can reproduce all features observed for the different classes and for the various formulations within a class. We conclude that our constitutive model is a good basis to design edible yield stress fluids for fiber-enrichment, starch and/or sugar replacement.

Numerical study on the role of ternary nanoparticles on heat transfer enhancement in MHD flow of cross-rheological-fluid

The heat transfer in the fluids over a disk occurs in several industrial applications. Thermal and cooling systems, spray coating, heat exchangers, and automobiles are sectors where heat transfer is encountered. In view of these applications, the present investigation is carried out. Therefore, the theoretical study related to heat transfer enhancement has significance. The governing laws are used to formulate the problems. For numerical formulations, the finite element method (FEM) is used. This method has proven to be a very good numerical scheme for complex models, along with complex mathematical corelations for involved thermo-physical properties. Accuracy and convergence are ensured, and mesh-free analysis is performed. The present results for their special case are compared with published data, and an excellent agreement is found between the present results and already published data. Hence, authenticity is ensured. The strongest effects of shear rate-dependent viscosity in the case of ternary nanofluids are seen. The highest wall heat flux is noticed in the case of a ternary nanofluid. The viscous dissipation results in a remarkable decrease in the wall heat flux. The highest viscous dissipation is noticed in the case of ternary nanofluids. The ternary nanofluid generates the most heat when it is subjected to thermal changes. However, the fluid with a single type of nanoparticles generates the least heat. The strongest effects of shear rate-dependent viscosity in the case of ternary nanofluids are seen. The viscous dissipation results in a remarkable decrease in the wall heat flux. Thus, the fluid should be less viscous and dissipative if the highest wall heat flux is required in any industrial application. The highest wall shear stress is noticed in the case of ternary nanofluids, whereas the smallest values of wall shear stress are noted in the case of monofluids. Therefore, sufficient strength of the wall over which ternary nanofluid flows should be ensured in order to avoid failure or breakage of the setup where ternary nanofluid is used.

Numerical and experimental studies on design of multi-lumen tube extruded with drawing and air flow

This study represents the design and optimization procedure of a multi-lumen tube used for endoscopic retrograde cholangiopancreatography (ERCP) catheter. The geometry of tip and die for the multi-lumen tube is designed based on numerical analysis of molten polymer and air flow. In particular, this numerical study consider the interaction between the molten polymer and the air flow in the lumen which is the main process variable of extrusion, and analyze the heat transfer and pressure distribution through the air flow for the first time. In addition, to reflect the reality of the multi-lumen extrusion process, the velocity is controlled at the end of the tube ejected to the free surface in consideration of the extrusion process, which is drawn by the puller downstream of the extruder. The shear rate and temperature dependent viscosity of PEBAX 7233 SA01 MED is measured for non-isothermal numerical simulations. The extrusion process for multi-lumen tubes with drawing is simulated using ANSYS Polyflow. The profile of extrudate is numerically predicted with the initial design of the tip and die with the manufacturing parameter is optimized. The predicted profile of extrudate is compared to the target profile with dimensional requirements. The design of the tip and die is modified based on numerical results following the design procedure. To suppress the die swell phenomena, the flow area of molten polymer is increased, and the velocity difference is reduced. Finally, the multi-lumen tube with the optimized tip and die is experimentally extruded and compared to the target profile of the extrudate. It has a good agreement with the target profile and satisfies the dimensional requirements. This design procedure and numerical analysis help achieve the desired target profile of extrudate.

Computational investigation on transport of heat energy by flow of dusty Carreau fluid with nanoparticles using finite element method

Thermal performance of the working fluid depends on its thermal conductivity which can be enhanced by dispersion of nanoparticles. Therfore, the role of the simultaneous suspension of AA7072 and AA7072 and AA7072/AA7075 is analyzed in Carreau fluid, which has shear rate dependent viscosity and contains dust particles. The nanoparticles AA7072 is combination of aluminium, zinc and other alloys with ratio 98%:1%:1%, respectively. Whereas nanoparticles AA7075 is the combination of aluminium, zinc, magnesium, and copper in ratio 90%:6%:3%:1%, respectively. Further, the nanoparticle AA7072 in Carreau liquid form homogenized mixture which is mono nanofluid whereas nanoparticle AA7075 in Carreau liquid form homogenized mixture called hybrid nanofluid. Thermal radiation have significant impact on the temperature of AA7072 and AA7072/AA7075. The Carreau-constitutive model and correlations for thermo-physical properties are used with conservation laws for fluid and dust phases for modelling purposes. The governing equations are non-dimensionalized, and their numerical solutions are derived using the finite element method (FEM). These derived solutions are used to predict the behavior of physical quantities and flow fields for both AA7072/AA7075 and AA7072 nanoparticles. An increasing tendency in the temperature of dust particles in AA7072/AA7075 is greater than in AA7072. The simulations have exposed that AA7072/AA7075 is more radiative than AA7072. The velocity interaction parameter has an increasing tendency in affecting the transport of dust particles.

Advancing on viscosity characterization and modeling of SMC for compression molding simulation

AbstractSheet molding compounds are thermoset‐based and glass or carbon fiber reinforced composites. SMCs are transformed through compression molding and for optimizing this process, virtual compression molding tools are employed. These tools require material model calibrations based on raw material data obtained by different characterization techniques. In this research, temperature and shear rate dependent viscosity of two SMCs has been experimentally characterized by oscillatory rheometer (RPA) and extensional rheometry. The obtained results were fitted to the modified Cross‐Castro‐Macosko viscosity model. Finally, the compression molding of two validation plates was performed virtually and experimentally. The obtained results demonstrate that, testing by RPA is preferable for industrial partners because tests are run with standard equipment and no manual post‐processing of the experimental data is required. Besides, the comparison of the virtual clamping force estimation with the experimental clamping force, shows that material models calibrated with RPA‐generated data foresee a lower clamping force overestimation.

On the flow of viscoplastic fluids in non-circular tubes

Steady flow of the viscoplastic Bingham and Herschel–Bulkley (H–B)​ fluids in tubes of non-circular cross-section is investigated analytically. The solution methodology is general in scope, does not put any restrictions on the Bingham number and thus allows the mapping of the flow field for high Bingham numbers in straight tubes with non-circular axially-symmetric but otherwise arbitrary cross-sectional contours. The circular tube contour is mapped onto an arbitrary non-circular contour on which the no-slip condition is satisfied via a one-to-one and continuous mapping. Governing equations are solved for the full spectrum of axially symmetrical cross-sectional shapes and a specific example is developed for the viscoplastic H–B fluid flow in a tube with an equilateral triangular cross-section. The shape and the extent of the plug zones centered on the tube axis and the stagnant zones in the corners are predicted for both Bingham and H–B fluids. The effect of the shear rate dependent viscosity of the H–B fluids, leading to either shear-thickening or shear-thinning behavior, on the formation of the plug and stagnation zones is examined.

A tip-coupled, two-cantilever, non-resonant microsystem for direct measurement of liquid viscosity

We report a non-resonant piezoelectric microelectromechanical cantilever system for the measurement of liquid viscosity. The system consists of two PiezoMEMS cantilevers in-line, with their free ends facing each other. The system is immersed in the fluid under test for viscosity measurement. One of the cantilevers is actuated using the embedded piezoelectric thin film to oscillate at a pre-selected non-resonant frequency. The second cantilever, the passive one, starts to oscillate due to the fluid-mediated energy transfer. The relative response of the passive cantilever is used as the metric for the fluid’s kinematic viscosity. The fabricated cantilevers are tested as viscosity sensors by carrying out experiments in fluids with different viscosities. The viscometer can measure viscosity at a single frequency of choice, and hence some important considerations for frequency selection are discussed. A discussion on the energy coupling between the active and the passive cantilevers is presented. The novel PiezoMEMS viscometer architecture proposed in this work will overcome several challenges faced by state-of-the-art resonance MEMS viscometers, by enabling faster and direct measurement, straightforward calibration, and the possibility of shear rate-dependent viscosity measurement.

GPU-optimized LBM-MRT simulation of free convection and entropy generation of non-Newtonian power-law nanofluids in a porous enclosure at REV scale

The present research investigates the heat transfer and entropy generation of a non-Newtonian power-law Cu-water nanofluid in a square porous enclosure at a representative elementary volume (REV) scale using the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). The Graphics Processing Unit (GPU) accelerated the computations involved. The Brinkman-Forchheimer-extended Darcy model and the shear rate dependent power-law viscosity model were taken into account to characterise the non-Newtonian fluid flow in porous medium. Three types of model validations have been conducted, followed by the mandatory grid independence test, to demonstrate the precision and accuracy of the computational code. The numerical results were obtained by varying five key parameters namely, Darcy number (Da = 10−3, 10−2, 10−1); power-law index (n = 0.6–1.0); Rayleigh number (Ra = 104, 105, 106); porosity parameter (ϵ = 0.6); volume fraction of nanoparticles (ϕ = 0.0–0.05), and the Darcy Rayleigh number (Ram = 100, 1000). The numerically simulated outcomes were presented in terms of streamlines, isotherms, velocity, and temperature profiles as well as the Nusselt (Nu) numbers. Furthermore, a correlation among the parameters to determine the average Nu was developed using the Levenberg-Marquardt (LM) algorithm. The mathematical correlation was also subject to validations, and, in general, good correlation coefficients were obtained.

Determination of Mixing and Compaction Temperatures for the Rubberized Asphalt Binders Based on Shear Rate Dependent Viscosity

Despite the numerous advantages of using modified asphalt binders, there are a number of challenges associated with their use. One of these challenges is related with specifying the temperatures at which modified asphalt binders should be mixed and compacted. The Equiviscous method aims to calculate the Mixing and Compaction Temperatures (MCTs) of the unmodified binder. Nevertheless, the implementation of this method for modified asphalt binder results in very high MCTs, which may not be appropriate during the asphalt mixes construction. This paper investigates two alternative methods for the modified binder with Crumb Rubber (CR), referred to as the High Shear Rate (HSR) viscosity and Zero Shear Viscosity (ZSV) methods. Besides, the MCTs obtained from these methods are compared to the ones obtained using the Equiviscous method. For this purpose, one type of asphalt binder modified with three percent of CR has been used. The results have shown that the application of the ZSV method has resulted in more reasonable MCTs for the rubberized binder, which have been from 30 to 50 °C lower than the ones obtained using the Equiviscous method.

Life in complex fluids: Swimming in polymers

How do microorganisms move in fluids that contain particles and/or polymers? Such fluids often display nonlinear rheological behavior such as shear-rate dependent viscosity and viscoelasticity. The effects of such rheological behavior on the swimming behavior of microorganism at low Reynolds number are only recently being elucidated. This article highlights a few of the key developments in the field of swimming in complex fluids.

Characterization of magnetorheological fluids based on capillary magneto-rheometer

Magnetorheological fluids (MRFs) are a class of smart magnetic controlled materials whose rheological properties can be controlled by a magnetic field. These materials have advantages of short response time, high dynamic range and low energy consumption. Due to their excellent properties, MRFs have a widely application potential in the field of impact mitigation. As the shear rate dependent viscosity of MRFs is astonishing for the shear thinning effect, thus it is crucial to study the rheological properties cross a wide range of shear rates for guiding the design and application of MRFs based adaptive impact absorbers. Commercial rotational rheometers are usually used to test the rheological properties of MRFs, but their range of measuring shear rates are limited. Commercial capillary rheometers are designed to measure the rheological behavior over a wide range of shear rates, but they’re usually lack of ability to measure with magnetic field. In order to study the rheological properties of MRFs under higher shear rate and applied magnetic field, a lab-made speed-controlled capillary magneto-rheometer is developed in the presnt work; The expressions for equivalent shear rate and apparent viscosity of MRFs under the dimensional constraint of the set-up are derived. In addition, the theoretical expression of shear rate of MRFs is modified by Rabinowitsch correction. Then, the rheological properties of three particle volume fractions (10%, 15%, and 20%)of MRFs with different magnetic field strengths (6 mT, 13 mT, 20 mT, and 25 mT)are tested and analyzed, and the rheological characteristic curves of MRFs with shear rate range of 101s−1–105s−1 are obtained with the normalized characterization using Mason number. According to the experimental results, the MRFs show an obvious shear thinning phenomenon as shear rate increases, and in the Mason number based normalized characterization, the curves of different particle volume fractions are collapse to a master curve.

Nonstationary Poiseuille flow of a non-Newtonian fluid with the shear rate-dependent viscosity

Abstract A nonstationary Poiseuille flow of a non-Newtonian fluid with the shear rate dependent viscosity is considered. This problem is nonlinear and nonlocal in time and inverse to the nonlinear heat equation. The provided mathematical analysis includes the proof of the existence, uniqueness, regularity, and stability of the velocity and the pressure slope for a given flux carrier and of the exponential decay of the solution as the time variable goes to infinity for the exponentially decaying flux.

An experimental investigation on the magnetoviscous effect and shear rate-dependent viscosity of a magnetic suspension under longitudinal and transverse magnetic fields

In the present investigation, we report experimental evidence that the magnetoviscous effect of a ferrofluid can be described by a suspension of ellipsoidal particles. The studies are carried out in shear and pipe flows, and comparison with theory for non-spherical particle is made. Flows of this type appear in many applications where magnetic fluids are used as lubricants or magnetic seals. The chain-like aggregates present in the magnetic fluid are modeled as equivalent prolate spheroids. A power-law correlation accounts for the breakup of aggregates due to the shear flow. The viscosity of a real ferrofluid is measured in a parallel disk rheometer with an applied magnetic field parallel to velocity gradient and in a capillary viscometer with a field in the velocity direction. An asymptotic solution for the low Péclet number limit presents an excellent agreement with the experimental results in this regime, while the numerical results provide a good agreement up to moderate values of Péclet. In addition, the numerical results for the non-dimensional viscosity of the fluid and the magnetic increment viscosity are verified by comparing results with the experimental measurements of the same quantities for moderate values of the Péclet number. The relative importance of the mean stresslet and rotlet contributions for the non-dimensional magnetic suspension viscosity is also examined in a regime of low Péclet number. The results also were important to verify our previous theoretical work presented recently in a companion paper Sinzato and Cunha [Phys. Fluids 33, 102006 (2021)] for the regime of Pe < 1.

Computational fluid dynamics modeling of multicomponent elastomeric complex profile while flowing through extrusion die

Extrusion is one of the most efficient and widely used methods for producing long elastomeric profiles, particularly for automotive industries. These include mono-component glass run, co-extrudate, multi-component, metal-reinforced rubber, and cellular elastomeric profiles. Die swell and the interface disturbance between the fluids creates additional complexities while designing an extrusion die for elastomeric products. The extrudate deformation depends on die geometry, processing parameters, and material properties of the elastomeric compound. In this study, the 3D model having three flow channels is constructed to perform the multi-component extrusion simulation with the help of computational fluid dynamics. Three different configurations of flowing material are considered; first for all the flow channels having the same material, second for two channels having the same material, and third for all the flow channels having different materials. The extrusion simulation was performed using shear rate dependent viscosity model and temperature-dependent viscosity model to compute the extrudate deformation along with the interfaces on carbon black filled ethylene propylene diene monomer rubber (EPDM) based elastomeric compound for a multi-component elastomeric profile. Moreover, the simulated results show that the extrudate having different materials possesses lower structural stability compared to the other two extrudates. Finally, the simulation carried out with a complex-shaped multi-component elastomeric profile revealed a good agreement with the structural profile of the physical extrudate.

Determining the Molecular Weight of Polyelectrolytes Using the Rouse Scaling Theory for Salt-Free Semidilute Unentangled Solutions

Chain dynamics in the semidilute unentangled regime can be used to determine the molecular weight of polyelectrolytes based on the Rouse scaling model. Four methods enable determination of the number density of chains via measurements of correlation length (ξ) by small-angle X-ray scattering, specific viscosity (ηsp) and relaxation time (τ) by rheometry, and diffusion coefficient (D) by NMR. Five narrow dispersity cesium polystyrene sulfonate (CsPSS) solutions without salt are studied in water, anhydrous ethylene glycol, and anhydrous glycerol to test all methods. Combining viscosity and correlation length yields the weight-average molecular weight (Mw) from the Rouse model. Combining diffusion coefficient and correlation length in water provides number-average molecular weight (Mn) reliably for chains with N < 2000 repeat units. Glycerol slows relaxation dynamics, and the shear rate dependence of viscosity yields reliable τ for CsPSS with N > 100, which is governed by the product of z-average and z + 1 average molecular weight (MzMz+1) in the Rouse model. Terminal modulus G = (η – ηs)/τ via rheometry correlates with Mw/MzMz+1.

Computational Analysis of the Dynamics of Generalized-Viscoelastic-Fluid-Based Nanofluids Subject to Exothermic-Reaction in Shear-Flow

A novel problem that describes laminar simple shear-flow of generalized-viscoelastic-fluid-based nanofluids (GVFBN) containing spherical shaped nano-particles under non-isothermal conditions but with isothermal walltemperature boundary-conditions is investigated. The GVFBN model is an extension of the VFBN to include shear-rate dependent viscosity effects. The Generalized non-isothermal Giesekus constitutive model (which is reducible to generalized Oldroyd-B model) with essential modifications for thermodynamics is used to account for the viscoelastic effects. Spherical shaped nano-particles are homogeneously mixed to the viscoelastic base fluid. To characterize the shear-thinning-viscosity, a viscosity-constitutive-model of the Carreau-type is employed. A temperature-dependent thermal conductivity is also considered. Additionally, empirical models are employed to account for to the nano-particle effects on the thermal conductivity. We use an efficient, semi-implicit, numerical scheme, based on finite difference methods (FDM), to obtain the numerical solutions of the model equations. The numerical scheme is computationally implemented in MATLAB. Results are graphically presented in both a qualitative and quantitative sense with regards to the various embedded parameters. Specifically, the thermodynamic and fluid-dynamical impacts of variations in the volume fraction of nano-particles are explored. In summary, we notice enhanced thermal conductivity and hence also increased temperature with increasing nano-particle volume fraction. The GVFBN model accounts for all four nanofluid types, Generalized-Newtonian-fluid-based nanofluids (GNFBN), Newtonian-fluid-based nanofluids (NFBN), Generalized-viscoelastic-fluid-based nanofluids (GNFBN), and viscoelastic-fluid-based nanofluids (VFBN). The comparative thermal runaway susceptibility of the four nanofluid types is presented and we demonstrate that the order of susceptibility from the most to the least susceptible is GNFBN, NFBN, GVFBN, VFBN.