Rheological Equation Research Articles

Effect of synthetic C-S-H seeds on hydration process, mechanical properties and microstructure of seashell powder calcined sludge cement

Seashell powder calcined sludge cement (SCSC) is a new type of green low-carbon ternary cement prepared by using waste sludge and waste seashells. It reduces carbon emissions in the cement production industry and solves environmental problems such as serious soil-water-air pollution caused by long-term stockpiling of waste sludge and waste seashells, which are difficult to be utilized in a resourceful manner. However, the reduced clinker content results in lower early strength of SCSC, which limits the application of SCSC in applications requiring high early strength such as precast concrete specimens. In this paper, the effects of different dosage of C-S-H seeds on the hydration process, mechanical properties and microstructure of SCSC slurries were investigated. The results showed that C-S-H seeds significantly increased the 12-hour compressive strength of SCSC, and the 2 % addition of C-S-H seeds increased its compressive strength by 271 %, but had less effect on its later strength. The proportion of large pores in the sample with a 1 % addition of C-S-H seeds decreased by 1 %. At 12 hours, 2 % addition of C-S-H seeds increased its total hydration exotherm by 141 %. The addition of C-S-H seeds decreased the fluidity of the slurry but did not change the flow pattern of the slurry. The relationship between the rheological parameters of the slurry and the addition of C-S-H seeds was well fitted with a primary function, and the rheological equations of SCSC slurries with different additions of C-S-H seeds were obtained. The results of this paper can further broaden the application scenarios of SCSC and lay the foundation for the large-scale application of SCSC.

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Investigating rheological characteristics of nonlinear fluid model in an asymmetric channel: A peristaltic pumping of blood with curvature and hydrodynamic impacts

Theoretical research is investigated for the steady rheology of incompressible blood from an asymmetric (penetrable) channel in the presence of curvature and non-linear hydrodynamic impacts. The motion takes place in an asymmetric channel due to a train of sinusoidal (complex nature) waves along the channel boundaries having different phases. In this study, the Casson fluid is used as blood. The governing equations are modeled in terms of Cartesian coordinates. The impacts of non-linear curvature become significant on the transportation of biological fluid in a complex domain such as the non-pregnant uterus at a higher Reynolds number. An approximate solution of flow models is obtained to the second order in the wavenumber (giving the curvature effect). A domain transformation is used to transform the variable cross-sectional of the flow regime into the uniform cross-section. This transformation helps to find the closed-form solution of transformed rheological equations in higher order. The physical impacts of the curvature parameter, Casson parameter, phase difference, flow rate, Reynolds number, and permeability parameter on the axial velocity, pressure gradient, stress tensor, trapping phenomena, and pressure rise are investigated. The velocity of blood is smaller as it is associated with the viscous fluid. The number of boluses was reduced by increasing the Casson parameter and Reynolds number in the trapping phenomenon. The stress tensor is an increasing function of the permeability parameter and the Reynolds number. The pressure gradient is affected by the permeability parameter. The comparison between viscous fluid and blood is also addressed in the current study. The outcomes of the current study arise in the medical domains, blood study, manufacturing of nano-blood pumps, bio-physical food processing, and chemical industry.

Viscosity of Clayey Soils: Experimental Studies

Due to the high rate of the development of housing, transportation and hydraulic engineering construction in the last hundred years, the study of the phenomenon of creep of clay soils has become a subject of scientific research. In the study, experimental investigations of clay soil were conducted using a simple shear device in kinematic loading mode, aimed at examining the influence of shear rate on the viscosity coefficient of the clay soil and its strength characteristics. The tests were performed at four different shear rates and three different vertical load values. Based on the results of experimental and theoretical studies, the viscosity coefficients of clay soil were obtained, and a new rheological equation was proposed, which simultaneously takes into account the influence of Coulomb friction, structural cohesion, cohesion of water–colloidal bonds and viscous resistance of the soil. It has been shown that the shear rate has a significant impact on the viscosity coefficient of clay soil, and the viscosity coefficient itself is a variable quantity, depending both on the magnitude of the applied load and the duration of its application. The obtained results can be used for further improvement of methods for calculating the settlement of structures over time, as well as for predicting the time until the bearing capacity of foundation soils is exhausted.

Calculation of noise field in main transformer room of indoor substation based on thermal-acoustic coupling

In order to calculate the noise field distribution in the main transformer room of an indoor substation accurately, a thermal-acoustic coupling idea was introduced, and a noise field solving the algorithm based on thermal-acoustic coupling was proposed in view of the noise quality loss caused by the effect of ambient temperature changes. Firstly, the fluid-structure coupling model of the main transformer room is established, and the computational fluid dynamics method is used to calculate the flow field distribution and temperature boundary conditions under the action of the heat source; Then, extracting the rheological equation of the environmental boundary conditions in the flow field calculation, and use the difference function to couple the rheological equation to the sound grid to obtain the sound field coupling model under the condition of variable temperature; Finally, the modified parameter acoustic integral equation under the sound field coupling model is calculated based on the conventional Gauss numerical integration method, and the sound field of the main transformer room considering the effect of variable temperature is obtained. The algorithm has been successfully applied in the analysis of the noise field of Xi'an 110 kV Zhenxing Substation, and the error with the measured value is 2.083%.

Non-linear electro-rheological model of a membrane immersed in Tanner-Power law fluids applied to outer hair cells: Shear-thinning mechanisms

Flexoelectric actuation employs an applied electric field to induce membrane curvature, which is the mechanism utilized by the outer hair cells (OHC) present in the inner ear. The model developed for this study, representing the OHC, integrates two key components: (i) an approximation of the flexoelectric membrane shape equation for circular membranes attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting liquid viscoelastic phases characterized by the Tanner-Power law rheological equation of state. A second-order non-linear differential equation for average curvature has been derived, and a robust numerical method has been programmed. This model simplifies to a linear model used previously. The main challenge involves identifying and describing the enhancement in curvature change rate. It was observed that low symmetry, low viscosity, and soft membrane and shear-thickening behavior of the phases enhance the curvature change rate. Additionally, there exists a critical electric field frequency value that maximizes the curvature change rate (resonance effect). The current theory, model, and computational simulations add to the ongoing development comprehension of how biological membrane shape actuation through electromechanical couplings.

RHEOLOGY OF STRUCTURED LIQUIDS. ADDICTION DYNAMIC MOD-ULES FROM STRAIN AMPLITUDE

A new interpretation is proposed for the dependence of dynamic moduli on the deformation amplitude during shear vibrations occurring at a xed vibration frequency. It is based on a structural rheological model, which includes the kinetic equations for the formation and destruction of particle aggregates under the action of an oscillating shear flow. Rheological equations have been obtained that are able to approximate rheological curves in separate sections with different amplitudes of shear deformation. The possibilities of the new rheological model are shown on the example of two polymer systems filled with solid particles.

Scraper factors investigation on Al2O3 paste flow based on marine predators algorithm-bidirectional gated recurrent unit pseudo-lattice Boltzmann method for stereolithography molding

The coating process is an essential part of stereolithography technology to mold alumina paste, achieved using a scraper. The characteristics of the scraper (geometry and roughness) are investigated to discover the potential influence mechanism on the coating process. To complete the analysis, the bidirectional gated recurrent unit (BiGRU) optimized by the marine predator algorithm (MPA) is proposed to provide a predicted model for the rheological data instead of the traditional fitting by using the known rheological equations. Then, a pseudo-lattice Boltzmann (pseudo-LB) method is proposed to conduct the coating flow simulation without a specific rheological equation, where the predicted rheological model is applied to obtain the relaxation time for each iteration. Based on the above MPA-BiGRU pseudo-LB method, three geometries and different roughnesses are explored for the coating process. The results indicate that the rectangle geometry suits the large coating speed, and the trapezium geometry is recommended for conditions with the small coating speed. The roughness significantly affects the coating process with the rectangle geometry, and the smoother scraper generates a minor disturbance. However, it is almost ineffective in the cases with trapezium geometry.

Разрешимость одномерной задачи движения жидкости в пороупругой среде с проницаемыми границами

The initial-boundary value problem of a one-dimensional viscous fluid flow in a deformable viscous porous medium with permeable boundaries is considered. The governing equations are the equations of mass conservation for each phase, the equation of momentum conservation for a liquid phase in terms of Darcy’s law, the equation of momentum conservation for the whole system, and the rheological equation for porosity. The original system of equations in the Lagrange variables is reduced to a third-order equation for the porosity function. The first part of this paper presents the formulation of the problem, the definition of the classical solution to the considered problem, and the existence and uniqueness theorem for the problem of Hölder classes. In the second part of this paper, the local theorem of existence and uniqueness for the problem of Hölder classes is proved for an incompressible fluid using the Tikhonov-Schauder fixed-point theorem. The physical principle of the maximum porosity function is determined.

Циклические испытания вязкоупругих высокоэластичных материалов по программе «Вложенных циклов»

Experimental studies of the viscoelastic properties of elastomeric nanocomposites based on styrene-butadiene rubber and binary filler (carbon black and detonation nanodiamonds) were carried out. In order to most effectively identify the features of the viscoelastic behavior of these materials (which depend not only on the deformation but also on its rate), we used a special test program with ‘nested cycles’ developed at the Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences. During testing, the sample is subjected to uniaxial cyclic loading with the amplitude and rate of deformation decreasing at each step. At the beginning and end of the cycle (i.e., at minimum and maximum cyclic deformations), the grips of the tensile testing machine are stopped for a fixed period of time to measure relaxation dependences. Such an approach allows obtaining the maximum amount of information about both viscous and elastic properties of the tested material in one experiment. The mass content of nanodiamond particles in all samples was the same (7 parts by mass), the proportion of carbon black varied (23, 33 and 43 parts by mass). The equilibrium stress-strain curves (which are very important for theorists for constructing the governing rheological equations) were calculated based on experimental relaxation dependences (stress versus time). An analysis of stress-strain loading curves made it possible to obtain concentration dependences of mechanical characteristics such as maximum and minimum cyclic stresses, initial, minimum and maximum moduli for the first loading curve (elastic properties), hysteresis of cyclic losses (viscous properties at different loading rates). The Mullins softening effect (a drop in elastomer stiffness after the first loading cycle) was also studied.

Study of the electroosmotic flow of a structured fluid with a new generalized rheological model

The electroosmotic flow of a viscoelastic fluid in a capillary system was investigated analytically. The rheology of the fluid was characterized by a novel generalized exponential model equation. The charge density obeys the Boltzmann distribution, which governs the electrical double-layer field and body force generated by the applied electrical field. Mathematically, this scenario can be modeled by the Poisson-Boltzmann partial differential equation, by assuming that the zeta potential is small, i.e., less than 25 mV (Debye-Hückel approximation). Considering a pulsating electric field, the shear viscosity and the alteration in the volumetric flow were presented as a function of the material parameters through the characteristic dimensionless numbers by using an exponential-type generalized rheological model. Thixotropy, shear thinning, yield stress mechanisms, and weight concentration were analyzed through numerical results. Finally, the flow properties and rheology were predicted using experimental data reported elsewhere for worm-like micellar solution of cetyl trimethyl ammonium tosilate (CTAT). The rheological equation of state proposed in this study describes the alterations in the structure resulting from applied forces (tangential and normal). These forces induced a structural evolution (kinetic model) due to the relaxation processes caused by shear strain. It is important to mention that in electroosmotic flows, complex behavior such as (i) thixotropy, (ii) rheopexy, and (iii) shear banding flow is scarcely explained in terms of the change in the structure of the fluid under flow.Graphical

Peristaltic rheology and thermal analysis of SWCNT-MWCNT/H2O hybrid nanofluid in a complex microchannel under electroosmotic effects

The primary goal of this research is to investigate the rheology and heat transport of a hybrid nanofluid in an asymmetric microchannel in the presence of an electric field. The mobility of hybrid fluid is caused by peristaltic waves that contract and relax sinusoidally along the channel length. The rheological equations system is simplified by introducing relevant similarity variables, which are then solved using the integration approach. In this study, convective boundary conditions are applied. The electric potential function, velocity profile, pressure gradient, stream function, and temperature profile are all mathematically expressed. The current study’s findings are based on three physiological estimates: first is known as the creeping phenomenon, second as the greater wavelength condition, and third as the Debye–Hückel linearization (DHL). Using two different nanoparticles (SWCNT-MWCNT), the peristaltic mechanism is used to model water-based nanofluids. The three-dimensional graphs of rheological features are generated using Mathematica Software to elaborate the influences of relevant parameters on the rheological characteristics. By enhancing both the Biot number and the heat source/sink parameter in the hybrid fluid, the magnitudes of the temperature profile and the Nusselt number are higher than in the [Formula: see text] nanofluids. The magnitude of velocity profile is enhanced by increasing the Buoyancy forces and slip velocity. The results of simple fluid are obtained in the absence of concentration parameter. To boost the pumping phenomena, the special nature of peristaltic waves is used. The comparative study of nanofluid and hybrid fluid is also addressed. Three-dimensional graphs are plotted to clearly observe the influence of rheological parameters on flow features.

Rheological properties and color indexes of ultrasonic treated aqueous solutions of basil, Lallemantia, and wild sage gums

This research aimed to analyze the impacts of sonication on the rheological properties and color indexes of aqueous solutions of Basil seed gum (BSG), Lallemantia seed gum (LSG), and Wild sage seed gum (WSG). The apparent viscosity (AV) of aqueous solutions of gums decreased with increasing shear rate (SR) from 12.2 s−1 to 134.5 s−1. Also, the AV (at SR = 61 s−1) of BSG, LSG, and WSG solutions reduced from 0.015 to 0.006 Pa.s, 0.023 to 0.010 Pa.s, and 0.009 to 0.004 Pa.s with enhancing the sonication time from 0 to 20 min, respectively. Various rheological equations were employed to fit the empirical values, and the findings confirmed that the Power law (PL) model was the best fit to explain the flow behaviour of these gums solutions. The consistency coefficient (k-index) of BSG, LSG, and WSG solutions significantly (p < 0.05) reduced from 0.108 to 0.017 Pa.sn, 0.143 to 0.033 Pa.sn, and 0.034 to 0.014 Pa.sn with increasing sonication time from 0 to 20 min, respectively. The flow behaviour index (n-index) of the gums solutions increased with increasing sonication time. By applying ultrasound, the lightness (L⁎) and blueness/yellowness (b⁎) indexes of the solutions were increased, and the greenness/redness (a⁎) index was reduced.

Infiltration Grouting Mechanism of Bingham Fluids in Porous Media with Different Particle Size Distributions

Although permeation grouting technology has been widely used in engineering practice, there has not been sufficient research on how the distribution of pore sizes in porous media affects the diffusion of grout. In this study, based on the fractal theory of porous media and the Bingham fluid rheological equation, a Bingham fluid permeation grouting mechanism considering the distribution of pore sizes in porous media is proposed. The mechanism is validated through laboratory experiments and numerical simulations using COMSOL 6.0. During the experiments, parallel electrical resistance imaging is employed to monitor the diffusion range of the grout. Furthermore, the effects of grouting pressure, porosity, and water–cement ratio on the diffusion radius of the grout are analyzed. The results show that the Bingham fluid grout diffuses in a semi-spherical shape in the gravel. Additionally, parallel electrical resistance imaging can analyze the diffusion range of the grout in the gravel. The diffusion radius of the Bingham fluid grout in the gravel is smaller than the diffusion radius obtained by considering the particle size distribution theory, with an average difference of 31.8%. Compared to the diffusion radius obtained without considering the particle size distribution theory, the diffusion radius obtained by considering the distribution of pore sizes is closer to the experimental results. The numerically simulated program, which was developed for this study, can effectively simulate the diffusion law of the Bingham fluid in the gravel. So far, the Bingham fluid seepage grouting model considering the different particle size distribution of porous media has been built. The findings of this study can provide theoretical support and technical reference for practical grouting projects.

Matematyczne modele hydromechaniki przepływu wielofazowego o zmiennej masie

The paper discusses the mathematical model of hydromechanics of multiphase flows with varying mass. A multiphase flow is considered a continuum consisting of a set of a large number of different groups of particles. The derivation of motion equations and similarity criteria are given taking into account both the externally attached (or detached) mass and phase transitions within the medium. The equations of mass, momentum and energy transfer for individual phases and the medium as a whole are derived based on fundamental conservation laws. It was demonstrated that in the absence of sources (or flow-offs) of mass, momentum and energy, the known equations of single- and multi-phase flow hydromechanics follow as a special case from the obtained systems of motion equations and similarity criteria. The obtained motion equations are valid for the description of an ingredient of mixture and the medium as a whole, regardless of their physical and mechanical properties. Thermodynamic and rheological state equations, as well as expressions for heat flow, interfacial mass forces phase transitions, and heat exchange between phases can be used to close them. The implemented models make it possible to simulate both the stationary distribution of parameters along the wellbore during production and non-stationary processes that occur, for example, when the pump shaft speed changes during oil production. The developed approaches were implemented in the DataFlow software tool for analysis of the hydrodynamics of multiphase hydrocarbon flows, taking into account heat exchange with the rocks surrounding the well, and phase transitions in the fluid. Using the software package, test calculations were carried out to demonstrate the performance of the proposed and implemented models.

Nonlinear effects at the deformation of amorphous polymers in warm and frozen states

One of the important problems of the modern rheology of polymer materials, namely, the possibility of describing the deformation of amorphous polymers within the framework of linear rheological relationships between relative deformation and deforming stress or the need to use nonlinear rheological equations is considered. The criteria for distinguishing these approaches, namely, the determination of the corresponding critical values of the macro- and microphysical characteristics of the material and the conditions for carrying out the mechanical tests are also discussed. In particular, the difference between the influence of kinetic and thermodynamic nonlinear effects on the regularities of deformation processes of amorphous polymers in warm and frozen states was noted. The influence of nonlinear effects on the general shape and characteristics of individual stages of the “relative strain - deforming stress” diagram at deformation of polymer samples with specified values of strain rate and temperature is analyzed in detail. The results of the theoretical analysis were used for the physical interpretation of the general form and features of individual stages of the tensile test diagrams of amorphous polyimide films (V. D. Natsik, H. V. Rusakova, S. V. Lubenets, V. A. Lototskaya, and L. F. Yakovenko, Fiz. Nyzk. Temp. 49, 569 (2023) [Low Temp. Phys. 49, 521 (2023)]), empirical estimates for the rheological characteristics of this polymer were obtained.

Rheological properties of carboxymethyl cellulose (CMC) solution: Impact of high intensity ultrasound

Today sonication process is used as a new green tool with unique impacts on foods preservation and processing. Ultrasonic modification is an appropriate strategy to obtain good gums with useful physicochemical characteristics and molecular structure. This research aimed to analyze the impacts of sonication at different intensities (0, 75, and 150 W) and time (0, 5, 10, 15, and 20 min) on the viscosity and rheological characteristics of carboxymethyl cellulose (CMC) solution. The results confirmed that the apparent viscosity of CMC solution reduced from 0.030 to 0.021 Pa.s with increasing shear-rate from 12.2 s−1 to 134.5 s−1 (75 W for 10 min). Also, the apparent viscosity of CMC solution reduced from 0.028 to 0.019 Pa.s with enhancing the sonication time from 0 to 20 min (shear-rate = 61 s−1, 150 W). Various rheological equations were employed to fit the empirical values, and the results confirmed that the Power law model was the best fit to explain the flow behaviour of CMC solution. The consistency coefficient of CMC solution significantly reduced from 0.065 Pa.sn to 0.032 Pa.sn (p < 0.05) with enhancing sonication time from 0 to 20 min (75 W). Furthermore, the consistency coefficient of CMC solution decreased significantly (p < 0.05) while the ultrasonic power enhanced. Flow behaviour index of CMC solution enhanced significantly (p < 0.05) while the intensity and time of sonication enhanced.

60 years of the Kaye–Bernstein, Kearsley, Zapas rheological constitutive law for polymers

The K–BKZ (Kaye–Bernstein, Kearsley, Zapas) rheological constitutive model is now 60 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experimental evidence in polymer melt flow, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction, an historical perspective is given on developments in the last 60 years of the K–BKZ model. Then, a section on mathematical modeling of polymer flows follows, including the governing equations of flow, the rheological constitutive equations (with emphasis on the viscoelastic integral constitutive equations of the K–BKZ type), dimensionless numbers controlling the flow, and relevant boundary conditions. The “Method of Solution” section reviews the major developments of numerical techniques for particle tracking and integral evaluation for the viscoelastic stresses. Finally, selected examples of successful application of the K–BKZ model in polymer flows are presented including considerations of wall slip and non-isothermal flows.

Non-Newtonian Flow of Hydrolyzed Polyacrylamide Solution

Structural rheological model is used to describe the rheological behavior of hydrolyzed polyacrylamide aqueous solutions. The change in viscosity during stationary flow is explained by structure change of the polymer solution associated with contacts between macromolecules. Flow curves are well approximated by the generalized flow equation, except for the region of high shear rates, where the phenomenon of shear thickening is observed. The behavior of the rheological equation coefficients with a change in the polymer concentration is consistent with the conclusions of the structural rheological model.

Ultra-slow transverse waves during continental breakup

Continental rifting is one of the four fundamental geological processes of the Wilson cycle. Rifting results from the continuous stretching of continental lithosphere and involves mechanical, thermodynamic, and rheological processes. It may be followed by a catastrophic breakup stage, which determines cessation of extensional deformation and the final separation of a continent into two distinct tectonic plates that grow by accretion of oceanic lithosphere. To date, the transition to sea−floor spreading and the conditions for the development of a new ocean have not been fully understood. We propose that a consistent description of this process must consider the existence of long−term retarded elasticity in the mantle lithosphere, the superadiabatic conditions of this layer, and the combined action of such elastic forces with the localized buoyancy arising from thermal anomalies. We present a solution of the rheological equation for a nonlinear viscoelastic model of the lithosphere mantle and numerical experiments showing that transient thermal anomalies are generated during the extension, which lead to the formation of transverse waves having wavelengths of the order of hundreds to thousands km and periods of several tens kyrs. These waves induce oscillating topography and influence the relief. Therefore, they could be responsible for eustatic cycles both in the axial rift lacustrine system and in off−axis (dendritic) lakes placed in areas of reversed drainage. At sufficiently high extension rates, deformation localizes and these ultra-slow waves determine cyclic shear failure, with formation of X−shaped cross structures through the lithosphere that prelude to the final rupture.