Small Shear Rates Research Articles

Experimental Study of Direct Shear Properties of Anisotropic Reservoir Shale

Understanding the shear mechanical properties of shale reservoirs is of great significance in the study of the formation stability around horizontal shale wells and the propagation and evolution of fractures for shale fracturing. However, the existing direct shear test results are limited due to small sample sizes and low shear rates. Based on previous experimental research results, the mechanical properties of anisotropic reservoir shale in direct shear tests with different experimental conditions were explored in this study. It was found that the shear mode, shear strain rate, and normal stress have a significant impact on the deformation and failure characteristics of shale. The peak shear displacement, peak shear strength, and shear stiffness of shale present an increasing trend of fluctuation, with an increase in the bedding angle. The peak shear strength of shale decreases with an increase in the shear strain rate, and this decrease trend descends with an increase in the shear strain rate. The shape of the shear fracture zone and the shear fracture mode of shale exhibit bedding effect characteristics. The fractal dimension of the shale shear fracture surface morphology shows a trend of fluctuation with the variation in the bedding angle. Further, the shear strain rate was found to play a dominant role in the fractal dimension of the shear fracture surface. The larger shear strain rate strengthens the bedding effect of the roughness for the shear fracture surface morphology. The results of this study provide a theoretical reference for determining the engineering geomechanics characteristics of shale reservoirs.

The Boltzmann equation for plane Couette flow

In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at y=\pm L moving relative to each other with opposite velocities (\pm \alpha L,0,0) along the x -direction. Assuming that the stationary state takes the specific form of F(y,v_{x}-\alpha y,v_{y},v_{z}) with the x -component of the molecular velocity sheared linearly along the y -direction, such steady flow is governed by a boundary value problem for a steady nonlinear Boltzmann equation driven by an external shear force under the homogeneous nonmoving diffuse reflection boundary condition. In the case of the Maxwell molecule collisions, we establish the existence of spatially inhomogeneous nonequilibrium stationary solutions to the steady problem for any small enough shear rate \alpha>0 via an elaborate perturbation approach using Caflisch’s decomposition together with Guo’s L^{\infty}\cap L^{2} theory. The result indicates a polynomial tail at large velocities for the stationary distribution. Moreover, the large time asymptotic stability of the stationary solution with exponential convergence is also obtained and as a consequence the nonnegativity of the steady profile is justified.

Entropy generation and flow characteristics of Powell Eyring fluid under effects of time sale and viscosities parameters

Shear thinning fluids are widely used in the food and polymer industries due to their unique flow characteristics. The flow behavior of these fluids has been commonly studied using the Powell Eyring model under a small shear rate assumption. However, this assumption is not always valid. In this study, we explore the transport characteristics of a Powell Eyring fluid over a variable thicker sheet, not only at small shear rates but also at medium and high shear rates. Furthermore, we calculate the rate of entropy generation based on the assumptions. Generalized Powell–Eyring model of viscosity is used for the fluid, representing the re-arrangements of molecules in the forward and backward directions through the theory of potential energy. The model concludes the sensitivity of the viscosity from zero to infinite shear rate along time sale and exponent parameters. The model is used in the transport phenomena equations. The solution of the equation is obtained by using the numerical method and used to calculate the rate of entropy generation. The results are presented in the form of velocity and temperature profiles, the average rate of entropy generation, skin friction coefficient and Nusselt number under the influence of various viscosity parameters. It is found that velocity and temperature profiles are decreased and increased respectively against the time scale parameter.

Hydrodynamic theory of p-atic liquid crystals.

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p=2) and hexatics (p=6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p>2. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any p-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates.

Underlying mechanism of shear-banding in soft glasses of charged colloidal rods with orientational domains

Soft glasses of colloidal rods (fd-virus particles) with orientational domains were recently shown to exhibit inhomogeneous flow profiles [Dhont et al., Phys. Rev. Fluids 2, 043301 (2017)]: fracture and accompanied plug flow at small shear rates, which transits to gradient shear-banding on increasing the shear rate, while a uniform flow profile develops at sufficiently high shear rates. These flow profiles coexist with Taylor-vorticity bands. The texture of such glasses under flow conditions consists of domains with varying orientations. The observed gradient shear-banding was solely attributed to the strong shear thinning behavior of the material inside the domains (henceforth abbreviated as domain-interior), without considering the texture stress that is due to interactions between the glassy domains. Here, we present new experiments on the shear-banding transition to assess the role played by the texture stress in comparison to the domain-interior stress. For a large concentration, well into the glassy state, it is found that both texture stress and domain-interior stress contribute significantly to the gradient shear-banding transition in the shear-rate region where it occurs. On the other hand, for a small concentration close to the glass-transition concentration, the domains are shown to coalesce within the shear-rate range where gradient shear-banding is observed. As a result, the texture stress diminishes and the domain-interior stress increases upon coalescence, leading to a stress plateau. Thus, a subtle interplay exists between the stresses arising from the structural order on two widely separated length scales from interactions between domains and from the rod-rod interactions within the domain-interior for both concentrations.

Thermally fluctuating, semiflexible sheets in simple shear flow.

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

Contact-mediated nucleation in melt emulsions investigated by rheo-nuclear magnetic resonance.

Increasing the efficiency of disperse phase crystallization is of great interest for melt emulsion production as the fraction of solidified droplets determines product quality and stability. Nucleation events must appear within every single one of the μm-sized droplets for solidification. Therefore, primary crystallization requires high subcooling and is, thus, time and energy consuming. Contact-mediated nucleation is a mechanism for intensifying the crystallization process. It is defined as the successful nucleation of a subcooled liquid droplet induced by contact with an already crystallized droplet. We investigated contact-mediated nucleation under shear flow conditions up to shear rates of 457 s-1 for a quantitative assessment of this mechanism. Rheo-nuclear magnetic resonance was successfully used for the time-resolved determination of the solids fraction of the dispersed phase of melt emulsions upon contact-mediated nucleation events. The measurements were carried out in a dedicated Taylor-Couette cell. The efficiency of contact-mediated nucleation decreased with increasing shear rate, whereas the effective second order kinetic constant increased approximately linearly at small shear rates and showed a linear decrease for shear rates higher than about 200 s-1 . These findings are in accordance with coalescence theory. Thus, the nucleation rate is optimal at specific flow conditions. There are limitations for successful inoculation at a low shear rate because of rare contact events and at a high shear rate due to too short contact time.

The Boltzmann Equation for Uniform Shear Flow

The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in time due to the shearing motion that induces viscous heat and the system becomes far from equilibrium. For Maxwell molecules, we establish the unique existence, regularity, shear-rate-dependent structure and non-negativity of self-similar profiles for any small shear rate. The non-negativity is justified through the large time asymptotic stability even in spatially inhomogeneous perturbation framework, and the exponential rates of convergence are also obtained with the size proportional to the second order shear rate. The analysis supports the numerical result that the self-similar profile admits an algebraic high-velocity tail that is the key difficulty to overcome in the proof.

Effect of particle dipolar interactions on the viscoelastic response of dilute ferrofluids undergoing oscillatory shear

In this work, we investigate the viscoelastic behavior of a ferrofluid undergoing an oscillatory simple shear flow and also under the influence of an external magnetic field. The main goal is to examine the influence of the dipolar interactions and formation of anisotropic structures on the macroscopic rheological response of these complex fluids. This study is performed by direct numerical simulation of neutrally buoyant, Brownian magnetic spheres in the limit of vanishingly small Reynolds numbers using Brownian dynamics. The long-range dipolar interactions are computed by the Ewald summation technique. We present the in-phase and out-of-phase rotational viscosity components as a function of the oscillatory frequency for several values of the dipolar interaction parameter and shear strain. The results show that the viscoelastic transition in the fluid is anticipated in the presence of dipolar interactions. These phenomena are probably related to the formation of complex structures in the fluid like anisotropic linear chains. In addition, a qualitative analysis of microstructure transitions during the suspension time evolution indicates the formation of long anisotropic chains for the high strength of the dipolar interaction and small shear rates. The simulation results are compared with the classical Maxwell linear viscoelastic model, and a characteristic relaxation time is identified for the investigated ferrofluid. We also offer evidence that this relaxation time has a quadratic power law scaling dependence on the dipolar interaction parameter and that the dipolar interactions are the main physical mechanics, which creates elastic response of the ferrofluid investigated here as a direct consequence of the gain of memory at the microscopic level due to the action of the magnetic torque on the particles and the formation of oriented aggregative structures like anisotropic chains.

Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces.

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a Péclet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation.

A constitutive hemorheological model addressing both the deformability and aggregation of red blood cells

Red blood cells (RBCs) in physiological conditions are capable of deforming and aggregating. However, both deformation and aggregation are seldom considered together when modeling the rheological behavior of blood. This is particularly important since each mechanism is dominant under specific conditions. To address this void, we herein propose a new model that accounts for the deformability of red blood cells, by modeling them as deformed droplets with a constant volume, and of their aggregation, by properly characterizing the network formed by red blood cells under small shear rates. To derive the model, we employ non-equilibrium thermodynamics that allows us to consistently couple the two mechanisms and guarantees model admissibility with the thermodynamic laws. Relative to our previous model, which addresses the rheological behavior of non-aggregating deformable red blood cells, one additional structural variable, λ, to properly characterize the network formed by RBCs, and another additional parameter, ε, that quantifies the relative importance between the regeneration/buildup and flow-induced breakup of the network, are considered here. The new model predicts a yield shear stress, in accord with experimental data, but also predicts non-vanishing yield normal stresses. Although no rheological measurements of yield normal stresses of blood have been reported in the literature, the recent measurement of yield normal stresses of other yield stress fluids indicates their potential existence in blood as well. We show that the new model is in complete accord with the experimental rheological behavior of normal blood in both steady-state and transient (step-change in shear-rate) simple shear.

Shear-induced ordering in liquid microjets seen by x-ray cross correlation analysis.

We applied shear to a silica nanoparticle dispersion in a microfluidic jet device and observed direction-dependent structure along and across the flow direction. The asymmetries of the diffraction patterns were evaluated by x-ray cross correlation analysis. For different Rayleigh nozzle sizes and shapes, we measured the decay of the shear-induced ordering after the cessation of the shear. At large tube sizes and small shear rates, the characteristic times of the decay become longer, but Péclet-weighted times do not scale linearly with Péclet numbers. By modeling particle distributions with the corresponding diffraction patterns and comparing measured shape asymmetry to simulations, we determined the variation of volume fraction over the azimuthal angle for the maximum ordered state in the jet.

Enskog kinetic theory of rheology for a moderately dense inertial suspension.

The Enskog kinetic theory for moderately dense inertial suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the background fluid on suspended particles is modeled via a viscous drag force plus a Langevin-like term defined in terms of the background temperature. In a previous paper [Hayakawa etal., Phys. Rev. E 96, 042903 (2017)10.1103/PhysRevE.96.042903], Grad's moment method with the aid of a linear shear-rate expansion was employed to obtain a theory which gave good agreement with the results of event-driven Langevin simulations of hard spheres for low densities and/or small shear rates. Nevertheless, the previous approach had a limitation of not being applicable to the high-shear-rate and high-density regime. Thus, in the present paper, we extend the previous work and develop Grad's theory including higher-order terms in the shear rate. This improves significantly the theoretical predictions, a quantitative agreement between theory and simulation being found in the high-density region (volume fractions smaller than or equal to 0.4).

Zero mass flux and convection boundary condition effects on Carreau-Yasuda fluid flow over a heated plat

A mathematical study is analyzed to explore the impact of zero normal flux condition on boundary layer flow of Carreau-Yasuda nanofluid flow over a heated surface. In this case the mean flow does not give the analytical solution of the Navier-Stocks, temperature, and concentration equations, hence for high Reynold's number the flow of boundary-layer can be determined by non-similarity transformations. The converted boundary-layer equations along with appropriate boundary conditions are then solved numerically. The solution of the modelled differential equations is calculated by utilizing moderate and well-known numerical technique namely BVP4C method. Carreau-Yasuda fluid model is employed to explore the characteristics of shear thinning and thickening fluids. It is generalized form of Carreau-Yasuda fluid which is applicable for having small and infinite shear rates.

Investigation of flow behaviour and lubrication capabilities of $$\hbox {MoS}_{2}$$

Flow behaviour of lubricants largely depends on their rheological properties which in turn strongly influence their lubrication capabilities and ultimately the machine life. Modern chemistry plays a great role in the synthesis of nano-additives that help in enhancing the rheological and tribological properties of the lubricants. In the present study, the rheological and tribological studies of $$\hbox {MoS}_{2}$$ nanofluids are presented in order to determine their flow behaviour and lubrication capabilities. For studying the effect of $$\hbox {MoS}_{2}$$ nanoparticles on the flow behaviour and lubrication capabilities of lubricants, two commercially available blended synthetic engine oils of SAE grades 5W-40 were selected. $$\hbox {MoS}_{2}$$ nanoparticles were synthesized by hydrothermal methods. Surface modification of the synthesized $$\hbox {MoS}_{2}$$ nanoparticles was performed before blending them with the base lubricants in 0.1, 0.15 and 0.2% concentrations. Standard ASTM and IS procedures were used to determine physicochemical properties and tribo-performance behaviour of oils, respectively. The rheological parameters of $$\hbox {MoS}_{2}$$ nanofluids were determined using a rheometer. The study reveals that tested $$\hbox {MoS}_{2}$$ nanofluids behaved as non-Newtonian lubricants with shear thinning behaviour at all tested temperatures and exhibited viscoelastic behaviour at small-shear rates. As a result of this anti-wear property showed a significant enhancement up to 20% for 0.2% $$\hbox {MoS}_{2}$$ indicating better anti-wear properties of $$\hbox {MoS}_{2}$$ nanofluids. However, a marginal reduction in friction for the tuning of 4% observed for 0.2 wt% of $$\hbox {MoS}_{2}$$ nanoparticles in the tested lubricants indicates that finished products have little scope to improve anti-friction properties under the influence of the already present additives.

Tethered Semiflexible Polymer under Large Amplitude Oscillatory Shear.

The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. For small shear rates, the tethering of the ends leads to a more-or-less linear oscillatory response. However, at high shear rates, we found a strongly nonlinear reaction, with a polymer (partially) wrapped around the fixation points. This leads to an overall shrinkage of the polymer. Dynamically, the location probability of the polymer center-of-mass position is largest on a spatial curve resembling a limaçon, although with an inhomogeneous distribution. We found shear-induced modifications of the normal-mode correlation functions, with a frequency doubling at high shear rates. Interestingly, an even-odd asymmetry for the Cartesian components of the correlation functions appears, with rather similar spectra for odd x- and even y-modes and vice versa. Overall, our simulations yielded an intriguing nonlinear behavior of tethered semiflexible polymers under oscillatory shear flow.

Assessment of the Tumbling-Snake Model against Linear and Nonlinear Rheological Data of Bidisperse Polymer Blends.

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems.

Instrumented test tube for rapid rheological behaviour of liquids estimation

For very small shear rates, many liquids are Newtonian and one of the simplest method to evaluate their viscosity is the so-called “falling-ball method”. Classically, a ball falling in a large tube, is optically observed and evaluation of its fall time enables simple deduction of the velocity, leading to shear viscosity estimation. In this communication, the tracking of a falling ball was made in a test tube with high-frequency ultrasonic sensors in transmission configuration leading to apparent shear viscosity measurement for very small shear rates (<a few s−1). With the same device, an estimation of dynamic shear viscosity in high frequency domain (5 MHz) was also obtained with the ultrasonic velocity and attenuation evaluation. Thanks to the comparison of results obtained with our adaptation of the falling ball method and with ultrasonic waves, a global rheological behaviour can be deduced very rapidly, in a simple way, on the same experimental bench, for transparent or opaque liquids.

Individual circular polyelectrolytes under shear flow

Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics.

On the effect of the thermostat in non-equilibrium molecular dynamics simulations.

The numerical investigation of the statics and dynamics of systems in non-equilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium systems can be successfully adapted to out-of-equilibrium cases. This is especially true for thermostats. Indeed, even though thermostats developed to work under equilibrium conditions sometimes display good agreement with rheology experiments, their performance rapidly degrades beyond weak dissipation and small shear rates. Here we focus on gauging the relative performances of three thermostats, Langevin, dissipative particle dynamics, and Bussi-Donadio-Parrinello under varying parameters and external conditions. We compare their effectiveness by looking at different observables and clearly demonstrate that choosing the right thermostat (and its parameters) requires a careful evaluation of, at least, temperature, density and velocity profiles. We also show that small modifications of the Langevin and DPD thermostats greatly enhance their performance in a wide range of parameters.