Shear Rate Gradient Research Articles

Tumor Metastasis in the Microcirculation.

Tumor cell metastasis through blood circulation is a complex process and is one of the great challenges in cancer research as metastatic spread is responsible for ∼90% of cancer-related mortality. Tumor cell intravasation into, arrest and adhesion at, and extravasation from the microvessel walls are critical steps in metastatic spread. Understanding these steps may lead to new therapeutic concepts for tumor metastasis. Vascular endothelium forming the microvessel wall and the glycocalyx layer at its surface are the principal barriers to and regulators of the material exchange between circulating blood and body tissues. The cleft between adjacent endothelial cells is the principal pathway for water and solute transport through the microvessel wall in health. Recently, this cleft has been found to be the location for tumor cell adhesion and extravasation. The blood-flow-induced hydrodynamic factors such as shear rates and stresses, shear rate and stress gradients, as well as vorticities, especially at the branches and turns of microvasculatures, also play important roles in tumor cell arrest and adhesion. This chapter therefore reports the current advances from in vivo animal studies and in vitro culture cell studies to demonstrate how the endothelial integrity or microvascular permeability, hydrodynamic factors, microvascular geometry, cell adhesion molecules, and surrounding extracellular matrix affect critical steps of tumor metastasis in the microcirculation.

Влияние внешних электромагнитных полей на значение градиента скорости сдвига слоев магнитореологической рабочей среды

The importance of improving machine drives requires constant development of alternative drive technologies which include magnetorheological, magnetodynamic and magneto-liquid technologies. In the recent years, magnetorheological, magnetodynamic, and magneto-liquid devices have proved to be effective; therefore their further development is considered relevant. Combined magnetorheological drives are promising innovation in drive systems. Such drive systems control the flow of magnetorheological working medium by changing its viscosity and generating rheological effects. It is obvious that in combined magnetorheological systems there is additional external shear force in working fluids. This requires revision of the main theoretical approaches to estimating the viscosity of the working medium in combined magnetorheological systems. When calculating and modeling combined or regular magnetorheological systems, it is important to estimate the viscosity characteristics of the working medium and forecast its possible rheological anomalies. The article describes a method for modeling the viscosity properties of magnetorheological working medium. A distinctive feature of the proposed method is that it allows us to take into account the effect of external electromagnetic fields on the shear rate gradient of magnetorheological liquid layers. The paper presents the results of numerical modeling obtained with the Matlab application package. The results of the computer experiment show that the proposed method can assess the effect of external electromagnetic fields on the shear rate gradient of layers under shear stresses and the electromagnetic component. This makes it possible to determine the probability of development of viscoplastic, pseudoplastic, and dilatant properties in the magnetorheological working medium and of appearance of rheological effects which are characteristic of magnetorheological working media.

Modeling a flow pattern of the granular fill in the cross section of a rotating chamber

The efficiency of working processes of machines of the drum type is determined by the mode of flow of the fill in a rotating chamber. But the numerical and experimental results obtained over a recent period approach the actual behavior of the examined medium only in terms of qualitative characteristics. A mathematical model is built for a three-phase flow mode of granular fill in the cross section of a cylindrical chamber that rotates around the horizontal axis. The analytical-experimental research method is applied. A calculation algorithm is derived that approximately establishes position of the flow regions and the distribution of velocities in the cross sections normal to the flow direction, depending on the kinematic, geometrical, inertial, and rheological parameters of the system. Based on the performed modeling, the effect of rotation velocity of the chamber on the characteristics of a three-phase flow mode of the fill was determined. We established conditions when mass fractions of the active sliding layer and the region of a non-free fall reach maximal values, while mass fraction of the passive quasi-solid-body region acquires a minimum value. The conditions are determined when thickness and mean velocity of the sliding layer reach a maximum. We revealed a predominant reduction in thickness, in the average velocity and the shear rate gradient in the normal cross section along the length of the layer. A decrease in the thickness and an increase in the average velocity and the gradient of shear rate of the sliding layer were registered with a decrease in the relative size of the chamber granular fill’s element. Visualization of flow patterns confirmed a convergence of the calculation results and experimental data within a range of 11–13 %

Numerical investigation of entropy generation to predict irreversibilities in nanofluid flow within a microchannel: Effects of Brownian diffusion, shear rate and viscosity gradient

In the present contribution, irreversibilities caused by heat transfer and friction for the water-TiO2 nanofluid flow in a circular microchannel are investigated by evaluating entropy generation rates. The effects of viscosity gradient, non-uniform shear rate and Brownian diffusion on particle migration are taken into account in order to examine the effect of nanoparticle arrangement on entropy generation rates. The results show that nanoparticle migration alters concentration distribution and consequently, changes entropy generation rates. Nanoparticle migration increases concentration of the particles in central regions, and this migration is more noticeable for higher mean concentrations and larger particles. Thermal entropy generation rate intensifies with increasing wall heat flux and particle size while decreases with increasing concentration. Frictional entropy generation rate increases by concentration increment and decreases by particles enlargement, while it changes trivially by increasing wall heat flux. Frictional entropy generation rate is larger than thermal entropy generation rate in the microchannel under study and therefore, total entropy generation mostly stems from friction. Thus, total entropy generation rate decreases by particles enlargement, which is a positive result according to second law of thermodynamics. Eventually, a model for entropy generation rates is developed using the numerical data by means of Artificial Neural Network (ANN).

Simulation of size segregation in granular flow with material point method

Segregation is common in granular flows consisting of mixtures of particles differing in size or density. In gravity-driven flows, both gradients in total pressure (induced by gravity) and gradients in velocity fluctuation fields (often associated with shear rate gradients) work together to govern the evolution of segregation. Since the local shear rate and velocity fluctuations are dependent on the local concentration of the components, understanding the co-evolution of segregation and flow is critical for understanding and predicting flows where there can be a variety of particle sizes and densities, such as in nature and industry. Kinetic theory has proven to be a robust framework for predicting this simultaneous evolution but has a limit in its applicability to dense systems where collisions are highly correlated. In this paper, we introduce a model that captures the coevolution of these evolving dynamics for high density gravity driven granular mixtures. For the segregation dynamics we use a recently developed mixture theory (Fan & Hill 2011, New J. Phys; Hill & Tan 2014, J. Fluid Mech.) which captures the combined effects of gravity and fluctuation fields on segregation evolution in high density granular flows. For the mixture flow dynamics, we use a recently proposed viscous-elastic-plastic constitutive model, which can describe the multi-state behaviors of granular materials, i.e. the granular solid, granular liquid and granular gas mechanical states (Fei et al. 2016, Powder Technol.). The platform we use for implementing this model is a modified Material Point Method (MPM), and we use discrete element method simulations of gravity-driven flow in an inclined channel to demonstrate that this new MPM model can predict the final segregation distribution as well as flow velocity profile well. We then discuss ongoing work where we are using this platform to test the effectiveness of particular segregation models under different boundary conditions.

Fabrication of circular microfluidic channels through grayscale dual-projection lithography

Circular microfluidic channels are in great demand since they are more realistic in mimicking physiological flow systems, generating axis-symmetrical flow, and achieving uniform shear stress. A typical microchannel with rectangular cross section can induce non-physiological gradients of shear rate, pressure, and velocity. This paper presents a novel method of fabricating microfluidic channels with circular and elliptical cross sections through grayscale dual-projection lithography. Our method utilizes two projecting systems to expose grayscale image face-to-face and simultaneously polymerize the photocurable material. The cross-sectional profiles of the fabricated microchannels are consistent with mathematical predictions and, therefore, demonstrate the capability of controlling the channel shapes precisely. Customized circular microchannels can be generated with complex features such as junctions, bifurcations, hierarchies, and gradually changed diameters. This method is capable of fabricating circular channels with a wide range of diameters (39 μm–2 mm) as well as elliptical channels with a major-to-minor axis ratio up to 600%. Microfluidic devices with circular cross sections suitable for particle analysis were made as a demonstrative application in nanoparticle binding and distribution within a mimetic blood vessel. A ready-to-use microfluidic device with customized circular channels can be fabricated within 1 h without the need of clean room or expensive photolithography devices.

Impact of thermophoresis on nanoparticle distribution in nanofluids

This research attempts to study the effects of particle migration on concentration distribution of the water-TiO2 nanofluid inside a circular tube. The scale analysis shows that thermophoresis can have an essential role on particle migration and consequently, on concentration distribution. Therefore, the concentration distribution of particles is obtained by considering the effects of thermophoresis, non-uniform shear rate, Brownian diffusion, and viscosity gradient. The results reveal that as the particles become larger, the concentration distribution becomes more non-uniform. Meanwhile, thermophoresis intensifies non-uniformity of concentration distribution and its effect is more noticeable at higher mean concentrations.

Dynamics of blood flow and thrombus formation in a multi-bypass microfluidic ladder network.

The reaction dynamics of a complex mixture of cells and proteins, such as blood, in branched circulatory networks within the human microvasculature or extravascular therapeutic devices such as extracorporeal oxygenation machine (ECMO) remains ill-defined. In this report we utilize a multi-bypass microfluidics ladder network design with dimensions mimicking venules to study patterns of blood platelet aggregation and fibrin formation under complex shear. Complex blood fluid dynamics within multi-bypass networks under flow were modeled using COMSOL. Red blood cells and platelets were assumed to be non-interacting spherical particles transported by the bulk fluid flow, and convection of the activated coagulation factor II, thrombin, was assumed to be governed by mass transfer. This model served as the basis for predicting formation of local shear rate gradients, stagnation points and recirculation zones as dictated by the bypass geometry. Based on the insights from these models, we were able to predict the patterns of blood clot formation at specific locations in the device. Our experimental data was then used to adjust the model to account for the dynamical presence of thrombus formation in the biorheology of blood flow. The model predictions were then compared to results from experiments using recalcified whole human blood. Microfluidic devices were coated with the extracellular matrix protein, fibrillar collagen, and the initiator of the extrinsic pathway of coagulation, tissue factor. Blood was perfused through the devices at a flow rate of 2 µL/min, translating to physiologically relevant initial shear rates of 300 and 700 s-1 for main channels and bypasses, respectively. Using fluorescent and light microscopy, we observed distinct flow and thrombus formation patterns near channel intersections at bypass points, within recirculation zones and at stagnation points. Findings from this proof-of-principle ladder network model suggest a specific correlation between microvascular geometry and thrombus formation dynamics under shear. This model holds potential for use as an integrative approach to identify regions susceptible to intravascular thrombus formation within the microvasculature as well as extravascular devices such as ECMO.

Dynamic viscosity study of barley malt and chicory concentrates

The purpose of research is to find optimal conditions for dispersing and subsequent dehydration of liquid food environments in the nozzle spray drying chamber through the study of dynamic changes in viscosity according to temperature, velocities gradients and dry residue content. The objects of study were roasted chicory and malt barley concentrates with dry residue content of 20, 40, 60 and 80%. Research of dynamic viscosity were carried out at the measuring complex based on the rotational viscometer Rheotest II, analog-to-digital converter, module Laurent and a personal computer with a unique software that allows to record in real time (not only on a tape recorder, but also in the form of graphic files) the behavior of the viscosity characteristics of concentrates. Registration of changes of dynamic viscosity was carried out at a shear rate gradient from 1,0 с -1 to 27,0 с -1 and the products temperature thermostating : 35, 55, 75˚ C. The research results are presented in the form of graphic dependences of effective viscosity on shear rate and flow curves (dependencies of shear stresses on the velocity gradient), which defined flow regimes, the optimal modes of dispersion concentrates into spray dryer chambers in obtaining of powdered semi-finished products and instanting were found: dry residue content - 40 %, concentrate temperature - 75 ˚C, velocity gradient in the air channel of the nozzle at least 20 c-1

Dynamic viscosity study of barley malt and chicory concentrates

The purpose of research is to find optimal conditions for dispersing and subsequent dehydration of liquid food environments in the nozzle spray drying chamber through the study of dynamic changes in viscosity according to temperature, velocities gradients and dry residue content. The objects of study were roasted chicory and malt barley concentrates with dry residue content of 20, 40, 60 and 80%. Research of dynamic viscosity were carried out at the measuring complex based on the rotational viscometer Rheotest II, analog-to-digital converter, module Laurent and a personal computer with a unique software that allows to record in real time (not only on a tape recorder, but also in the form of graphic files) the behavior of the viscosity characteristics of concentrates. Registration of changes of dynamic viscosity was carried out at a shear rate gradient from 1,0 с -1 to 27,0 с -1 and the products temperature thermostating : 35, 55, 75˚ C. The research results are presented in the form of graphic dependences of effective viscosity on shear rate and flow curves (dependencies of shear stresses on the velocity gradient), which defined flow regimes, the optimal modes of dispersion concentrates into spray dryer chambers in obtaining of powdered semi-finished products and instanting were found: dry residue content - 40 %, concentrate temperature - 75 ˚C, velocity gradient in the air channel of the nozzle at least 20 c-1

A modified lattice Bhatnagar–Gross–Krook model for convection heat transfer in porous media

The lattice Bhatnagar–Gross–Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability at low fluid viscosity and effective thermal diffusivity. In this paper, a modified LBGK model, which incorporates the shear rate and temperature gradient in the equilibrium distribution functions, is developed for incompressible thermal flows in porous media at the representative elementary volume scale. With two additional parameters, the relaxation times in the collision process can be fixed at a proper value invariable to the viscosity and the effective thermal diffusivity. In addition, by constructing a modified equilibrium distribution function and a source term in the evolution equation of temperature field, the present model can recover the macroscopic equations correctly through the Chapman–Enskog analysis, which is another key point different from previous LBGK models. Several benchmark problems are simulated to validate the present model with the local computing scheme for the shear rate and temperature gradient, and the numerical results agree well with analytical solutions and/or those well-documented data in previous studies. It is also shown that the present model and the computational schemes for the gradient operators have a second-order accuracy in space, and better numerical stability of the present modified LBGK model than previous LBGK models is demonstrated.

Shear-induced segregation of particles by material density.

Recently, shear rate gradients and associated gradients in velocity fluctuations (e.g., granular temperatures or kinetic stresses) have been shown to drive segregation of different-sized particles in a manner that reverses at relatively high solids fractions (〈f〉>0.50). Here we investigate these effects in mixtures of particles differing in material density through computational and theoretical studies of particles sheared in a vertical chute where we vary the solids fraction from 〈f〉=0.2 to 0.6. We find that in sparse flows, 〈f〉=0.2 to 0.4, the heavier (denser) particles segregate to lower shear rates similarly to the heavier (larger) particles in mixtures of particles differing only in size. However, there is no segregation reversal at high f in mixtures of particles differing in density. At all solids fractions, heavier (denser) particles segregate to regions of lower shear rates and lower granular temperatures, in contrast with segregation of different-sized particles at high f, where the heavier (larger) particles segregate to the region of higher shear rates. Kinetic theory predicts well the segregation for both types of systems at low f but breaks down at higher f's. Our recently proposed mixture theory for high f granular mixtures captures the segregation trends well via the independent partitioning of kinetic and contact stresses between the two species. In light of these results, we discuss possible directions forward for a model framework that encompasses segregation effects more broadly in these systems.

Effect of particle migration on flow and heat transfer characteristics of magnetic nanoparticle suspensions

Flow and heat transfer characteristics of the suspensions containing Fe3O4 magnetic nanoparticles have been evaluated in turbulent flow regime. The effects of particle migration which lead to non-uniform concentration distribution have been considered in the simulation. For this purpose, the effects of Brownian motion, shear rate and viscosity gradient have been taken into account on diffusion of the particles. By applying the effects of particle migration, the amount of concentration at the wall vicinity will be lower than that at the tube center. Non-uniformity of the concentration distribution is more significant for the coarser particles. Meanwhile, this non-uniformity intensifies by increasing mean concentration and Reynolds number. Thermophysical properties of the suspension also demonstrate a non-uniform distribution. Nusselt number increases by raising the Reynolds number and mean concentration. The effect of concentration on Nusselt number reduces at higher Reynolds numbers. The increase of the concentration will raise the friction coefficient, which has an almost similar trend at various Reynolds numbers. The results obtained are properly consistent with the experimental results.

Rheological behavior of an Algerian crude oil containing Sodium Dodecyl Benzene Sulfonate (SDBS) as a surfactant: Flow test and study in dynamic mode

Abstract In order to improve the flow characteristics, this work aims to study the rheological behavior of the oil crude (coming from the oil field of Tin Fouye Tabankort/South Algeria) with and without additive friction reducing. An experimental study was performed by measuring the rheological characteristics by flow tests and dynamic mode (oscillation) at different temperatures (20 °C, 30 °C and 50 °C) using the rheometer AR2000. The temperature of the crude oil varies between these extreme values in the south of Algeria. For this, the effect of the shear rate, the temperature and the additive concentration of Sodium Dodecyl Benzene Sulfonate (SDBS) on the rheological parameters have been studied. The obtained results show that the crude oil exhibits a non-Newtonian behavior at a low shear rate which can be described by the Herschel–Bulkley model. It was also noted that the Newtonian behavior occurs at high values of the gradient of shear rate. The viscoelasticity character of the crude oil by identifying of the elastic modulus (G′) and the viscous modulus (G″), has indicated that the rheological properties of crude oil were significantly influenced by the additive.

Studying nanoparticle distribution in nanofluids considering the effective factors on particle migration and determination of phenomenological constants by Eulerian–Lagrangian simulation

In this study, concentration distribution was obtained for nanofluid laminar flow in circular pipe. The effects of viscosity gradient, shear rate and Brownian diffusion on particle migration were considered. One needs to determine the phenomenological constants in order to find the diffusion fluxes. The two-phase Euler–Lagrange method was used to find these constants, where gravity, drag, Saffman’s lift, Brownian and thermophoretic forces were considered. The constants are not much dependent on the concentration, but they change significantly by varying Peclet number. They increase with increasing Peclet number, which shows that at higher Peclet numbers, the effects of shear rate and viscosity gradient are intensified on particle migration. Meanwhile, by raising Peclet number, the role of shear rate becomes more pronounced in comparison with the viscosity gradient. At lower Peclet numbers with intensified effect of the Brownian diffusion, a more uniform concentration distribution was achieved. Moreover, the particles enlargement considerably intensifies the non-uniformity in concentration distribution. Furthermore, particle migration causes non-uniformity in the properties distribution and consequently reduces the thermal conductivity and viscosity adjacent to the wall due to lower concentration there. Thus, smaller pressure drop and heat transfer coefficient were obtained in comparison with the case of applying uniform properties.

Drop deformation in two-roll mills considering wall effects

Experimental, theoretical and numerical results of dynamics of drop deformation in strong flows generated by a co-rotating two-roll mill and considering the influence of near rigid walls are presented. The drop dynamics is altered, with respect to a drop free of wall effects, by the proximity of the rigid boundaries as well as caused by a non-linear and non-uniform flow due to gradients of flow-type parameter and shear rate. Simulations were carried out using the Boundary Element Method (BEM). Since the inclusion of the whole boundaries (drop and rollers surfaces) is not an easy and trivial task, bi-dimensional numerical simulations was performed as a first approach. The experimental and numerical results were obtained for a flow type of α = 0.03 and two values of viscosity ratio λ = 0.012 and 16. In general, numerical results for the stationary deformation parameters, up to intermediate confinements, are in agreement with the experiments, with and without wall effects. Since the case of drops with a high viscosity ratio did not match existing theoretical models, the wall-effect theory of Shapira and Haber was modified, considering Cox's second-order theory as the converging theory without wall effects. From low to intermediate confinements, the new Cox-Shapira-Haber model fitted the observed experimental deformations.

Molecular-scale simulation of cross-flow migration in polymer melts.

The first ever molecular-scale simulation of cross-flow migration effects in dense polymer melts is presented; simulations for both unentangled and entangled chains are presented. At quiescence a small depletion next to the wall for the segmental densities of longer chains is present, a corresponding excess exists about one-half a radii of gyration away from the wall, and uniform values are observed further from the wall. In shear flow the melts exhibit similar behavior as the quiescent case; a constant shear rate across the gap does not induce chain length based migration. In contradistinction, parabolic flow (where gradients in shear rate are present) causes profound migration for both unentangled and entangled melts. Mapping onto polyethylene and calculating stress shows the system is far below the stress required to break chains. Accordingly, our findings are consistent with flow induced migration mechanisms predominating over competing chain degradation mechanisms thus resolving a 40 year old controversy.

A novel thermal dispersion model to improve prediction of nanofluid convective heat transfer

This study numerically investigates the hydrothermal characteristics of the nanofluid in a laminar flow inside a straight tube. A new model is proposed for dispersion thermal conductivity while a theoretical approach is adopted to predict the particle distribution at the tube cross section considering the effects of non-uniform shear rate, Brownian diffusion and viscosity gradient on particle migration. It is observed that nanoparticles are not distributed uniformly at the tube cross section such that the values of concentration are higher at central regions of the tube and this non-uniformity intensifies at higher mean concentrations and Reynolds numbers. The particle distribution is applied in the proposed dispersion model. The findings show that this dispersion model presents more accurate results than traditional homogenous one. For dispersion model, the velocity profile is flatter than that obtained from the homogenous model. In addition, in the vicinity of the wall, the value of temperature and its gradient obtained from the dispersion model are respectively lower and higher than those from the homogenous model. Increasing the mean concentration results in convective heat transfer enhancement, while causing not much penalty in pressure drop. This indicates that application of nanofluids can result in energy efficiency improvement.

Particle migration in nanofluids considering thermophoresis and its effect on convective heat transfer

The effects of particle migration on concentration distribution and convective heat transfer coefficient of the water-TiO2 nanofluid were investigated inside a circular tube. The concentration distribution was obtained considering thermophoresis, non-uniform shear rate, Brownian diffusion and viscosity gradient. Using the scale analysis, it was demonstrated that thermophoresis can have a significant effect on the particle migration. Dispersion approach was used for simulation, while a non-uniform concentration was applied. An experimental study was conducted to examine the numerical solution accuracy and there was a good agreement between the experimental and numerical results. Non-uniformity of the concentration is intensified by increasing the Reynolds number and the particle size. Thermophoresis makes the concentration more non-uniform and the velocity profile flatter as well. At greater mean concentrations, the effect of thermophoresis on particle distribution and convective heat transfer coefficient is highlighted. Meanwhile, considering thermophoresis yields greater convective heat transfer coefficient in all Reynolds numbers.

Analysis of boundary slip in a flow with an oscillating wall

Molecular dynamics (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes' second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical model for slip is established, which estimates the increment in slip at the boundary. The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid at the wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteady flows is governed by the gradient of shear rate and shear rate of the fluid. Nondimensionalizing the model gives a time dependent yet universal curve, independent of wall-fluid properties, which can be used to find the slip boundary condition at the fluid-solid interface based on the information of shear rate, gradient of shear rate of the fluid, and the instant of time during the cycle. A governing nondimensional number, defined as the ratio of phase speed to speed of sound, is identified to help in explaining the mechanism responsible for the transition of slip boundary condition from finite to a perfect slip and determining when this would occur. Phase lag in fluid velocity relative to wall is observed. The lag increases with decreasing time period of wall oscillation and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slip velocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The cause for hysteresis is attributed to the unsteady inertial forces of the fluid. The rate of heat generated by viscous shear is compared for an unsteady Stokes' second problem and simple Couette flow and is shown to be higher for the unsteady flow.