scholarly journals Time dependent power law behaviour at low shear rates for paint systems

1971 ◽  
Vol 10 (4) ◽  
pp. 607-607 ◽  
Author(s):  
M. Camina ◽  
C. G. Roffey
Keyword(s):  
Power Law ◽  
Time Dependent ◽  
Shear Rates ◽  
Paint Systems ◽  
Low Shear

Non-Newtonian Flow Behavior in Microchannels for Emulsion Formation

2006 ◽  
Author(s):  
Ravi Arora ◽  
Eric Daymo ◽  
Anna Lee Tonkovich ◽  
Laura Silva ◽  
Rick Stevenson ◽  
...  
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Power Law ◽  
Flow Behavior ◽  
Scale Up ◽  
High Wall Shear Stress ◽  
Shear Rates ◽  
Wall Shear ◽  
Low Shear

Emulsion formation within microchannels enables smaller mean droplet sizes for new commercial applications such as personal care, medical, and food products among others. When operated at a high flow rate per channel, the resulting emulsion mixture creates a high wall shear stress along the walls of the narrow microchannel. This high fluid-wall shear stress of continuous phase material past a dispersed phase, introduced through a permeable wall, enables the formation of small emulsion droplets — one drop at a time. A challenge to the scale-up of this technology has been to understand the behavior of non-Newtonian fluids under high wall shear stress. A further complication has been the change in fluid properties with composition along the length of the microchannel as the emulsion is formed. Many of the predictive models for non-Newtonian emulsion fluids were derived at low shear rates and have shown excellent agreement between predictions and experiments. The power law relationship for non-Newtonian emulsions obtained at low shear rates breaks down under the high shear environment created by high throughputs in small microchannels. The small dimensions create higher velocity gradients at the wall, resulting in larger apparent viscosity. Extrapolation of the power law obtained in low shear environment may lead to under-predictions of pressure drop in microchannels. This work describes the results of a shear-thinning fluid that generates larger pressure drop in a high-wall shear stress microchannel environment than predicted from traditional correlations.

An efficient lubrication-based code for solving non-Newtonian flow in geological rough fractures

2021 ◽  
Author(s):  
Alessandro Lenci ◽  
Yves Méheust ◽  
Mario Putti ◽  
Vittorio Di Federico
Keyword(s):  
Power Law ◽  
Fractured Reservoirs ◽  
Numerical Code ◽  
Symmetric System ◽  
Finite Volume Scheme ◽  
Single Fracture ◽  
Newtonian Flow ◽  
Shear Rates ◽  
Ellis Model ◽  
Low Shear

<p>The study of the flow in a single fracture is the starting point to understand the complex hydraulic behaviour of geological formations and fractured reservoirs, whose comprehension is of interest in many natural phenomena (e.g., magma intrusion) and the optimization of numerous industrial activities in fractured reservoirs (e.g., Enhanced Oil Recovery, drilling engineering, geothermal energy exploitation). Despite the considerable technical prospects of this topic, the associated mathematical complexity and computational burden have so far mostly discouraged investigations of the combined effects of fracture heterogeneity and of the complex rheology of relevant fluids. Indeed, magmas, foams, muds, and suspensions of natural colloids such as clay particles in water are complex fluids and often present in subsurface applications and natural processes. These fluids are characterized by a shear-thinning behavior, which can be well described by the Ellis model, a continuous three-parameter model that behaves as a power-law fluid at high shear rates and as a Newtonian fluid at low shear rates. The Ellis model parameters are: <em>n</em> the power law exponent, <em>μ</em><sub>0</sub> the low shear rates viscosity, and <em>τ</em><sub>1/2</sub> the shear rate such that <em>μ<sub>app</sub></em>(<em>τ</em><sub>1/2</sub>)=<em>μ</em><sub>0</sub>/2. We use this rheological description in combination with the lubrication theory, which is a depth-averaged formalism permitting us to reduce the full 3-D problem to a 2-D plane formulation. It has been applied to study Newtonian flow in a single fracture for decades and, as far as the aperture gradient remains small (∇<em>d</em>«1), the approximation error introduced by this model is limited. We present here a lubrication-based numerical code aiming at simulating the flow of an Ellis fluid in rough-walled fractures. The code is composed of two modules: a 2D FFT-based fracture aperture field generator and a lubrication-based non-Newtonian flow solver. The former module generates a random aperture field <em>d</em>(<em>x</em>,<em>y</em>) with isotropic spatial correlations, given a mean aperture ⟨<em>d</em>⟩, a coefficient of variation <em>σ<sub>d</sub></em>/⟨<em>d</em>⟩, a Hurst exponent (<em>H</em>) and a correlation length (<em>l<sub>c</sub></em>), reproducing realistic geometries of geological fractures. In the latter module, a 2-D finite volume scheme is adopted to solve the non-linear lubrication equation describing the flow of an Ellis fluid. The equation is discretized on a staggered grid, so that <em>d</em>(<em>x</em>,<em>y</em>) and the pressure field <em>p</em>(<em>x</em>,<em>y</em>) are defined at different locations. Computational efficiency is achieved by means of the inexact Newton algorithm, with the linearized symmetric system of equations solved via variable-fill-in Incomplete Cholesky Preconditioned Conjugate Gradient method (ICPCG), and a parameter-continuation strategy for the cases with strong nonlinearities. The code proves to be stable and robust when solving flow within strongly heterogeneous fractures (e.g., <em>σ<sub>d</sub></em>/⟨<em>d</em>⟩=1), even on very fine and coarse meshes (e.g., 2<sup>14</sup>×2<sup>14</sup>) and considering a wide range of power-law exponents (e.g., 0.1≤<em>n</em>≤1). The code is validated by comparing the results against analytical solutions (e.g., parallel plates model, sinusoidal profile) and full 3-D CFD simulations, considering different closures.</p>

Rheological Modelling of Complex Flow Behaviour of Bitumen-Solvent Mixtures and Implication for Flow in a Porous Medium

2021 ◽  
pp. 1-34
Author(s):  
Olalekan Alade
Keyword(s):  
Shear Rate ◽  
Power Law ◽  
Rheological Model ◽  
Flow Characteristics ◽  
Solvent Mixtures ◽  
Pore Scale ◽  
Rheological Models ◽  
Shear Rates ◽  
Rate Region ◽  
Low Shear

Abstract The viscosity of extra-heavy oils including bitumen can be reduced significantly by adding solvent such as toluene to enhance extraction, production and transportation. Thus, prediction of viscosity and/or rheology of bitumen-solvent mixtures has become necessary. More so, selecting a suitable rheological model for simulation of flow in porous media has an important role to play in engineering design of production and processing systems. While several mixing rules have been applied to calculate the viscosity of bitumen-solvent mixtures, rheological model to describe the flow characteristics has rarely been published. Thus, in this investigation, rheological behaviour of bitumen and bitumen-toluene mixtures (weight fractions of bitumen WB = 0, 0.25, 0.5, 0.6, 0.75, and 1 w/w) have been studied at the flow temperature (75 °C) of the bitumen and in the range of shear rates between 0.001 and 1000 s−1. The data was fitted using different rheological models including the Power Law, Cross Model, Carreau-Yasuda Model, and the newly introduced ones herein named as Cross-Logistic and Logistic models. Then, a computational fluid dynamics (CFD) model was built using a scanning electron image (SEM) of rock sample (representing a realistic porous geometry) to simulate pore scale flow characteristics. The observations revealed that the original bitumen exhibits a Newtonian behaviour within the low shear rate region (0.001 to 100 s−1) and shows a non-Newtonian (pseudoplastic) behaviour at the higher shear rate region (100 to 1000 s−1). Conversely, the bitumen-toluene mixtures show shear thinning (pseudoplastic) behaviour at low shear rate region (0.001 to 0.01), which appears to become less significant within 0.01 to 0.1 s−1, and exhibit shear independent Newtonian behaviour within 0.1 and 1000 s−1 shear rates. Moreover, except for the original bitumen, statistical error analysis of prediction ability of the tested rheological models as well as the results from the pore scale flow parameters suggested that the Power Law might not be suitable for predicting the flow characteristics of the bitumen-toluene mixtures compared to the other models.

Dynamic rheology of a dilute suspension of elastic capsules: effect of capsule tank-treading, swinging and tumbling

2011 ◽  
Vol 669 ◽  
pp. 498-526 ◽  
Author(s):  
PROSENJIT BAGCHI ◽  
R. MURTHY KALLURI
Keyword(s):  
Shear Viscosity ◽  
Periodic Variation ◽  
Time Dependent ◽  
Simple Shear Flow ◽  
Marginal Effect ◽  
Shear Rates ◽  
Dilute Suspension ◽  
Elastic Capsules ◽  
Tumbling Motion ◽  
Low Shear

Three-dimensional numerical simulations are used to study the effect of unsteady swinging and tumbling motion on the rheology of a dilute suspension of oblate-shaped elastic capsules. Unlike a suspension of initially spherical capsules undergoing the steady tank-treading motion for which the rheology is constant in time, the suspension of non-spherical capsules is time-dependent due to the unsteady capsule motion. In a simple shear flow, the non-spherical capsules undergo a transition from the tank-treading/swinging to the tumbling motion with a reduction in the shear rate or an increase in the ratio of the internal to external fluid viscosities. We find that the time-averaged rheology obtained for the non-spherical capsules undergoing the unsteady motion is qualitatively similar to that obtained for the spherical capsules undergoing the steady tank-treading motion, and that the tank-treading-to-tumbling transition has only a marginal effect. The time-averaged rheology exhibits a shear viscosity minimum when the capsules are in a swinging motion at high shear rates but not at low shear rates. This is a remarkable departure from the behaviour of a vesicle suspension which exhibits a shear viscosity minimum at the point of transition. We find that the shear viscosity in a capsule suspension can decrease as well as increase with increasing viscosity ratio during both tank-treading and tumbling motions, while that of a vesicle suspension always decreases in tank-treading motion and increases in tumbling motion. We then seek to connect the time-dependent rheology with the time-dependent membrane tension, capsule orientation, deformation and tank-treading velocity. At low shear rates, the numerical results exhibit a similar trend to that predicted by analytical theory for rigid ellipsoids undergoing tumbling motion. The trend differs during swinging motion due to the periodic deformation and time-dependent variation of the membrane stress. The elastic component of the shear stress is minimum when the capsules are maximally compressed, and is maximum when the capsules are maximally elongated. In contrast, the viscous component is related to the periodic variation of the tank-treading velocity synchronized with the swinging motion, and the rate of capsule elongation or compression. The swinging or tumbling velocity makes no contribution to the time-dependent rheology.

scholarly journals Viscoelastic Property of an LDPE Melt in Triangular- and Trapezoidal-Loop Shear Experiment

Polymers ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3997
Author(s):  
Shuxin Huang
Keyword(s):  
Small Strain ◽  
Time Dependent ◽  
Time Interval ◽  
Shear Rates ◽  
Viscoelastic Behaviors ◽  
Polyethylene Melt ◽  
Ldpe Melt ◽  
Dynamic Frequency ◽  
Low Shear

The time-dependent viscoelastic behaviors of a low-density polyethylene melt (LDPE) in a triangular- and trapezoidal-loop shear experiment reported previously are described here by an integral-type Rivlin–Sawyers (RS) constitutive equation. The linear viscoelasticity of the melt was obtained through a dynamic frequency sweep experiment at a small strain and fitted by a relaxation spectrum. The nonlinear viscoelasticity was characterized by viscosity. All the experimental viscoelastic behaviors of the melt can be divided into two types in terms of the predictions of the RS model: (1) predictable time-dependent viscoelastic behaviors at low shear rates or during short-term shear, and (2) unpredictable shear weakening behavior occurring at the high shear rate of 3–5 s−1 during long-term shear with the characteristic time interval of about 40–100 s. The influence of experimental error caused possibly by inhomogeneous samples on the viscoelasticity of the melt was analyzed, and the large relative error in the experiment is about 10–30%.

Effect of Blood Viscosity on Thrombosis Potential Near a Step Wall Transition

2009 ◽  
Author(s):  
Scott C. Corbett ◽  
Amin Ajdari ◽  
Ahmet U. Coskun ◽  
Hamid N.-Hashemi
Keyword(s):  
Blood Flow ◽  
Vessel Wall ◽  
Coagulation Factors ◽  
Artificial Organs ◽  
Physical Factors ◽  
Local Geometry ◽  
Induce Platelet Aggregation ◽  
Shear Rates ◽  
Chemical Factors ◽  
Low Shear

Thrombosis and hemolysis are two problems encountered when processing blood in artificial organs. Physical factors of blood flow alone can influence the interaction of proteins and cells with the vessel wall, induce platelet aggregation and influence coagulation factors responsible for the formation of thrombus, even in the absence of chemical factors in the blood. These physical factors are related to the magnitude of the shear rate/stress, the duration of the applied force and the local geometry. Specifically, high blood shear rates (or stress) lead to damage (hemolysis, platelet activation), while low shear rates lead to stagnation and thrombosis [1].

scholarly journals Hydroxyurea Improves Oxygen Transport Effectiveness in Sickle Cell Anemia Patients

Blood ◽  
2014 ◽  
Vol 124 (21) ◽  
pp. 2716-2716
Author(s):  
Vivien A. Sheehan ◽  
Sheryl Nelson ◽  
Caroline Yappan ◽  
Bogdan R. Dinu ◽  
Danielle Guffey ◽  
...  
Keyword(s):  
Blood Flow ◽  
Sickle Cell ◽  
Blood Viscosity ◽  
Whole Blood ◽  
Patient Characteristics ◽  
Whole Blood Viscosity ◽  
Shear Rates ◽  
High Shear Rates ◽  
Altered Blood ◽  
Low Shear

Abstract Background: Sickle cell disease (SCD) patients have altered blood rheology due to erythrocyte abnormalities, including increased aggregation and reduced deformability, which together affect microcirculatory blood flow and tissue perfusion. At equal hematocrit, sickle cell blood viscosity is increased compared to normal individuals. The hematocrit to viscosity ratio (HVR) is a measure of red blood cell (RBC) oxygen carrying capacity, and is reduced in SCD with clinical consequences related to altered blood flow and reduced tissue oxygenation. Erythrocyte transfusions reduce HVR at low shear rates that mimic venous circulation, and do not change HVR at high shear rates that mimic arterial blood flow. Hydroxyurea is a safe and effective therapy for SCD; however, its effects on sickle cell rheology and HVR have not been fully investigated. Evaluating the effects of hydroxyurea on viscosity is especially critical, before its use is extended widely to patients with cerebrovascular disease or genotypes with higher hematocrit and higher viscosity such as Hemoglobin SC (HbSC). Methods: To determine the effects of hydroxyurea on viscosity and HVR, we designed a prospective study to measure whole blood viscosity at 45 s-1 (low shear) and 225 s-1(high shear) rates in pediatric patients with SCD using a Brookfield cone and plate viscometer under oxygenated conditions. Venous blood samples (1-3mL) were collected in EDTA and analyzed no more than 4 hours after phlebotomy; samples were run in duplicate by persons blinded to the patient’s sickle genotype and treatment status. Laboratory values were obtained using an ADVIA hematology analyzer. Samples were analyzed from three non-overlapping cohorts of patients with SCD and HbAA individuals for comparison: untreated HbSS patients (n= 43), HbSS patients treated with hydroxyurea at maximum tolerated dose (n=98), untreated HbSC patients (n=53) and HbAA patients (n=19). Laboratory parameters that differed significantly among the SCD groups were analyzed by simple linear regression. Results: Patient characteristics and viscosity measurements are shown in the Table. Within the SCD population, the viscosity was lowest among the untreated HbSS patients, presumably due to their low hematocrit, while viscosity was higher in HbSS patients on hydroxyurea and HbSC patients. When the HVR was calculated for each group, no significant difference was identified between untreated HbSS and untreated HbSC patients. However, hydroxyurea treatment significantly increased HVR at both 45s-1 and 225 s-1 (p<0.001), indicating that the slightly increased viscosity in this cohort was more than compensated by a higher hematocrit. Correlations were tested for hemoglobin (Hb), mean corpuscular volume (MCV), white blood cell count (WBC), absolute neutrophil count (ANC), absolute reticulocyte count (ARC), % fetal hemoglobin (HbF), and average red cell density in g/dL with HVR, at both shear rates. The hydroxyurea-associated HVR increase at both shear rates was independent of %HbF or MCV, but the increased HVR at 225 s-1was associated with lower WBC (p<0.001), lower ANC (p=0.002), and lower red cell density (p=.009). Conclusions: We provide prospective data on whole blood viscosity measurements in a large cohort of children with SCD. Hydroxyurea increases the hematocrit in HbSS patients more than the viscosity, and thus improves HVR. These findings imply that hydroxyurea improves RBC oxygen transport at both high and low shear rates, which should confer clinical benefits, and these effects are independent of HbF induction. Concerns about hydroxyurea increasing whole blood viscosity and reducing tissue oxygenation in children with cerebrovascular disease or HbSC patients may not be warranted, if the same beneficial HVR effects are achieved. Abstract 2717. Table 1. Patient characteristics. Viscosity was typically measured in duplicate and averaged for each patient. HVR at 45 s-1 and 225s-1 was calculated as hematocrit/viscosity. Results are presented as mean ± 2SD. HbAAn=19 HbSS, untreatedn=43 HbSS, on Hydroxyurean=98 HbSCn=53 Age (years) 15.4 ± 3.8 10.4 ± 5.1 10.7 ± 3.4 10.5 ± 4.3 Hemoglobin (gm/dL) 13.5 ± 1.7 8.5 ± 1.0 9.9 ± 1.4 11.0 ± 1.2 Hematocrit (%) 40.9 ± 5.3 25.5 ± 3.1 28.4 ± 3.7 31.3 ± 3.2 Viscosity (cP) at 45s-1 5.3 ± 0.9 4.6 ± 1.2 4.3 ± 0.9 5.5 ±0.9 HVR at 45s-1 7.5 ± 0.9 5.8 ± 1.1 6.75 ± 1.0 5.77 ± 0.7 Viscosity (cP) at 225s-1 3.8 ± 0.5 3.3 ± 0.5 3.4 ± 0.5 4.1 ± 0.5 HVR at 225s-1 10.3 ± 0.7 7.7 ± 0.8 8.53 ± 0.8 7.72 ± 0.6 Disclosures Off Label Use: Hydroxyurea is not FDA approved for use in pediatric sickle cell patients.

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