Shear dependence of the reduced viscosity—concentration slope constant

The rate of breakage of duplex DNA molecules by laminar flow through a capillary has been studied. For λb2b5c DNA (molecular wt., M = 25 × 106) the point at which breakage occurs is normally distributed around the center of the molecule with a standard deviation of 12.5% of the molecular length. At constant shear stress or shear rate, the breakage rate is independent of ionic strength. Thus, shear induced local denaturation is not a rate limiting, preliminary step in breakage. In experiments at constant temperature with varying solvent viscosity (controlled by added sucrose) the breakage rate is a function of shear rate, not of shear stress. The rate of opening of hydrogenbonded circles into linear molecules by hydrodynamic shear is also shown to be a function of shear rate and not of shear stress. The breakage rate at constant shear rate is not greatly dependent on temperature. The shear rate required to achieve breakage is inversely proportional to M1,2. The breakage rate constant, k varies as a very high power of the shear rate; at 25°C, d In k/d In Gm ∼ 15; at 10°C, d In k/d In Gm ∼ 26, where Gm is the maximum shear rate at the capillary wall. The unexpected result that breakage rate is mainly dependent on shear rate, not shear stress, supports a model in which the DNA molecule is distorted with a driving force which depends on the hydrodynamic shear stress, ηG, but the rate limiting step is segment diffusion into a highly extended configuration. The characteristic time to achieve this configuration is proportional to solvent viscosity, η, hence the breakage rate is dependent on ηG/η or G, the shear rate.

The effect of dynamic deformation on the stationary flow of a rubber composition has been experimentally investigated for comparable values of the stationary and dynamic strain rates. The dependence of the effective viscosity on the stationary shear rate is not equivalent to its dependence on the periodic shear rate amplitude. An expression is given for calculating the effective viscosity in the case of combined stationary and dynamic shear deformation. The effectiveness of the dynamic deformation, estimated in terms of the effective viscosity, depends on whether it is superimposed on the stationary flow at constant stationary shear rate or at constant stress. It is proposed to estimate the effectiveness of dynamic deformation of a stationary non-Newtonian flow in terms of the change in the power of the stationary forces. When the effective viscosity is reduced by dynamic deformation of the stationary flow, the power of the stationary forces increases at constant shear stress and falls at constant stationary shear rate.

Complex fluids exhibit time-dependent changes in viscosity that have been ascribed to both thixotropy and aging. However, there is no consensus for which phenomenon is the origin of which changes. A novel thixotropic model is defined that incorporates aging. Conditions under which viscosity changes are due to thixotropy and aging are unambiguously defined. Viscosity changes in a complex fluid during a period of rest after destructuring exhibit a bifurcation at a critical volume fraction ϕc2. For volume fractions less than ϕc2 the viscosity remains finite in the limit t →∞. For volume fractions above critical the viscosity grows without limit, so aging occurs at rest. At constant shear rate there is no bifurcation, whereas under constant shear stress the model predicts a new bifurcation in the viscosity at a critical stress σB, identical to the yield stress σy observed under steady conditions. The divergence of the viscosity for σ≤σB is best defined as aging. However, for σ > σB, where the viscosity remains finite, it seems preferable to use the concepts of restructuring and destructuring, rather than aging and rejuvenation. Nevertheless, when a stress σA(≤σB) is applied during aging, slower aging is predicted and discussed as true rejuvenation. Plastic behaviour is predicted under steady conditions when σ > σB. The Herschel-Bulkley model fits the flow curve for stresses close to σB, whereas the Bingham model gives a better fit for σ >> σB. Finally, the model’s predictions are shown to be consistent with experimental data from the literature for the transient behaviour of laponite gels.

Vinyl ester resins with varied acid values (11, 22, 32, 38, and 48 mg KOH/g solid) were prepared by reacting epoxy-novolac resin with methacrylic acid. The rheological behavior of these synthesized vinyl ester resin (VER) samples containing styrene as reactive diluent was studied using a Haake Rotovisco RV 20 viscometer. The apparent viscosity was found to be inversely proportional to the square root of the acid value in the temperature range of 25–40°C and at shear rates ranging from 100–800 sec−1. The zero-shear viscosity of these VER samples containing styrene (40% w/w) as reactive diluent decreased linearly with temperature. The activation energies for flow at constant shear stress (25–100 Pa) for a particular sample were found to be constant. The activation energy at constant shear rate decreases with the increase in the shear rate (50–400 sec−1). The activation energy at constant shear rate and shear stress decreased with the increase in the acid value. The viscosity of vinyl ester resin containing styrene as reactive diluent decreased almost 50 times with the increase in the concentration of reactive diluent from 30% to 100% (w/w of the resin).

The viscosities of a number of monodisperse polystyrene melts have been measured using a capillary rheometer. The materials covered a molecular weight range of 43,000–460,000. Shear rates of 1.54–1540 sec.−1 and temperatures of 350–450°F. were studied. The effect of molecular weight distribution of polydisperse polystyrene was also measured. It was found that while low shear viscosity was dependent on Mw, higher shear melt viscosities depended on averages between Mw and Mn until at 1000–2000 sec.−1, Mn controlled viscosity. Agreement with the 3.4‐power dependence of zero shear viscosity was good. Similar exponential relationships were found, with higher rates of shear, corresponding to smaller values of the exponent. Constant values of the exponent were found at constant shear stress but not at constant shear rate. Agreement with the constancy of the activation energy for viscous flow for various molecular weights and distributions at constant shear stress was good. However at constant shear rate, ΔE decreased as the molecular weight average increased and as the distribution broadened. Viscosity versus shear rate master curves were constructed by using the Buehe‐Harding procedure. All monodisperse polystyrenes showed excellent fit with the master curve. Other molecular weight distributions did not. Master curves also were constructed for measurements of dynamic viscosity versus frequency for monodisperse polystyrene. These curves when compared to steady state viscosities failed to confirm the correspondence of ηa to either |η*| or to η′.

Melt rheology and extrudate swell properties of talc filled polyethylene compounds

At high shear rates a steady state of shear flow with constant shear rate, constant shear stress, and constant recoverable shear strain is observed in the short-time sandwich rheometer after some few shear units already. The melt exhibits rather high elastic shear deformations and the recovery occurs at much higher speed than it is observed in the newtonian range. The ratio of first normal stress difference and twice the shear stress, being equal to the recoverable strain in the second-order fluid limit, significantly underestimates the true elastic shear strains at high shear rates. The observed shear rate dependence of shear stress and first normal stress difference as well as of the (constrained) elastic shear strain is correctly described on the basis of a discrete relaxation time spectrum. In simple shear a stick-slip transition at the metal walls is found. Necessary for the onset of slip is a critical value of shear stress and a certain amount of elastic shear deformation or orientation of the melt.

Cardiovascular blood-recirculating devices provide life saving cardiopulmonary support to critically ill populations. Unfortunately, common device-related thrombotic complications continue to result in significant mortality, neurological morbidity, and limb loss. Past studies have shown that increased wall shear stress from blood-recirculating devices activates circulating monocytes and platelets. Less well studied is the enhancement of thrombosis by platelet-derived (PMPs) and monocyte-derived microparticles (MoMPs). These are small (0.1-1 micron) cell-derived membrane vesicles released from activated cells. Studies using a biological stimulant demonstrate that MoMPs initiate clotting whereas PMPs enhance clotting. Few if any studies have defined the contributions of device-produced microparticles (MPs) to changes in thrombotic potential. Our hypothesis is the increased dynamic or constant shear stress generated by a blood-recirculating device promotes release of prothrombotic MPs. Using an Anton Paar MCR Rheometer we exposed whole human blood in vitro to both dynamic (70 dynes/cm 2 at 0.05hz) and constant (70 and 35 dynes/cm 2 ) shear stress conditions for two minutes. After shear, MPs were collected with dual centrifugation and then quantified using a BD FACS Canto II flow cytometer with forward scatter photomultiplier tube (resolution=200nm). Then we pelleted and washed MPs to measure changes in thrombin generation with a Calibrated Automated Thrombogram (CAT). Dynamic shear stress generated 3841±1171 PMPs/μL and 3522±1090 MoMPs/μL, (MEAN±SE, n=6). Constant shear stress at 70 dynes/cm 2 and 35 dynes/cm 2 generated PMPs/μL of 4937±1655 and 1880±389 and MoMPs/μL of 6935±2029 (n=3) and 2262±1041 respectively (MEAN±SE, n=3 for each). All shear conditions generated an increase in MP concentration over static conditions of 644±120 PMPs/μL and 538 MoMPs/μL (p<0.01). Dynamic and constant sheared MPs increased the estimated thrombin potential and peak thrombin generation by at least 30% compared to static (p<0.05). This study is the first to demonstrate that device relevant constant and dynamic shear stresses can generate PMPs and MoMPs that promote thrombosis.

The melt viscosities of three low density polyethylenes of widely varying melt indices were studied as a function of temperature over a broad range of shear rates and shear stresses. Apparent viscosities at constant shear stress could be fitted adequately to a simple Arrhenius equation over the entire temperature range studied. However, pronounced curvature of the log ηa–1/T curves was observed for apparent viscosities at constant shear rate. The apparent activation energies for viscous flow at constant shear stress were found to decrease slowly with increasing shear stress and also to decrease with decreasing molecular weight. A temperature‐shear rate superposition was demonstrated to hold, and the shift factor dependence on temperature was determined.

A capillary rheometer equipped with a pressure chamber is used to measure the pressure-dependent viscosity of polymethylmethacrylate (PMMA), poly-α-methylstyrene-co-acrylonitrile (PαMSAN), and low-density polyethylene (LDPE). Data analysis schemes are discussed to obtain pressure coefficients at constant shear rate and at constant shear stress. It is shown that the constant shear stress pressure coefficients have the advantage of being shear stress independent for the three polymers. The constant shear rate pressure coefficients, on the other hand, turn out to depend on shear rate, which makes them less suitable for use, e.g., in process simulations. In addition to the commonly used superposition method, a direct calculation method for the pressure coefficients is tested. Values obtained from both methods are equivalent. However, the latter requires less experimental and calculational efforts. From the obtained pressure coefficients, it is clear that PMMA and PαMSAN have a very similar pressure dependence, while LDPE is less sensitive to pressure.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross-linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt%, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt%, and after that shows a maximum at a gel fraction of about 25 wt%, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40wt%. The flow activation energy at a constant shear rate, ΔHγ, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70wt%.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt. %, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt. %, and after that shows a maximum at a gel fraction of about 25 wt. %, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end-correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40 wt. %. The flow activation energy at a constant shear rate, ΔHγ̇, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70 wt. %.

Rheological study under simple shear of six gelled waxy crude oils

The rheological properties of a sodium tallow-coconut oil soap (15% water) have been determined using a high pressure capillary extrusion viscometer over shear rates of 14.7 to 2560 sec−1 and temperatures of 70–103°C. Capillary flow measurements were also made on sodium stearate (25% water) at 90°C. The data indicated shear thinning characteristics and were fitted to an equation of the form: $$\log \tau _R = \log A + n\log \dot \gamma _R $$ over the above shear rate range. The flow indices (n) of 0.337–0.437 were comparable to those obtained from polyethylene data in the literature. A zero shear activation energy of 57.2 Kcal/mole was calculated for the tallow-coconut soap. The activation energy at constant shear stress was greater than that at constant shear rate and decreased with increasing shear stress and shear rate. The soap flow unit was estimated to contain about 2 · 104 molecules.

Apparent flow activation energies evaluated from viscosity changes with temperature can be calculated in the non‐Newtonian region at either constant shear rate, E, or at constant shear stress, E. For many linear, amorphous polymere, it can be shown that E is independent of stress over the full range for which shear stress data tire reported. This conclusion also holds for solutions of several polymer types. Anomalous results are documented only for branched polyethylene. E decreases with shear in the non‐Newtonian region approaching a lower limit corresponding to the “power law” region. The relative changes in E with shear rate can be expressed in terms of reduced variables. The absolute change in E with shear rate can he used as a measure of polymer molecular weight distribution.