Viscosity Eta Research Articles

Steady-state cracks in viscoelastic lattice models.

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity eta allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement Delta and the number of transverse rows N. At any N, the continuum theory misses the lattice-trapping phenomenon; this is well known, but the introduction of eta introduces some new twists. More importantly, for large N even at large Delta, the standard two-dimensional elastodynamics approach completely misses the eta-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.

Viscoelastic behaviour of a disk-like thermotropic nematic phase (ND) versus temperature

We have investigated 'hexa- n -alcanoyloxytruxene' HATXC H which exhibits a disk-like thermotropic nematic phase between 65 and 84 C. Using a light-beating technique we have measured the orientational diffusivities D a correspond respectively to twist and bend deformations. D twist increases monotonically as temperature increases, while D remains constant. This result means that the curvature bend elastic constant K changes more rapidly than the viscosity eta 22 in the same ratio. This means also that in the discotic thermotropic nematic phase, when temperature increases the effective hydrodynamic object, in orientational fluctuation, changes shape to be disk-like rather than rod-like. 9 19 nd D for several temperatures, which twist bend, while K and eta change twist 33 bend

Article

As a foundation for a future measurement of solvated electron mobilities in alcohol-water mixed solvents, the electrical conductances of sodium tetraphenylboride (STPB) in methanol-water, ethanol-water, and 2-propanol-water were measured at different temperatures. The molar conductivity LAMBDA 0 (10-4 S m2 mol-1) of STPB at 298 K is 70 in pure water and 82 in pure methanol; in methanol-water mixed solvents it passes through a minimum, the value being 45 at 70 mol% water. In 2-propanol-water LAMBDA 0 (10-4 S m2 mol-1) at 298 K decreases rapidly from 70 in pure water to 22.6 in 80 mol% water, then gradually to 16.5 in pure 2-propanol. Behavior in ethanol-water is intermediate, with a minimum of 29.5 in 70 mol% water, gradually increasing to 35.5 in pure ethanol. The product of LAMBDA 0 and the solvent viscosity eta has a maximum at about 75 mol% water in methanol, 90 mol% water in ethanol, and 95 mol% water in 2-propanol. The effects are attributed to changes of solvent structure and of solvated ion radius as alcohol is added to water.Key words: alcohol-water mixed solvents, electrical conductivity, large ions, solvent effects, activation energy.

Viscoelastic properties of bioadhesive, chlorhexidine-containing semi-solids for topical application to the oropharynx.

This study examined the viscoelastic properties of bioadhesive, chlorhexidine-containing semi-solid formulations, designed for topical application to the oropharynx. Oscillatory rheometry was performed using a Carri-Med CSL2-100 rheometer at 20.0 +/- 0.1 degrees C in conjunction with parallel plate geometry (2 cm diameter, 0.5 mm sample thickness). Samples were subjected to a constant strain (6.5 x 10(-3) rad) and defined viscoelastic parameters, namely storage modulus (G'), loss modulus (G"), loss tangent (tan delta) and dynamic viscosity (eta'), measured over a defined frequency range (0.01-1.0 Hz). As the oscillatory frequency was increased, G' G" of all formulations increased, whereas both eta' and tan delta significantly decreased. The magnitude of increase of G' and G" as a function of frequency was relatively small, indicating that, in general, the formulations were non-cross-linked elastic systems. Increasing concentrations of HEC, PVP and PC significantly increased G', G", eta' yet decreased tan delta, observations that may be attributed to the physical state of each polymer in the formulations. Formulation elasticity increased (i.e. tan delta decreased) as a result of increased entanglement of polymeric chains of dissolved components (i.e. HEC and PVP) and the restrained extension of swollen, cross-linked chains of PC. Additionally, in formulations where the saturation solubility of PVP was exceeded and/or insufficient "free-water" was available for maximal swelling of PC, formulation elasticity increased as a result of the increasing mass of dispersed solid particles of PVP and/or PC. Formulation eta' increased due to the attendant effects of polymer chain entanglement and polymer state on overall formulation viscosity. Following application to the oropharynx, the formulations will behave as elastic systems. Thus, these formulations would be expected to offer advantageous clinical properties, e.g., prolonged drug release, increased bioadhesion. However, it is noteworthy that the final choice of formulation for clinical evaluation will involve a compromise between viscoelastic characteristics and acceptable textural properties, e.g. ease of product application. This study has shown the applicability of oscillatory rheometry for both the characterisation and selection of candidate, topical bioadhesive formulations for clinical evaluation.

Light scattering and viscosity study of heat aggregation of insulin.

Aggregation behavior and hydrodynamic parameters of insulin have been determined from static and dynamic light scattering experiments and intrinsic viscosity measurements carried out at pH 4.0, 7.5, and 9.0 in the temperature range 20-40 degrees C in aqueous solutions. The protein aggregated extensively at elevated temperatures in the acidic solutions. Intermolecular interactions were found to be attractive and to increase with temperature. The measured intrinsic viscosity [eta], diffusion coefficient D0, molecular weight M, and radius of gyration Rg exhibited the universal behavior: M[eta] = (2.4 +/- 02) x 10(-27) (Re, eta/Re, D)3(D0 eta 0/T)-3 and (D0 square root of n)-1 approximately equal to (square root of pi eta 0 xi beta/kBT) [1 + 0.201)(v/beta 3) square root of n], where n is the number of segments in the polypeptide. The effective hydrodynamic radii deduced from [eta], (Re, eta) and the same deduced from D0, (Re, D) showed a constant ratio, (Re, eta/Re, D = 1.1 +/- 0.1). Re, D/Rg = xi was found to be (0.76 +/- 0.07). From the known solvent viscosity eta 0, the segment length beta was deduced to be (10 +/- 1) A. The excluded volume was deduced to be (5 A)3 regardless of pH. The Flory-Huggins interaction parameter was found to be chi = 0.45 +/- 0.04, independent of pH and temperature.

Flow Induced Instability of the Interface between a Fluid and a Gel

The stability of the flow of a fluid adjacent to a polymer gel is studied using a linear stability analysis. The system consists of a Newtonian fluid of density rho, viscosity eta and thickness R flowing adjacent to a polymer gel of density rho, modulus of elasticity E, viscosity eta(g) and thickness HR. The base flow in the fluid is a plane Couette flow. The Navier-Stokes equations for the fluid and the elasticity equations for the gel are solved numerically, and the characteristic equation is obtained using the boundary conditions at the interface. The characteristic equation for the growth rate is a non-linear equation, so analytical solutions cannot be obtained in general. Numerical solutions are obtained by analytic continuation using the exact solutions at zero Reynolds number as the starting guess. The growth rate depends on the parameter Sigma = (rho ER2/eta(2)), the ratio of thickness H, the ratio of viscosities eta(r) = (eta(g)/eta) and wave number k. For eta(r) = 0, it is found that the perturbations become unstable when the Reynolds number is increased beyond a transition value Re-t for all Sigma and k. The critical Reynolds number Re-c, which is the minimum of the Re-t - K curve, increases proportional to Sigma for Sigma much less than 1, and it shows a scaling behavior Re-c proportional to Sigma(beta) for Sigma much greater than 1, where 0.75 less than or equal to beta less than or equal to 0.8. Re-c decreases with increase in the ratio of thickness of gel to fluid H, but the scaling behavior remains unchanged. A variation in the ratio of viscosities eta(r) qualitatively changes the stability characteristics. For relatively low values of 1 less than or equal to Sigma less than or equal to 10(3), it is found that the transition Reynolds number decreases as eta(r) is increased, indicating that an increase in the gel viscosity has a destabilizing effect. For relatively higher values of 10(4) less than or equal to Sigma less than or equal to 10(5), the transition Reynolds number increases as eta(r) is increased and goes through a turning point. In this case, perturbations are unstable only when eta(r) is less than a maximum value eta(max), and there is no instability for eta(r) > eta(max).

Rheology of Confined Polymer Melts under Shear Flow: Weak Adsorption Limit

The dynamics of a confined polymer melt between weakly adsorbing surfaces is considered theoretically. The finite chain extensibility is taken into account explicitly, and the tangential stress and the first and the second normal-stress differences are calculated as functions of shear rate gamma. For small shear velocities (u <u**) the surface slip is large, and the apparent viscosity, eta(app), is proportional to the layer thickness h and is independent of the shear rate. For very high shear rates, the surface slip is small and the tangential stress increases with velocity to the power 1/3. Alternatively, the apparent viscosity eta decreases as a function of gamma with a characteristic -2/3 power law.

Determination of activation energy for nanometre-scale grain-boundary sliding in copper

Abstract The activation energy Q for grain-boundary-dependent sliding in copper has been measured below 573 K from experiments using an electron microscope on Cu-Fe-Co alloy bicrystals with various [011] symmetric tilt boundaries. The technique utilizes the sliding-induced rotation of moire fringes in b.c.c. Fe-Co particles on grain boundaries and is capable of detecting sliding of less than 1 nm. It is concluded that grain boundaries slide in a viscous manner with inherent viscosity eta = etaoT exp(QIRT), where etao is a constant related to the boundary structure. The misorientation angle dependences of the values of Q and etao display cusps and are similar to that of the boundary energy in copper. The larger the degree of disorder in the atomic arrangement at a boundary, the lower is the boundary viscosity.

Ionic structure in a binary fluid

The tracer diffusion coefficient D3+ of the trivalent lanthanide cation 153Gd3+ is studied in mixtures of isobutyric acid, water and 5*10-4 M Gd(NO3)3 using an open-ended capillary tube. These data are given over the complete composition range at T-Tc=0.171 K. The coefficients D3+ are combined with the shear viscosity eta of the electrolyte. The results are discussed in terms of the Einstein-Stokes law; our analysis suggests three different behaviours of the diffusing entity in the mixtures and it is based on the preferential solvation phenomenon.

Transport coefficients for rigid spherically symmetric polymers or aggregates

In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a dilute suspension of these molecules, starting from a continuum description based on the Debye-Brinkman equation. Instead of numerical methods for solving equations we use perturbative methods, especially methods from boundary-layer analysis. The calculations provide simple analytical formulae for the shear viscosity eta , and the translational and rotational diffusion coefficients DT and DR. The results can also be applied to suspensions of other porous objects, such as aggregates of colloidal particles in which D=3- lambda is called the fractal dimension of the aggregate.

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G''(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G''(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G'' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G'' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.

Does Cholesterol Depletion Have Adverse Effects on Blood Rheology?

Blood viscosity (eta B) at shear rates 10 and 100s-1, plasma viscosity (eta P), hematocrit (Hct), and whole blood cholesterol (Chol) were measured in 50 patients with a history of myocardial infarction or unstable angina pectoris. Erythrocyte morphology was also studied by scanning electron microscopy to determine the proportion of nondiscocytic erythrocytes (NDE). There was a significant positive correlation between Chol and eta P (r = 0.41, P < 0.004) and a highly significant negative correlation (r = -0.69, P < 0.001) between Chol and Tk, a viscometric index of erythrocyte rigidity based on relative blood viscosity at high shear (eta B/eta P) corrected for Hct. This latter result indicates Chol reduction in this population may increase erythrocyte rigidity. Twenty-five patients with Chol values in the range 4.0-8.0 mmol/L were commenced on a standard lipid-lowering diet and after eight weeks half were also given pravastatin (40 mg daily). After thirty-two weeks Chol had fallen significantly more in the pravastatin group (28%) than in the diet only group (11%, P = 0.005). There was no change in eta P for either group but a significant increase in Tk for the pravastatin group only (P = 0.011). The change in total cholesterol (delta Chol) for each patient over thirty-two weeks was negatively correlated with both the change in the index of erythrocyte rigidity (delta Tk) (r = -0.40, P = 0.044) and the change in the proportion of nondiscocytic erythrocytes (delta NDE) (r = -0.47, P = 0.026). These data suggest that cholesterol reduction within the normolipemic range may be associated with unfavorable changes in blood rheology.

Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials

The influence of inertial, thermal and rate - sensitive effects on the void growth at high strain rate in a thermal - viscoplastic solid is investigated by means of a theoretical model presented in the present paper. Numerical analysis of the model suggests that inertial, thermal and rate - sensitive effects are three major factors which greatly influence the behavior of void growth in the high strain rate case. Comparison of the mathematical model proposed in the present work and Johnson's model shows that if the temperature - dependence is considered, material viscosity eta can take the experimentally measured values.

Shear rate dependent viscoelastic behavior of human glandular salivas.

Rheological properties of unstimulated human whole saliva (CHWS) and human glandular salivas (parotid, submandibular, sublingual, and palatal) of 7 healthy persons were investigated. The viscosity eta' and elasticity eta" of these salivas were measured as a function of oscillating shear rate gamma on an oscillating capillary viscoelasticity analyzer (Vilastic 3). Viscosity eta' and elasticity eta" of total and glandular salivas decreased in the following order: SL > Pal approximately CHWS approximately SM > Par. Rheological behavior of submandibular, palatal and sublingual saliva displayed a comparable pattern, although sublingual saliva showed significantly higher absolute values. The difference in viscoelasticity between submandibular and sublingual saliva was not due to differences in mucin concentration between SM and SL saliva. Flow curves of a range of SL saliva dilutions and flow curves of concentrated SM saliva showed that sublingual saliva was intrinsically more elastic than submandibular saliva.

Work of adhesion of respiratory tract mucus.

A method was devised to measure the work of adhesion (WA) to a substrate of mucus, a viscoelastic gel, from the measured contact angle of glycerol on a mucus substrate and the known physical properties of a Teflon surface. Fifteen sputum samples from cystic fibrosis (CF) patients were compared with 25 mucus samples from canine tracheal pouches (CP), studied in the hydrated and partially dehydrated states. Apparent viscosity (eta A) and recoverable shear strain (SR) were measured by fluxgate magnetometry, and water content was inferred from vapor pressure osmometry. Na+, K+, and Ca2+ concentrations were measured with specific ion electrodes and Cl- with a chloridimeter. The Cl- concentration of the CP mucus was inversely proportional to its osmolality, and the Cl- concentration of the CP mucus was 102.5 +/- 1.6 meq/l compared with 55.6 +/- 2.5 meq/l for CF sputum. When CP mucus osmolality was increased from 316.0 +/- 5.5 to 430.0 +/- 7.5 mosmol/kg, WA increased from 25.1 +/- 1.8 to 31.1 +/- 1.2 ergs/cm2 and eta A increased from 391 +/- 55 to 622 +/- 121 P, respectively. CF sputum WA was 30.2 +/- 0.6 ergs/cm2, eta A was 1,110 +/- 316 P, and osmolality was 466.0 +/- 14.0 mosmol/kg. The increased WA and eta A of mucus in CF patients may thus be dependent on the hydration of mucus, which is related to the documented Cl- transport defect.

Effects of endurance training and long distance running on blood viscosity

The effect of endurance training on blood viscosity was studied by comparing blood rheological properties in control subjects (untrained) and endurance trained subjects. The effect of running on blood viscosity was studied in the 33 endurance trained subjects before and after a 48-km mountain race (Sandia Wilderness Crossing Research Run). Runners started at an altitude of 1700 m, ran 26 km to 3300 m, then descended 22 km to finish at 1900 m. Venous blood viscosity (eta b) and plasma viscosity (eta p) were measured at 37 degrees C at shear rates of 11.25, 22.5, 45, 90, and 225.s-1, using a cone-plate viscometer. Endurance trained subjects had significantly higher pre-race blood viscosity at 11.25 and 22.5.s-1 than control subjects but similar plasma viscosity and hematocrits. Following the race, there was no significant change in mean hematocrit, but eta b increased significantly at all shear rates except 225.s-1. Plasma viscosity at 225.s-1 increased significantly from 1.44 to 1.53 cP following the run. Since eta b did not increase, an increase in red cell deformability is inferred. The mechanism of the increase in eta b at lower shear rates in runners is due in part to the higher plasma viscosity. An additional mechanism at lower shear rates is in an increase in red cell aggregation. Increased plasma fibrinogen was measured in six of six resting subjects taken from 1600 m to 3300 m and is speculated to be the mechanism of enhanced aggregation and deformability in the runners.

Effects of gender and age on thixotropic properties of whole blood from healthy adult subjects

The thixotropic parameters of whole blood from 314 healthy subjects (154 women, 160 men) were measured with our modified method by Low shear 30 Rheometer and calculated according Huang's equation. This communication offered the reference range of thixotropic parameters from man and woman group. The results demonstrated that no significant differences existed in the plasma viscosity and fibrinogen between man and woman group. Man group had statistically higher values in HCT, yield stress (tau 0), Newtonian contribution of viscosity (mu), non-Newtonian contribution of viscosity (eta s--mu), apparent viscosity at 2.37 sec-1 (eta s), the equilibrium value of the structural parameter (A) and apparent kinetic rate constant of rouleaux breakdown (ARC) than those in woman group. The man and woman groups could be separately divided into five subgroups in terms of age. It was found that the levels of fibrinogen and plasma viscosity had a tendency of increasing with aging. In the old subgroup (greater than 60 years) of men and women HCT, tau v, mu, eta s, (eta s--mu) and A had significant lower values than those in young and middle-age subgroups. However, it was very interested that there were differences of ARC versus age between man group and woman group, i.e. ARC in the man subgroup II, IV had lower and the woman subgroup II, III, IV had higher values than their respective older subgroup did.

Viscoelastic and rheological properties of concentrated solutions of proteoglycan subunit and proteoglycan aggregate

The oscillatory and steady shear rheological properties of concentrated solutions of proteoglycan subunit (PGS) and aggregate (PGA) from bovine articular cartilage have been studied using a Rheometrics fluids spectrometer. At comparable concentrations in the physiological range tan delta increases from 0.5 to 1.0 for PGA as the oscillation frequency (omega) increases from 10(-1) to 10(2) rads/s, compared to a decrease from 40 to 5 for PGS. Thus PGA solutions exhibit predominantly elastic response whereas those of PGS exhibit primarily viscous behavior. PGA solutions show pronounced shear-thinning behavior at all shear rates (gamma) in the range 10(-2) less than gamma (s-1) less than 10(2), whereas PGS solutions exhibit predominantly Newtonian flow. For PGA, the small-strain complex viscosity eta* (omega) is substantially smaller than the steady-flow viscosity eta(gamma) at comparable values of omega and gamma. These observations indicate that the presence of proteoglycan aggregates leads to formation of a transient or weak-gel network. Since aggregation leads to a large increase in molecular hydrodynamic volume and hence in the relaxation times for macromolecular rotation, it appears that role of aggregate formation is to shift the linear viscoelastic response from the terminal viscous flow into the plateau elastomeric regime of relaxational behavior. Normal or pathological changes that produce a decrease in aggregation will result in a loss of elastomeric behavior of the proteoglycan matrix.

Viscoelastic properties of tissue conditioners — stress relaxation test using Maxwell model analogy

In order to measure the viscoelastic properties of tissue conditioners, a series of stress relaxation tests was carried out using poly ethyl methacrylate polymer powders and liquids composed of butyl phthalyl butyl glycolate/ethyl alcohol mixtures, respectively. The analysis method using the Maxwell model analogy is discussed. The results may be summarized as follows. (i) In this study it was feasible to make the stress relaxation curves for 30 min analogous to the Maxwell model, using a model with a maximum of 5 elements. (ii) The elastic modulus Ei, the coefficient of viscosity eta i, and relaxation time tau i, for each element, and the instantaneous modulus E0, tended to increase with time. These values in the element of the longest relaxation time were most marked in the increase among those in all the elements. Furthermore, in every element the rate of increase of eta i was greater than that of Ei. The method described is considered to be one of the most useful techniques available for the study of the viscoelastic properties of tissue conditioners.

Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization

The undulatory excitations (flickering) of human and camel erythrocytes were evaluated by employing the previously used flicker spectroscopy and by local measurements of the autocorrelation function K (t) of the cell thickness fluctuations using a dynamic image processing technique. By fitting theoretical and experimental flicker spectra relative values of the bending elastic modulus Kc of the membrane and of the cytoplasmic viscosity eta were obtained. The effects of shape changes were monitored by simultaneous measurement of the average light intensity I0 passing the cells and by phase contrast microscopic observation of the cells. Evaluation of the cellular excitations in terms of the quasi-spherical model yielded values of Kc/R3(0) and mu.R0 (R0 = equivalent sphere radius) and allowed us to account (1) for volume changes, (2) for effects of surface tension and spontaneous curvature and (3) for the non-exponential decay of K (t). From the long time decay of K (t) we obtained an upper limit of the bending elastic modulus of normal cells of Kc = 2-3 x 10(-19) Nm which is an order of magnitude larger than the value found by reflection interference contrast microscopy (RICT, Kc = 3.4 x 10(-20) Nm, Zilker et al. 1987) but considerably lower than expected for a bilayer containing 50% cholesterol (Kc = 5 x 10(-19) Nm, Duwe et al. 1989). The major part of the paper deals with long time measurements (order of hours) of variations of the apparent Kc and eta values of single cells (and their reversibility) caused (1) by osmotic volume changes, (2) by discocyte-stomatocyte transitions induced by albumin and triflouperazine, (3) by discocyte-echinocyte transitions induced by expansion of the lipid/protein bilayer (by incubation with lipid vesicles) and by ATP-depletion in physiological NaCl solution, (4), by coupling or decoupling of bilayer and cytoskeleton using wheat germ agglutinin or erythrocytes with elliptocytosis and (5) by cross-linking the cytoskeleton using diamide. These experiments showed: (1) Kc and eta are minimal at physiological osmolarity and temperature and well controlled over a large range of these parameters. (2) Echinocyte formation does not markedly alter the apparent membrane bending stiffness. (3) During swelling the cell may undergo a transient discocyte-stomatocyte transition. (4) Strong increases of the apparent Kc and eta after cup-formation or strong swelling and deflation are due to the effect of shear elasticity and surface tension. Our major conclusions are: (1) The erythrocyte membrane exhibits a shear free deformation regime which requires ATP for its maintenance.(ABSTRACT TRUNCATED AT 400 WORDS)