Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

The role of the mathematical mean value theorem (MVT) in rheometry: an easy way to convert apparent flow curves into correct ones

The mean value theorem of integral calculus guarantees that the apparent viscosity η _a can easily be converted into the correct viscosity η. For ordinary liquids there is a direct identity between η _a and η but the apparent shear rate (or apparent shear stress) has to be shifted to the representative shear rate γ˙^ (or representative shear stress τ^). A model free approximation scheme is introduced which implies a constant shift factor. The corresponding approximation for η is acceptable for liquids most commonly encountered. For plastic fluids the relation between η and η _a is more complex since it involves a function depending upon α; the yield stress relative to the maximum stress within the viscometer. Using the same approximation scheme as before the shift factor will involve α as well. The corresponding approximation of η is shown to be acceptable for the whole range of α. Received: 7 February 2000/Accepted: 15 February 2000     

Recoverable strains and retardation times of monodisperse suspensions of silicon dioxide spheres in poly(dimethylsiloxane)

Steady-state viscosities η, steady-state recoverable strains γ _rs and characteristic retardation time τ _1/2 were measured for suspensions of monodisperse silicon dioxide (SiO₂) spheres in poly(dimethylsiloxane) (PDMS) with various volume fractions Φ of the suspended spheres at various creep stresses σ ₀. Two different regions are found in plots of η/η _m vs γ _rs, where η/η _m denotes the relative viscosity of the suspensions. In one region, η/η _m is proportional to γ _rs, while γ _rs is independent of η/η _m in the other region. In both regions, τ _1/2 is the functions of the shear strain rate in the steady-state of creep test independently of Φ. The origin of the elasticity is related to the ‘maximally distorted’ cages recovered owing to the repulsive interaction between the SiO₂ spheres and recovery of the cages in the shear-induced clusters of the suspended spheres.     

Steady-shear viscosity and transient stress response for elasto-thixotropic fluids

A phenomenological model for dispersed systems which exhibit complex rheological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to different kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus functionG of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic ordersn=m=2.     

Electrorheological determination of the Leslie viscosity coefficient (α2) of a main-chain liquid crystal polymer in a nematic solvent

Analysis of the electrorheological response of thermotropic solutions of a main-chain liquid crystal polymer (MCLCP) in a low molar mass nematic solvent is performed at a fixed shear rate as a function of the applied field strength. The Leslie viscosity coefficient α₂ can be obtained by least squares fits to an equation describing the balance between the viscous and electric torques, formulated via the two dimensional Leslie-Ericksen-Parodi theory. We find that the increment Δα₂ on dissolving the MCLCP increases linearly with molecular weight, consistent with earlier light scattering measurements of the increment in the twist viscosity, Δγ₁, and also with previous electrorheological measurements of the increment in the Miesowicz viscosity Δη_c. Received: 1 December 1998 Accepted: 28 April 1999     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

Influence of NaClO3 on the rheological behaviour of a micellar solution of CPCl

It is now well know that a small addition of salt to a micellar solution often increases the zero-shear viscosity η₀ of the solution, the understanding of the behaviour at high salt content is more questionable. In this situation, addition of more salt induces a decrease of η₀. In this experimental work we investigate the linear and non-linear rheological behaviour of a new micellar system: CPCl (surfactant)/NaClO₃ (salt). Studies of the evolution of η₀ as well as G₀ (the elastic modulus) or τ_R (the relaxation time) are in agreement with the hypothesis of a diminution of the mean micellar length when, after the maximum η₀, the salt content increases. In the non-linear behaviour (non-Newtonian viscosity) the evolution of γ˙ _c, (which defines the occurrence of the shear thinning) with salt concentration C_S is also in agreement with such a hypothesis. Received: 29 March 1999/Accepted: 20 March 2000     

Shear and elongational flow behavior of acrylic thickener solutions

We investigate the effect of hydrophobic aggregation in alkali-swellable acrylic thickener solutions on shear and extensional flow properties at technically relevant polymer concentrations using the commercial thickener Sterocoll FD as model system. Apparent molecular weight of aggregates in water is M _w  ≈ 10⁸ g/mol and decreases by more than an order of magnitude in ethanol. Zero shear viscosity η ₀ is low and shear thinning is weak compared to the high molecular weight of the aggregates. Linear viscoelastic relaxation is described by the Zimm theory up to frequencies of 10⁴ rad/s, demonstrating that no entanglements are present in these solutions. This is further supported by the concentration dependence of η ₀ and is attributed to strong association within the aggregates. Extensional flow behavior is characterized using the capillary break-up extensional rheometry technique including high-speed imaging. Solutions with ϕ ≥ 1% undergo uniform deformation and show pronounced strain hardening up to large Hencky strains. Elongational relaxation times are more than one order of magnitude lower than the longest shear relaxation times, suggesting that aggregates cannot withstand strong flows and do not contribute to the elongational viscosity.

Elastic properties of a dilute surfactant solution in the shear induced state

The first normal stress differences N ₁ of a highly dilute cationic surfactant solution are investigated in a cone-and-plate rheometer. In continuation of a previous paper (Nowak 1998), where the buildup of a shear induced structure in such a solution was attained after a reduced deformation, the N ₁ turned out to be in proportion to the square of the shear rate γ˙ reduced by a critical value γ˙ _c in a first range above γ˙ _c . At higher shear rates the N ₁ tend to lower values than predicted by this relation. Relaxation experiments were performed in the same geometry to determine the characteristic time scales of the shear induced state's decay. In the lower range above &γdot; _c the stress decay is a monoexponential process, while a second time constant has to be introduced to describe the relaxation in that range, where the N ₁ deviate from the parabolic dependence of the reduced shear rate. Received: 10 May 1999 Accepted: 15 November 2000     

Measurement of pressure coefficient of melt viscosity: drag flow versus capillary flow

The pressure coefficient of viscosity of poly(α-methylstyrene-co-acrylonitrile) was measured using a high-pressure sliding plate rheometer (HPSPR) and two types of capillary rheometer: a piston-driven device with a throttle at the exit [piston capillary rheometer with throttle (PCRWT)] operated at a fixed flow rate, and a counter-pressure nitrogen capillary rheometer (CPNCR) operated at a fixed pressure drop. In the HPSPR, the pressure, shear rate, density, and viscosity are all uniform throughout the sample, while the analysis of capillary data is complicated by the axial pressure gradient and the radial shear rate gradient. The polymer was found to be piezorheologically simple, and the HPSPR data indicated that the pressure coefficient of viscosity β ≡ dln(a _P)/dP decreased slightly with increasing pressure at high pressure. While β from PCRWT data from different laboratories and instruments agreed fairly well, the β values were on average about 2/3 of that from the HPSPR. The CPNCR yields β about 18% lower than that of the HPSPR.     

The effect of 1,3:2,4-<Emphasis Type="Italic">bis</Emphasis>-<Emphasis Type="Italic">O</Emphasis>-(<Emphasis Type="Italic">p</Emphasis>-methylbenzylidene)-<Emphasis Type="SmallCaps">d</Emphasis>-sorbitol (PDTS) on uniaxial elongational viscosity of polypropylene

We investigated the dynamic viscoelasticity and elongational viscosity of polypropylene (PP) containing 0.5 wt% of 1,3:2,4-bis-O-(p-methylbenzylidene)-d-sorbitol (PDTS). The PP/PDTS system exhibited a sol–gel transition (T _gel) at 193 °C. The critical exponent n was nearly equal to 2/3, in agreement with the value predicted by a percolation theory. This critical gel is due to a three-dimensional network structure of PDTS crystals. The elongational viscosity behavior of neat PP followed the linear viscosity growth function 3η ⁺ (t), where η ⁺ (t) is the shear stress growth function in the linear viscoelastic region. The elongational viscosity of the PP/PDTS system also followed the 3η ⁺ (t) above T _gel but did not follow the 3η ⁺ (t) and exhibited strong strain-softening behavior below T _gel. This strain softening can be attributed to breakage of the network structure of PDTS with a critical stress (σ _c) of about 10⁴ Pa.     

An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions

The relationship between particle size distribution and viscosity of concentrated dispersions is of great industrial importance, since it is the key to get high solids dispersions or suspensions. The problem is treated here experimentally as well as theoretically for the special case of strongly interacting colloidal particles. An empirical model based on a generalized Quemada equation is used to describe η as a function of volume fraction for mono- as well as multimodal dispersions. The pre-factor η˜ accounts for the shear rate dependence of η and does not affect the shape of the η vs φ curves. It is shown here for the first time that colloidal interactions do not show up in the maximum packing parameter and φ_max can be calculated from the particle size distribution without further knowledge of the interactions among the suspended particles. On the other hand, the exponent ɛ is controlled by the interactions among the particles. Starting from a limiting value of 2 for non-interacting either colloidal or non-colloidal particles, ɛ generally increases strongly with decreasing particle size. For a given particle system it then can be expressed as a function of the number average particle diameter. As a consequence, the viscosity of bimodal dispersions varies not only with the size ratio of large to small particles, but also depends on the absolute particle size going through a minimum as the size ratio increases. Furthermore, the well-known viscosity minimum for bimodal dispersions with volumetric mixing ratios of around 30/70 of small to large particles is shown to vanish if colloidal interactions contribute significantly. Received: 7 June 2000/Accepted: 12 February 2001     

Melt viscosity of linear and branched poly(butyleneisophthalate)

Linear and branched poly(butyleneisophthalate) samples were synthesized and characterized in terms of the intrinsic viscosity, the molecular weight and the melt viscosity over a wide range of shear rates at 200 °C. An exponent of about 4.6 in the equation relating ₀ to was found for linear samples; this high value is probably due to the high content of cyclic oligomers in low molecular weight samples. Both linear and branched samples exhibited Newtonian behaviour over a rather wide range of shear rates, but for any given melt-viscosity, the branched samples became shear thinning at lower shear rates than the linear ones. Our experimental data were found to fit a previously proposed correlation between the melt viscosity ratio ( _{0, b} / _{0, 1} ) and a branching index quite well.     

Rheology of lyotropic and thermotropic lamellar phases

We investigate the steady-state rheological behaviour of the lamellar phase of a lyotropic system (CpCl, hexanol, brine) and of a thermotropic system (8CB). Power laws characterize the behaviour of the imposed stress as a function of the measured shear rate and similarities are observed for both systems; the same regime γ˙∼σ ^m with m≈1.7 is obtained at low shear stresses corresponding to a texture of oily streaks oriented in the direction of the flow, as shown by microscopic observations. The “onion state” only exists in the case of dilute samples of the lyotropic lamellar phase; the stress then varies as γ˙∼σ ^m with m≈4.8, as already observed by other groups with different systems. Rheological measurements at different temperatures allow determination of different activation energies relating to the still badly understood processes involved in the different rheological regimes. We propose a model which reproduces the experimental power laws and which is based on an analogy with the theory of high-temperature creep in metals and alloys. Received: 19 October 1999/Accepted: 1 November 1999     

Scherk-Type Capillary Graphs

This paper concerns the regularity of a capillary graph (the meniscus profile of liquid in a cylindrical tube) over a corner domain of angle α. By giving an explicit construction of minimal surface solutions previously shown to exist (Indiana Univ. Math. J. 50 (2001), no. 1, 411–441) we clarify two outstanding questions. Solutions are constructed in the case α = π/2 for contact angle data (γ₁, γ₂) = (γ, π − γ) with 0 < γ < π. The solutions given with |γ − π/2| < π/4 are the first known solutions that are not C² up to the corner. This shows that the best known regularity (C^{1, ∈}) is the best possible in some cases. Specific dependence of the H?lder exponent on the contact angle for our examples is given. Solutions with γ = π/4 have continuous, but horizontal, normal vector at the corners in accordance with results of Tam (Pacific J. Math. 124 (1986), 469–482). It is shown that our examples are C^{0, β} up to and including the corner for any β < 1. Solutions with |γ − π/2| > π/4 have a jump discontinuity at the corner. This kind of behavior was suggested by numerical work of Concus and Finn (Microgravity sci. technol. VII/2 (1994), 152–155) and Mittelmann and Zhu (Microgravity sci. technol. IX/1 (1996), 22–27). Our explicit construction, however, allows us to investigate the solutions quantitatively. For example, the trace of these solutions, excluding the jump discontinuity, is C^2/3.     

Rheological behavior of cellulose/monohydrate of n-methylmorpholine n-oxide solutions Part 1: Liquid state

Steady-state and dynamic experiments have been performed on solutions containing cellulose dissolved in monohydrate of N-methylmorpholine N-oxide (NMMO). The dependence of the zero-shear viscosity η₀, and of the terminal relaxation time τ _c , on concentration, average degree of polymerization (DP) and temperature are discussed. The behavior of this semi-rigid, polymolecular polymer in solution differs from that of flexible monodisperse ones. The slope of the plot of log(η₀) versus, on the one hand, log(c) at fixed molecular weight (DP)=600, and, on the other hand, log(DP) at fixed concentration (c=5%w/w) are equal to 4.6 and 5 respectively, instead of 3.4 in the concentrated region. Experimental data for the shear modulus were fitted using the classical Doi-Edwards equation with a log normal distribution of relaxation time. This distribution is compared to the distribution of DP. Received: 25 February1997 Accepted: 30 December 1997     

Molecular orientation in sheared molten thermotropic random copolyester

The macromolecular alignment and texture orientation in sheared thermotropic copolyester were investigated using in situ wide-angle X-ray scattering (WAXS) and polarizing optical microscopy (POM). The molecular behavior was correlated with viscoelastic properties. The polymer is a random copolyester based on 60 mol% 1,4-hydroxybenzoic acid (B) and 40 mol% ethylene terephthalate (ET) units. X-ray scattering showed that the molecular chains were aligned along the flow direction. The degree of molecular orientation, , is an increasing function of the applied shear rate. However, rheo-optics showed that shear flow could not orient the polydomain texture, i.e., neither defect stretching nor elimination of defects was observed. Instead, shear compressed the microdomains and gave rise to long-range orientation correlations. Rheology showed that the nematic melt is viscoelastic, the loss modulus G″ dominates the elastic modulus G′, and the dynamic viscosity η* is shear thinning. Moreover, the steady shear viscosity, η, also behaved shear thinning, while the first normal stress difference N ₁ remained positive. The empirical Cox–Merz rule did not hold, , within the shear rate range studied. The microscopic and rheological properties suggest that B–ET is a flow-aligning nematic polymer.     

Nonlinear rheology of concentrated spherical silica suspensions: 3. Concentration dependence

Nonlinear rheology was examined for concentrated suspensions of spherical silica particles (with radius of 40 nm) in viscous media, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture and pure ethylene glycol. The particles were randomly and isotropically dispersed in the media in the quiescent state, and their effective volume fraction φ_eff ranged from 0.36 to 0.59. For small strains, the particles exhibited linear relaxation of the Brownian stress σ_B due to their diffusion. For large step strains γ, the nonlinear relaxation modulus G(t,γ) exhibited strong damping and obeyed the time-strain separability. This damping was related to γ-insensitivity of strain-induced anisotropy in the particle distribution that resulted in decreases of σ_B/γ. The damping became stronger for larger φ_eff. This φ_eff dependence was related to a hard-core volume effect, i.e., strain-induced collision of the particles that is enhanced for larger φ_eff. Under steady/transient shear flow, the particles exhibited thinning and thickening at low and high γ˙, respectively. The thinning behavior was well described by a BKZ constitutive equation using the G(t,γ) data and attributable to decreases of a Brownian contribution, σ_B/γ˙. The thickening behavior, not described by this equation, was related to dynamic clustering of the particles and corresponding enhancement of the hydrodynamic stress at high γ˙. In this thickening regime, the viscosity growth η₊ after start-up of flow was scaled with a strain γ˙t. Specifically, critical strains γ_d and γ_s for the onset of thickening and achievement of the steadily thickened state were independent of γ˙ but decreased with increasing φ_eff. This φ_eff dependence was again related to the hard-core volume effect, flow-induced collision of the particles enhanced for larger φ_eff. Received: 26 June 1998 Accepted: 9 December 1998     

Linear and non linear rheology of a wormlike micellar system in presence of sodium tosylate

In this experimental work, we investigate the influence of an organic counterion, sodium tosylate, on the rheological properties of an aqueous solution of CTAB at the concentration of 0.05M. With this system we can clearly see shear thickening for small salt concentrations C _s and only shear thinning behavior at higher C _s characterized by a linear evolution of η=f(γ) in a log-log representation. In these evolutions it is only in a very small domain of concentrations of the salt (near C _s =0.035M) that we can observe a nearly constant plateau of the shear stress against shear rate. The values of σ₀ (characterizing the stress plateau), G ₀ (the plateau modulus) and τ_R (the relaxation time) obtained by dynamical rheological measurements, allow to compare experimental results obtained to predicted values of the theory of Cates corresponding to the occurrence of shear induced banding structures. Received: 22 July 1997 Accepted: 3 February 1998