共查询到20条相似文献,搜索用时 31 毫秒
1.
The one-dimensional, gravity-driven film flow of a linear (l) or exponential (e) Phan-Thien and Tanner (PTT) liquid, flowing
either on the outer or on the inner surface of a vertical cylinder or over a planar wall, is analyzed. Numerical solution
of the governing equations is generally possible. Analytical solutions are derived only for: (1) l-PTT model in cylindrical
and planar geometries in the absence of solvent, b o [(h)\tilde]s/([(h)\tilde]s +[(h)\tilde]p)=0\beta\equiv {\tilde{\eta}_s}/\left({\tilde{\eta}_s +\tilde{\eta}_p}\right)=0, where [(h)\tilde]p\widetilde{\eta}_p and [(h)\tilde]s\widetilde{\eta}_s are the zero-shear polymer and solvent viscosities, respectively, and the affinity parameter set at ξ = 0; (2) l-PTT or e-PTT model in a planar geometry when β = 0 and x 1 0\xi \ne 0; (3) e-PTT model in planar geometry when β = 0 and ξ = 0. The effect of fluid properties, cylinder radius, [(R)\tilde]\tilde{R}, and flow rate on the velocity profile, the stress components, and the film thickness, [(H)\tilde]\tilde{H}, is determined. On the other hand, the relevant dimensionless numbers, which are the Deborah, De=[(l)\tilde][(U)\tilde]/[(H)\tilde]De={\tilde{\lambda}\tilde{U}}/{\tilde{H}}, and Stokes, St=[(r)\tilde][(g)\tilde][(H)\tilde]2/([(h)\tilde]p +[(h)\tilde]s )[(U)\tilde]St=\tilde{\rho}\tilde{g}\tilde{\rm H}^{2}/\left({\tilde{\eta}_p +\tilde{\eta}_s} \right)\tilde{U}, numbers, depend on [(H)\tilde]\tilde{H} and the average film velocity, [(U)\tilde]\widetilde{U}. This makes necessary a trial and error procedure to obtain [(H)\tilde]\tilde{H}
a posteriori. We find that increasing De, ξ, or the extensibility parameter ε increases shear thinning resulting in a smaller St. The Stokes number decreases as [(R)\tilde]/[(H)\tilde]{\tilde{R}}/{\tilde{H}} decreases down to zero for a film on the outer cylindrical surface, while it asymptotes to very large values when [(R)\tilde]/[(H)\tilde]{\tilde{R}}/{\tilde{H}} decreases down to unity for a film on the inner surface. When x 1 0\xi \ne 0, an upper limit in De exists above which a solution cannot be computed. This critical value increases with ε and decreases with ξ. 相似文献
2.
In-line measurement of rheological properties of polymer melts 总被引:1,自引:0,他引:1
Shear viscosity (), first normal stress difference (N
1), and extensional viscosity (
E
) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure , N
1, and the planar extensional viscosity (
p
) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure and the uniaxial extensional viscosity (
u
) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N
1, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate
E
.The hole pressure method was considered better than the exit pressure method to estimate N
1 (due to the greater susceptibility of the latter to experimental errors). From the hole pressure method N
1 was obtained from 100 kPa to 500 kPa over a range of shear rates from 40 s–1 to 700 s–1. Among the analyses used to estimate the extensional viscosity, Cogswell's is recommended due to its simpler equations without loss of much information compared to the other analyses. The range of extension rates achieved was 1 to 30 s–1. The combination of the hole pressure and entrance pressure drop methods in a slit rheometer is a feasible design for a process rheometer, allowing the simultaneous measurement of the shear viscosity, first normal stress difference and planar extensional viscosity under processing conditions. Similarly, combining the entrance pressure drop measurements with a tube rheometer is also feasible and convenient. 相似文献
3.
Saeid Kheirandish Ilshat Guybaidullin Wendel Wohlleben Norbert Willenbacher 《Rheologica Acta》2008,47(9):999-1013
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.
相似文献
Norbert WillenbacherEmail: |
4.
A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations
studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small
volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3, 102–111, 1960; Kogarko Dokl. AS USSR 137, 1331–1333, 1961; Wijngaarden J. Fluid Mech. 33, 465–474, 1968), and the dispersive shallow water model (Green and Naghdi J. Fluid Mech. 78, 237–246, 1976; Salmon 1988). These models are obtained for special types of the potential function W(r,[(r)\dot],S){W(\rho,\dot \rho,S)} (Gavrilyuk and Teshukov Continuum Mech. Thermodyn. 13, 365–382, 2001). The main feature of the present paper is the study of the potential functions with W
S
≠ 0. The group classification separates these models into 73 different classes. 相似文献
5.
The accurate calculation of the viscosity η as function of the shear rate &γdot; from capillary viscometry is still a matter of debate in the literature. In fact, this problem involves the inversion of
an integral equation, which leads to multiple solutions due to the unavoidable noise present in the experimental data. The
purpose of this work is to develop an efficient procedure to determine the viscosity function from experimental data of capillary
flow without presenting the difficulties inherent in other methods discussed previously in the literature. The system identification
procedure is used here to estimate the parameters of a viscosity model, which is appropriately selected for the fluid under
study through preliminary calculations involving the apparent shear rate – shear stress data. Once the model is chosen by
satisfying criteria for the fit goodness and its parameters are evaluated, a smooth and continuous function η(γdot;) is obtained in the range of experimental shear rates. The procedure proposed is also applicable to fluids in shear flow
that present two Newtonian plateaus, as it is typically found in macromolecular dilute solutions. The mean value theorem of
continuous functions is used to reduce significantly the computational time.
Received: 15 November 1999 Accepted: 7 November 2000 相似文献
6.
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 相似文献
7.
Mette Krog Jensen Ole Hassager Henrik Koblitz Rasmussen Anne Ladegaard Skov Anders Bach Henning Koldbech 《Rheologica Acta》2010,49(1):1-13
A new test fixture for the filament stretch rheometer (FSR) has been developed to measure planar elongation of soft polymeric
networks with application towards pressure-sensitive adhesives (PSAs). The concept of this new geometry is to elongate a tube-like
sample by keeping the perimeter constant. To validate this new technique, soft polymeric networks of poly(propylene oxide)
(PPO) were investigated during deformation. Particle tracking and video recording were used to detect to what extent the imposed
strain rate and the sample perimeter remained constant. It was observed that, by using an appropriate choice of initial sample
height, perimeter, and thickness, the planar stretch ratio will follow l(t) = h(t)/h0 = exp([(e)\dot] t)\lambda(t) = h(t)/h_0= \exp({\dot{\varepsilon}} t), with h(t) being the height at time t and [(e)\dot]{\dot{\varepsilon}} the imposed constant strain rate. The perimeter would decrease by a few percent only, which is found to be negligible. The
ideal planar extension in this new fixture was confirmed by finite element simulations. Analysis of the stress difference,
σ
zz
− σ
xx
, showed a network response similar to that of the classical neo-Hookean model. As the Deborah number was increased, the stress
difference deviated more from the classical prediction due to the dynamic structures in the material. A modified Lodge model
using characteristic parameters from linear viscoelastic measurements gave very good stress predictions at all Deborah numbers
used in the quasi-linear regime. 相似文献
8.
The stress dependencies of the steady-state viscosity η and, particularly, that of the steady-state elastic compliance J
e of various linear isotactic polypropylenes (PP) and one long-chain branched PP are investigated using creep-recovery tests.
The creep stresses applied range from 2 to 10,000 Pa. In order to discuss the stress-dependent viscosity η and elastic compliance J
e with respect to the influence of the weight average molar mass M
w and the polydispersity factor M
w/M
n the PP are characterized by SEC–MALLS. For the linear PP, linear steady-state elastic compliances Je0J_{\rm e}^0 in the range of 10 − 5–10 − 3 Pa − 1 are obtained depending on the molar mass distribution. Je0J_{\rm e}^0 of the LCB-PP is distinctly higher and comes to lie at around 10 − 2 Pa − 1. Je0J_{\rm e}^0 is found to be independent of M
w but strongly dependent on polydispersity. η and J
e decrease with increasing stress. For the linear PP, J
e as a function of the stress τ is temperature independent. The higher M
w/M
n the stronger is the shear thinning of η and the more pronounced is the stress dependence of J
e. For the LCB-PP, the strongest stress dependence of η and J
e is observed. Furthermore, for all PP J
e reacts more sensitively to an increasing stress than η. A qualitative explanation for the stronger stress dependence of J
e compared to η is given by analyzing the contribution of long relaxation times to the viscosity and elasticity. 相似文献
9.
Angel Romo-Uribe 《Rheologica Acta》2007,46(9):1139-1152
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. 相似文献
10.
Yuji Aoki Kentaro Hirayama Koji Kikuchi Masataka Sugimoto Kiyohito Koyama 《Rheologica Acta》2010,49(10):1071-1076
A poly(vinyl chloride) (PVC, Mw = 102×103)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity
and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition
behavior with elevating temperature. The critical gel temperature (Tgel) characterized with a power–law relationship between the storage and loss moduli, G′ and G″, and frequency ω, G¢=G¢¢/tan ( np/2 ) μ wn{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the Tgel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This
finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations
were expressed by the neo-Hookean model at high temperature (135°C) near the Tgel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature.
These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated
from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions. 相似文献
11.
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 Δηc.
Received: 1 December 1998 Accepted: 28 April 1999 相似文献
12.
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. 相似文献
13.
Hideyuki Uematsu Yuji Aoki Masataka Sugimoto Takashi Taniguchi Kiyohito Koyama 《Rheologica Acta》2008,47(2):237-242
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. 相似文献
14.
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. 相似文献
15.
At the same solid volume fraction (Φ) the relative viscosity (η
r
) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension.
In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method.
In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction
Φ
m
which depends upon both the diameter ratio (λ) of large to small particles and the volume fraction of large particles (ξ=Φ
l
/Φ). This model shows that at high solid volume fraction, Φ > 0.40, both λ and ξ significantly influence η
r
. For example, at Φ=0.5, it predicts that for monodisperse suspensions η
r
=70, while for bidisperse suspensions (λ=2 and ξ=0.7) η
r
=40. Comparison shows that, at high solid volume fraction (0.4–0.5), the relative viscosity predicted by this model is in
good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than
that predicted by the work of others.
Received: 27 February 2001 Accepted: 25 April 2001 相似文献
16.
We analyze the quasiperiodic damped Mathieu equation
[(x)\ddot]+ g[(x)\dot]+ x ( 1 + d+ eq(t) )=0 ,\ddot{x}+ \gamma\dot{x}+ x \bigl( 1 + \delta+ \epsilon q(t) \bigr )=0 , 相似文献
17.
In high shear rate capillary rheometry the combined effect of pressure dependent viscosity and dissipative heating becomes significant. Analytical expressions are derived to treat curved Bagley plots and throttle experiments. End effects are taken into account by using an effective length over radius ratio. The non-adiabatic case is described using a lump heat transfer coefficient ? following Hay et al. (1999). The latter enters into the dissipative heating coefficient % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacqaH1oqzdaWgaaWcbaGaemiCaahabeaakiabg2da % 9iabeg8aYnaaCaaaleqabaGaeyOeI0IaeGymaedaaOWaaeWaaeaacq % WGJbWydaWgaaWcbaGaemiCaahabeaakiabgUcaRmaalyaabaGaeu4M % dWeabaGafmyBa0MbaiaaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacq % GHsislcqaIXaqmaaaaaa!4D6C! ep = r - 1 ( cp + L \mathord | / | \vphantom L [(m)\dot] [(m)\dot] ) - 1 \varepsilon _p = \rho ^{ - 1} \left( {c_p + {\Lambda \mathord{\left/ {\vphantom {\Lambda {\dot m}}} \right. \kern-\nulldelimiterspace} {\dot m}}} \right)^{ - 1} ( ? density, c p heat capacity, % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacuWGTbqBgaGaaaaa!3C5E! [(m)\dot] \dot m mass flow rate). A rigorous treatment is possible for incompressible melts, assuming a flat radial temperature profile. For compressible melts, the downstream density variation reduces the effective temperature and pressure coefficients of viscosity. In addition, it causes less dissipative heating. The applicability of the treatment was carefully checked for a well characterised LDPE melt and consistent results from throttle experiments and the Bagley plot curvature are found. The pure dissipation effect was treated by a viscous FEM simulation. A fit of the expected analytical expression to the simulated axial pressure profile allows to extract ?. Throttle experiments allow a reliable determination of the pressure coefficient of viscosity ß ? from a fit of the analytical prediction for the measured pressure loss ? p as function of the die inlet pressure P i, provided the dissipation coefficient from the FEM simulation is used. An analytical solution for the Bagley plot was derived for the pure dissipation or pressure effect, respectively. In the parabola approximation, however, the two contributions may be superimposed. Whereas dissipative heating increases the curvature of the axial pressure profile in a die in the same direction as the pressure effect, it operates in the opposite direction for the Bagley plot curvature. Pressure coefficients solely determined from Bagley plots are not reliable. The effect of variable melt density on the temperature and pressure coefficients of the LDPE remains below 5%. 相似文献
18.
A filament stretching extensional rheometer with a custom-built oven was used to investigate the effect of uniaxial flow on
the crystallization of polypropylene. Prior to stretching, samples were heated to a temperature well above the melt temperature
to erase their thermal and mechanical histories and the Janeschitz-Kriegl protocol was applied. The samples were stretched
at extension rates in the range of 0.01 s-1 £ [(e)\dot] £ 0.75 s-10.01\,\mbox{s}^{-1}\le \dot{{\varepsilon }}\le 0.75\,{\rm s}^{-1} to a final strain of ε = 3.0. After stretching, the samples were allowed to crystallize isothermally. Differential scanning calorimetry was applied
to the crystallized samples to measure the degree of crystallinity. The results showed that a minimum extension rate is required
for an increase in percent crystallization to occur and that there is an extension rate for which percent crystallization
is maximized. No increase in crystallization was observed for extension rates below a critical extension rate corresponding
to a Weissenberg number of approximately Wi = 1. Below this Weissenberg number, the flow is not strong enough to align the contour path of the polymer chains within
the melt and as a result there is no change in the final percent crystallization from the quiescent state. Beyond this critical
extension rate, the percent crystallization was observed to increase to a maximum, which was 18% greater than the quiescent
case, before decaying again at higher extension rates. The increase in crystallinity is likely due to flow-induced orientation
and alignment of contour path of the polymer chains in the flow direction. Polarized light microscopy verified an increase
in number of spherulites and a decrease in spherulite size with increasing extension rate. In addition, small angle X-ray
scattering showed a 7% decrease in inter-lamellar spacing at the transition to flow-induced crystallization. Although an increase
in strain resulted in a slight increase in percent crystallization, no significant trends were observed. Crystallization kinetics
were examined as a function of extension rate by observing the time required for molten samples to crystallize under uniaxial
flow. The crystallization time was defined as the time at which a sudden increase in the transient force measurement was observed.
The crystallization time was found to decrease as one over the extension rate, even for extension rates where no increase
in percent crystallization was observed. As a result, the onset of extensional-flow-induced crystallization was found to occur
at a constant value of strain equal to ε
c
= 5.8. 相似文献
19.
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 τR (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 CS is also in agreement with such a hypothesis.
Received: 29 March 1999/Accepted: 20 March 2000 相似文献
20.
We show that if a Leray–Hopf solution u of the three-dimensional Navier–Stokes equation belongs to C((0,T]; B-1¥,¥){C((0,T]; B^{-1}_{\infty,\infty})} or its jumps in the B-1¥,¥{B^{-1}_{\infty,\infty}}-norm do not exceed a constant multiple of viscosity, then u is regular for (0, T]. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya–Prodi–Serrin
criterion. 相似文献
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