共查询到20条相似文献,搜索用时 359 毫秒
1.
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
2.
Mathematical modeling is performed to simulate forced convection flow of 47 nm- Al2O3/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Single channel flow and conjugate heat transfer
problem are taken into consideration and the heat transfer rate using a nanofluid is examined. Simulations are conducted at
low Reynolds numbers (2 ≤ Re ≤ 16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range
of 0.6 £ [`(Nu)] £ 13 0.6 \le \overline{Nu} \le 13 . Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration.
The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations
of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The
results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and
a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for
practical applications. 相似文献
3.
Zdeněk Skalák 《Journal of Mathematical Fluid Mechanics》2010,12(4):503-535
In the first part of the paper we study decays of solutions of the Navier–Stokes equations on short time intervals. We show,
for example, that if w is a global strong nonzero solution of homogeneous Navier–Stokes equations in a sufficiently smooth (unbounded) domain Ω
⊆ R3 and β ∈[1/2, 1) , then there exist C0 > 1 and δ0 ∈ (0, 1) such that
\frac |||w(t)|||b|||w(t + d)|||b £ C0{\frac {|||w(t)|||_\beta}{|||w(t + \delta)|||_{\beta}}} \leq C_0 相似文献
4.
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
5.
In this article, a similarity solution of the steady boundary layer flow near the stagnation-point flow on a permeable stretching
sheet in a porous medium saturated with a nanofluid and in the presence of internal heat generation/absorption is theoretically
studied. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary
differential equations with the appropriate boundary conditions via Lie-group analysis. Copper (Cu) with water as its base
fluid has been considered and representative results have been obtained for the nanoparticle volume fraction parameter f{\phi} in the range 0 £ f £ 0.2{0\leq \phi \leq 0.2} with the Prandtl number of Pr = 6.8 for the water working fluid. Velocity and temperature profiles as well as the skin friction coefficient and the local
Nusselt number are determined numerically. The influence of pertinent parameters such as nanofluid volume fraction parameter,
the ratio of free stream velocity and stretching velocity parameter, the permeability parameter, suction/blowing parameter,
and heat source/sink parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results
are also presented. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change
the flow pattern. 相似文献
6.
The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density
polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed
at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced
crystallization behavior at rates relevant to processing (elongational rates up to 30 s − 1 and shear rates 1 to 1,000 s − 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation.
In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At
temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was
no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR,
Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures. 相似文献
7.
Drag correction factors are calculated for the creeping motion of spheres descending in various associative polymers of different
concentration with various sphere-container ratios and Weissenberg numbers. The simple-shear rheology and linear viscoelasticity
of these polymeric fluids have been previously presented and modeled with the BMP (Bautista–Manero–Puig) equation of state
(Mendoza-Fuentes et al., Phys Fluids 21:033104, 2009). The drag on the sphere is initially kept nearly constant for small Weissenberg numbers, We < 0.1. As the Weissenberg number
increases, We < 0.1, a reduction in drag is found. Experimental results show the presence of a critical Weissenberg number
at which a drag reduction occurs. The reduction in the drag correction factor is associated to the onset of extension-thinning,
which coincides with the formation of a negative wake. No increase in the drag correction factor was observed, due to the
simultaneous opposing effects of extension-thickening and shear-thinning viscosity. The shape of the drag correction factor
curve may be predicted considering the extensional properties of the solutions, as suggested elsewhere (Chen and Rothstein,
J Non-Newton Fluid Mech 116:205–215, 2004). 相似文献
8.
Turbulence in rough-wall boundary layers: universality issues 总被引:1,自引:0,他引:1
Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine
the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer.
Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements,
a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds
number (Re
θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of
the ratio of roughness element height h to boundary layer thickness δ was covered (0.04 £ h/d £ 0.400.04 \leq h/\delta \leq 0.40). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly
large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously
found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing
with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis
confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken
together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results
provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the
data also confirm that mean flow and turbulence quantities are essentially independent of Re
θ; all the Reynolds stresses match those of smooth-wall flows at very high Re
θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even
at quite low h/δ. 相似文献
9.
In this article a semi-analytical approach is employed to obtain dimensionless heat transfer correlations for forced convection
from isothermal circular cylinders with active ends and different aspect ratios (l/d £ 8) (l/d \le 8) in laminar axial air flows. Then, using the present results and previous works, the modeling is extended to higher aspect
ratios (l/d 3 8) (l/d \ge 8) ) as long as the entire flow field remains completely laminar. Validations of the present work are done not only with the
available data on drag coefficients but with previous works for long cylinders with inactive ends and long spheroids. Two
general correlations are also developed for a rough estimate of forced convection heat transfer from isothermal cylinders
with active ends and arbitrary aspect ratios in the range of
\frac12 £ \fracld £ 8 \frac{1}{2} \le \frac{l}{d} \le 8 and l/d 3 8 l/d \ge 8 . 相似文献
10.
Mahesh Nerurkar 《Journal of Dynamics and Differential Equations》2011,23(3):451-473
Consider the class of C
r
-smooth
SL(2, \mathbb R){SL(2, \mathbb R)} valued cocycles, based on the rotation flow on the two torus with irrational rotation number α. We show that in this class,
(i) cocycles with positive Lyapunov exponents are dense and (ii) cocycles that are either uniformly hyperbolic or proximal
are generic, if α satisfies the following Liouville type condition:
|a-\fracpnqn| £ C exp (-qr+1+kn)\left|\alpha-\frac{p_n}{q_n}\right| \leq C {\rm exp} (-q^{r+1+\kappa}_{n}), where C > 0 and 0 < k < 1{0 < \kappa <1 } are some constants and
\fracPnqn{\frac{P_n}{q_n}} is some sequence of irreducible fractions. 相似文献
11.
Henning Storz Ulrich Zimmermann Heiko Zimmermann Werner-Michael Kulicke 《Rheologica Acta》2010,49(2):155-167
Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHVN, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHVT, 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. 相似文献
12.
A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation
imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as where ε is the Hencky strain, is a constant elongational rate for the base elongational flow, Λ the strain amplitude (Λ ≥ 0), and Ω the strain frequency. A narrow molecular mass distribution linear polystyrene with a molecular weight of 145 kg/mol was subjected
to the oscillative flow. The onset of the steady periodic regime is reached at the same Hencky strain as the onset of the
steady elongational viscosity ( Λ = 0). The integral molecular stress function formulation within the ‘interchain pressure’ concept agrees qualitatively with
the experiments. 相似文献
13.
Olivier Lafitte Mark Williams Kevin Zumbrun 《Archive for Rational Mechanics and Analysis》2012,204(1):141-187
The rigorous study of spectral stability for strong detonations was begun by Erpenbeck (Phys. Fluids 5:604–614 1962). Working with the Zeldovitch–von Neumann–D?ring (ZND) model (more precisely, Erpenbeck worked with an extension of ZND to
general chemistry and thermodynamics), which assumes a finite reaction rate but ignores effects such as viscosity corresponding
to second order derivatives, he used a normal mode analysis to define a stability function V(t,e){V(\tau,\epsilon)} whose zeros in ${\mathfrak{R}\tau > 0}${\mathfrak{R}\tau > 0} correspond to multidimensional perturbations of a steady detonation profile that grow exponentially in time. Later in a remarkable
paper (Erpenbeck in Phys. Fluids 9:1293–1306, 1966; Stability of detonations for disturbances of small transverse wavelength, 1965) he provided strong evidence, by a combination of formal and rigorous arguments, that for certain classes of steady ZND profiles,
unstable zeros of V exist for perturbations of sufficiently large transverse wavenumber e{\epsilon} , even when the von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in the sense defined (nearly 20 years
later) by Majda. In spite of a great deal of later numerical work devoted to computing the zeros of V(t,e){V(\tau,\epsilon)} , the paper (Erpenbeck in Phys. Fluids 9:1293–1306, 1966) remains one of the few works we know of [another is Erpenbeck (Phys. Fluids 7:684–696, 1964), which considers perturbations for which the ratio of longitudinal over transverse components approaches ∞] that presents
a detailed and convincing theoretical argument for detecting them. The analysis in Erpenbeck (Phys. Fluids 9:1293–1306, 1966) points the way toward, but does not constitute, a mathematical proof that such unstable zeros exist. In this paper we identify
the mathematical issues left unresolved in Erpenbeck (Phys. Fluids 9:1293–1306, 1966) and provide proofs, together with certain simplifications and extensions, of the main conclusions about stability and instability
of detonations contained in that paper. The main mathematical problem, and our principal focus here, is to determine the precise
asymptotic behavior as e?¥{\epsilon\to\infty} of solutions to a linear system of ODEs in x, depending on e{\epsilon} and a complex frequency τ as parameters, with turning points x
* on the half-line [0,∞). 相似文献
14.
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
15.
Two-dimensional flow over periodically arranged hills was investigated experimentally in a water channel. Two-dimensional
particle image velocimetry (PIV) and one-dimensional laser Doppler anemometry (LDA) measurements were undertaken at four Reynolds
numbers (
\text5,600 £ Re £ \text37,000\text{5,600} \le Re \le \text{37,000}). Two-dimensional PIV field measurements were thoroughly validated by means of point-by-point 1D LDA measurements at certain
positions of the flow. A detailed study of the periodicity and the homogeneity was undertaken, which demonstrates that the
flow can be regarded as two-dimensional and periodic for
Re 3 \text10,000Re \ge \text{10,000}. We found a decreasing reattachment length with increasing Reynolds number. This is connected to a higher momentum in the
near-wall zone close to flow separation which comes from the velocity speed up above the obstacle. This leads to a velocity
overshoot directly above the hill crest which increases with Reynolds number as the inner layer depth decreases. The flow
speed up above that layer is independent of the Reynolds number which supports the assumption of inviscid flow disturbance
in the outer layer usually made in asymptotic theory for flow over small hills. 相似文献
16.
Heinrich Freistühler Peter Szmolyan 《Archive for Rational Mechanics and Analysis》2010,195(2):353-373
A planar viscous shock profile of a hyperbolic–parabolic system of conservation laws is a steady solution in a moving coordinate
frame. The asymptotic stability of viscous profiles and the related vanishing-viscosity limit are delicate questions already
in the well understood case of one space dimension and even more so in the case of several space dimensions. It is a natural
idea to study the stability of viscous profiles by analyzing the spectrum of the linearization about the profile. The Evans
function method provides a geometric dynamical-systems framework to study the eigenvalue problem. In this approach eigenvalues
correspond to zeros of an essentially analytic function E(rl,rw){\mathcal{E}(\rho\lambda,\rho\omega)} which detects nontrivial intersections of the so-called stable and unstable spaces, that is, spaces of solutions that decay
on one (“−∞”) or the other side (“ + ∞”) of the shock wave, respectively. In a series of pioneering papers, Kevin Zumbrun
and collaborators have established in various contexts that spectral stability, that is, the non-vanishing of E(rl,rw){\mathcal{E}(\rho\lambda,\rho\omega)} and the non-vanishing of the Lopatinski–Kreiss–Majda function Δ(λ,ω), imply nonlinear stability of viscous shock profiles in several space dimensions. In this paper we show that these conditions
hold true for small amplitude extreme shocks under natural assumptions. This is done by exploiting the slow-fast nature of
the small-amplitude limit, which was used in a previous paper by the authors to prove spectral stability of small-amplitude
shock waves in one space dimension. Geometric singular perturbation methods are applied to decompose the stable and unstable
spaces into subbundles with good control over their limiting behavior. Three qualitatively different regimes are distinguished
that relate the small strength e{\epsilon} of the shock wave to appropriate ranges of values of the spectral parameters (ρλ, ρ
ω). Various rescalings are used to overcome apparent degeneracies in the problem caused by loss of hyperbolicity or lack of
transversality. 相似文献
17.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}
18.
A polystyrene-b-poly-4-vinypyridine (PS-b-P4VP) diblock copolymer is modified with a gold precursor to obtain an organic–inorganic (hybrid) block copolymer in bulk
with gold nanoparticles selectively incorporated in the P4VP block. In the linear viscoelastic regime, temperature sweep tests
over a series of these hybrid block copolymer systems revealed consistent shifts (ΔT) in the glass transition temperatures (both T
g\text-PS_{\rm g\text{-}PS} and T
g\text-P4VP_{\rm g\text{-}P4VP}) of the hybrid materials in comparison to the pristine polymers. Studying different volume fractions of the pyridine block,
a level-off point was found for block copolymers with f
P4VP > 0.26, where the shifts in T
g\text-P4VP_{\rm g\text{-}P4VP} consistently increased up to ΔT = 25°C. By artificially increasing the volume fraction of the pyridine block, the nanoparticles reduce the transition regime
determined in master curves. At higher volume fractions of the pyridine block, crossover frequencies were not detected after
the entanglement regime, indicating that the material does not relax from topological constraints (entanglements and nanoparticles)
into the terminal regime. Above a specific volume fraction of nanoparticles (Φ
P = 0.05), the flow behaviour of the hybrid materials becomes increasingly elastic, exhibiting wall-slip from the geometry
at lower strain values in comparison to the pristine material. In the non-linear viscoelastic regime, Fourier-transformed
rheology was used to analyse the raw signals from strain sweep experiments. It was clearly demonstrated the nanoparticle effect
by following the second and third harmonic (I
2/1, I
3/1) of the stress response. Comparing the behaviour of the third and second harmonics provided an unambiguous fingerprint for
the effect of the nanoparticles. 相似文献
19.
The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity
components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Red of 7,200 based on free stream velocity (U
∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream
locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further
to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases
by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing
α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise
spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence
slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v2)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u2)] \overline{{u^{2}}} and [`(w2)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u2)] \overline{{u^{2}}} and [`(v2)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for
a larger α. 相似文献
20.
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
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