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1.
Rubber compounds are known to exhibit slip at the wall in particular flow conditions. The slip velocity is usually determined by using the classical Mooney method. The rheological behavior of a styrene butadiene rubber (SBR) compound was studied with three different rheometers. Biconical rotational, capillary and slit die rheometers were used to define the true viscous behavior of the compound and the slip velocity. It was shown that it was impossible to apply the Mooney method to our experimental data. New characterizations were thus developed for both capillary and slit die experiments. They were based on the dependency of the slip velocity on the local flow gap. Contrarily to the Mooney method, they provided physically acceptable results and led to a power-law relationship between wall slip, wall shear stress and local geometry of the flow. 相似文献
2.
Flow experiments through capillaries with 0.2% xanthan in aqueous solution and 0.1 N NaCl brine were carried out to study the influence of the molecular conformation on the flow development at relatively low shear rates, from 20s–1 to 400s–1. Capillaries with a wide range of length-to-diameter ratios, L/D = 4.5 to 1015 were used.The apparent viscosity as a function of L/D at a constant shear rate shows a continuous decrement of the viscosity as L/D increases, until an asymptotic value is reached. The decrement in the apparent viscosity is partially explained in terms of slip. It was found that slip is a function of L/D as well as shear stress, i.e., slip develops during flow, thus inducing spatial anisotropy in the fluid until a stable state is reached. However, the substantial difference in apparent viscosity between short capillaries and capillaries longer than 300 D may be attributed to dominant elongational flow due to the contraction in the small capillaries and slip in long capillaries.The flow in a sufficiently long capillary can be divided in four regions rather than three, as is usually assumed. In the first region, which corresponds to the entry, elongational and shear flow coexist and elongational flow dominant. In the second region, end effects and slip development are coupled. In the third region the flow is fully developed and end effects are negligible. However, the fluid shows physical characteristics different from those of the fluid at rest, as a consequence of prior slip development. The fourth zone is the exit region in which the velocity rearranges due to the change of boundary conditions. The length of each region depends on the conformation of the macromolecules and shear rate. In addition, it was found that the stiffness of xanthan increases with the increase of the ionic strength.Finally, a performance of Bagley's analysis in the whole range of L/D studied showed that the use of the Bagley correction is not a reliable way to correct for end effects when the flow is not fully developed and/or in the presence of slip.Dedicated to Arthur S. Lodge at the occasion of his 70th birthday and his retirement from the University of Wisconsin. 相似文献
3.
《力学快报》2022,12(5):100357
Hybrid nanofluids have attracted burgeoning attention owing to their outstanding capacity to improve heat transfer. The influence of velocity and temperature slip parameter and nanoparticls' (NPs') volume fraction on a vertical plate in the existence of suction has been explored in this work. The investigation's controlling partial differentiation equations were transformed into a conventional differential equation mechanism using resemblance modifications. Equations were then solved employing the fifth-order Runge-Kutta method. The skin coefficient of friction, temperature, and temperature gradient all rise when the volume percentage of NPs increases from 0 to 2%. Furthermore, a rise in the temperature slip variable was linked to a drop in the Nusselt number (heat transfer).The Nusselt number increased 0.15% and 5.63% respectively when the velocity slip parameter enhanced from 0 to 5 and the NPs volume percentage were increased from 0 to 1.5%. Furthermore, an increase in the temperature slip from 0 to 3 inflated the x-direction skin friction coefficient 8.2%, while inflation in the velocity slip from 0 to 5 was associated with a decline in the x-direction skin friction coefficient 95%. 相似文献
4.
Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using
an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for
interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization
to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and
wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence,
are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding
approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with
interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures
for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates
determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C.
Mean flow velocity in the capillaries was between 5 × 10−3 and 5 × 10−1 m s−1. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about
100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear
flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear
stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional
viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high
extension rates (up to 800 s−1) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put
into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional
flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful
means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion
and optimization of die design. 相似文献
5.
Single-phase and two-phase flow pressure drops caused by flow area expansion and contraction were measured using air and water. The test section consisted of two capillaries with 0.84 mm and 1.6 mm diameters. For single-phase flow, the Reynolds numbers defined based on the smaller diameter capillary covered the range 160–11,000. For two-phase flow, the all-liquid Reynolds number based on the smaller capillary varied in the 410–1020 range, and the flow quality varied in the 0.018–0.2 range. The single-phase flow loss coefficients for both flow area expansion and contraction were empirically correlated. For two-phase flow, the data indicated the occurrence of significant velocity slip, and the one-dimensional homogeneous flow model utterly disagreed with the data. For flow area expansion the one-dimensional slip flow model along with an Armand-type slip ratio correlation could predict the data well. For flow area contraction, the one-dimensional slip flow model along with the slip ratio expression of Zivi agreed with the data very well, provided that no vena-contracta was considered. 相似文献
6.
In this paper, a theoretical analysis is presented for magnetohydrodynamic flow of blood in a capillary, its lumen being porous and wall permeable. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Thermal radiation, velocity slip and thermal slip conditions are taken into account. In order to study the flow field as well as the temperature field, the problem is formulated as a boundary value problem consisting of a system of nonlinear coupled partial differential equations. The problem is analysed by using similarity transformation and boundary layer approximation. Solution of the problem is achieved by developing a suitable numerical method and using high speed computers. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented in graphical/tabular form. Effects of different parameters are adequately discussed. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding/regulating blood flow and heat transfer in capillaries. 相似文献
7.
When the flow behaviour of fluids is investigated with capillary-or rotational rheometers, adhesion of the fluid to the wall is normally one of the boundary conditions. For many fluids, especially for suspensions, this assumption is not valid. These fluids tend to slip at the wall. Therefore the normal evaluation of rheometer measurements leads to apparent but not compatible flow functions. The flow behaviour of these fluids can be characterized with two material functions which describe separately slipping in the boundary layer and shearing within the fluid. Only if both functions are known, correct predictions of flow processes are possible. A simple equipment to separate the shear function and the slip function is described.List of symbols Y*
apparent shear rate
- Y
w
*
apparent wall shear rate
- Yw
wall shear rate corrected with Rabinowitsch and Weissenberg correction
- Ys
reduced shear rate (slip corrected)
- Yws
reduced wall shear rate (slip corrected)
- * (r)
velocity distribution in a capillary
- G
slip velocity (at the wall)
- * (r)
velocity distribution in a capillary (without slip)
-
shear stress
-
w
wall shear stress
- VS
total volume rate
- VG
shear volume rate
- VG
slip volume rate
-
p
1
pressure in the reservoir channel of the capillary rheometer
-
p
0
athmospheric pressure
-
L
capillary length
-
R
capillary radius 相似文献
8.
《ournal of non Newtonian Fluid Mechanics》2005,129(1):38-45
A slip analysis has been developed to calculate the slip velocities from the capillary rheometry data for a polydimethylsiloxane (PDMS) gum, and two silicon rubber compounds. The analysis generalises the classical Mooney method [J. Rheol. 2 (1931) 210–222] to incorporate the influence of die geometry on the slip behaviour. For the PDMS gum, no slippage was observed below a stress level of about 60 kPa, and there was a jump in the slip velocity at a stress level of about 80 kPa. The complex rheological behaviour of the rubbers meant that the analysis was only applicable at higher stress levels. For each material, a reasonable fit to the slip velocity was obtained using a generalised Navier slip law, which can easily be implemented into computational fluid dynamic simulations. Ultimately, a more realistic slip law is required to model the observed flow behaviour correctly. 相似文献
9.
Francisco Rodríguez-González José Pérez-González Lourdes de Vargas Benjamín M. Marín-Santibáñez 《Rheologica Acta》2010,49(2):145-154
The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without
slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison
was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing
additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities
with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from
the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function
of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a
power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct
proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a
maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity
profile to become plug like in the presence of shear thinning. 相似文献
10.
The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields
acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800
≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing
Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the
parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing
direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely
laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity
fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow
in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear
to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these
“trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed
in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the
non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches
of disordered motion toward a fully-turbulent state with increasing Re. 相似文献
11.
The phenomenon of wall slip during flow of rubber compounds through capillaries is investigated for a typical styrene-butadiene elastomer with carbon black. It was found that at low temperature (110°C) the dependencies of slip velocity V
c
on shear stress are described by the power law but, additionally, V
c
depends on radius of a channel. At high temperatures there is a critical shear stress below which sliding is absent. Sliding appears only at higher shear stresses where, again, V
c
depends on shear stress and the radius of a channel. 相似文献
12.
G. Hetsroni L.P. Yarin E. Pogrebnyak 《International Journal of Multiphase Flow》2004,30(12):1299-1449
We study the stability of flow in a heated capillary tube with an evaporating meniscus. The behavior of the vapor/liquid system, which undergoes small perturbations, is analyzed by linear approximation, in the frame of a one-dimensional model of capillary flow, with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes, on the flow stability is studied. The velocity, pressure and temperature oscillations in a capillary tube with a constant wall heat flux or a constant wall temperature are determined. A scenario of a possible process at small and moderate Peclet numbers corresponding to the flow in capillaries is considered. The boundaries of stability, subdividing the domains of stable and unstable flows, are outlined, and the values of geometrical and operating parameters corresponding to the transition from stable to unstable flow are estimated. It is shown that the stable capillary flow occurs at relatively small wall heat fluxes, whereas at high ones, the flow is unstable, with continuously growing velocity, pressure and temperature oscillations. 相似文献
13.
14.
A large capacity RAM extruder was designed which provides the opportunity to study high Deborah number (D) flows, with D < 1,000. A modified version of particle image velocimetry was developed to enable the measurement of the velocity field in
dies of arbitrary cross section. During the measurement process, tracer particles were simultaneously illuminated by both
a focused laser beam locally and a lamp globally. Only those particles that passed through the laser beam were taken into
account. The beam was scanned to achieve full field measurements. This method of measurement allowed us to find the location
of a particle in the direction of the optical axis of the lens, i.e. that which makes the particle image on the CCD detector
of the video camera. A device employing this method was designed and used to measure velocity profiles. The results of these
measurements in two cross sections of the square die, at three values of pressure, are presented. The velocity was defined
as the ratio of displacement to the elapsed time during which this displacement occurred. Errors in measurements of the coordinates
and the observation time of particles were estimated as ±20 μm and less than 0.1%, respectively. A large plateau in the axial
velocity profile was found at relatively small Deborah numbers, e.g. D ≈ 28. In flows with higher Deborah numbers, e.g. D ≈ 766, an almost flat velocity profile was detected. Two components of velocity, one longitudinal and one transversal, were
measured simultaneously. However, the transversal component appeared to be less than the error of measurements and less than
1% of the axial velocity.
Received: 4 August 1998 Accepted: 5 April 1999 相似文献
15.
José Pérez-González Juan Javier López-Durán Benjamín M. Marín-Santibá?ez Francisco Rodríguez-González 《Rheologica Acta》2012,51(11-12):937-946
An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid?Cliquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid?Cliquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress. 相似文献
16.
The mechanism of peristaltic magnetohydrodynamic (MHD) flow based on slip and heat transfer effects is studied in an asymmetric channel. An incompressible viscous fluid fills the porous space inside the channel. Long wavelength and zero Reynolds number approximation are used in the flow modeling. Expressions of stream function, longitudinal pressure gradient, and temperature are developed. Various interesting phenomena associated with peristalsis, such as pumping and trapping, are discussed in detail. Further the effects of various pertinent parameters on temperature field and heat transfer coefficient are explained with the help of graphs and tables. It is found that pressure rise over one wavelength decreases in pumping region for large values of slip parameter. Similar behavior is observed for temperature field by increasing the slip parameter. However, the volume of trapped bolus decreases by increasing the slip parameter. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
The flow behavior of a filled suspension consisting of ferrite particles suspended in a polypropylene matrix with and without the addition of a commercial dispersant (Solplus DP310) was studied. The composites were filled with 10, 20, 30, and 40 vol.%. Both capillary and parallel disk rotational flows were employed. On the one hand, dynamic results confirm general trends found for highly concentrated systems. The higher is the filler level, the lower is the linear viscoelastic domain. When adding the dispersant agent, it was shown a larger linear viscoelastic domain, lower moduli values and thus, lower viscosity. Also, the critical strain, G′ and G′′ showed a power law dependency on the volume fraction. On the other hand, the capillary results showed no dependency of the flow properties on the die. Thus, no slip of the suspension at the wall was observed. Actually, this experimental finding elucidated that the significant decrease on viscosity produced by the addition of the dispersant agent at 40 vol.% is principally due to lubricant effects and not at all to slip contributions. The results also reveal three distinct flow regimes. Low, moderate, and high shear rates lead to different microstructure under flow. 相似文献
18.
The shear flow of mayonnaise is generally characterized by an apparent yield stress, shear thinning in steady flow, stress
overshoots upon inception of flow and other time-dependent effects. These observations are usually understood to be the result
of structural rearrangement within the material. Additionally and separately, the possibility that emulsions may exhibit apparent
wall slip on a microscopic scale at a solid-liquid boundary has been reported by some researchers. Thus, observed rheological
behavior is likely to be the result of the interplay between these two phenomena.
In the present work, it is demonstrated that when measurements are sought to be made on mayonnaise using rotational viscometers
visible wall slip occurs, rendering such instruments ineffective for the purpose of making viscosity measurements even at
shear rates as low as 10–3s–1. The factors that influence the onset and extent of slip are investigated with the help of parallel plate viscometers, and
it is concluded that the observed “yielding” of mayonnaise is actually an artifact of the onset of macroscopic slip. Slip
effects are also found in capillary flow but are ameliorated with increasing shear rate. To circumvent these problems, it
is proposed that extensional viscometry be employed for determining the flow behavior of mayonnaises.
Received: 18 August 1997 Accepted: 1 April 1998 相似文献
19.
主要比较了无水乙醇在单根、线性单排、双排毛细管道条件下,其稳定的锥-射流模式喷洒的几项重要指标:在稳定的锥-射流喷洒模式下,雾化的起始电压、电流以及粒径与流量的关系。在实验过程中,由于温度、湿度等环境的不稳定以及装置的制作/安装过程中的精密度不高等因素的影响,实验现象细节存在少量不确定性。但是单管道、单排管道、双排管道三种情况下其起始电压、回滞电压、电流、粒径与流量之间的关系有着相似的规律。即在稳定的电压下:(1)电雾化总流量(Q)的1/2次方与总电流(I)之间成正比;(2)电雾化总流量(Q)的1/2次方与雾化液滴的粒径均值(D)成正比。 相似文献
20.
Norhayani Othman Bashar Jazrawi Parisa Mehrkhodavandi Savvas G. Hatzikiriakos 《Rheologica Acta》2012,51(4):357-369
The wall slip and melt fracture behaviour of several commercial polylactides (PLAs) as well as their rheological properties
under shear and extensional have been investigated. The PLAs have had weight-average molecular weights in the range of 104–105 g/mol and studied in the temperature range of 160–200°C. The solution properties and linear viscoelastic behaviour of melts
indicate linear microstructure behaviour. PLAs with molecular weights greater than a certain value were found to slip, with
the slip velocity to increase with decrease of molecular weight. The capillary data were found to agree well with linear viscoelastic
envelope once correction for slip effects was applied. The onset of melt fracture for the high molecular weight PLAs was found
to occur at about 0.2 to 0.3 MPa, depending on the geometrical characteristics of the dies and independent of temperature.
Addition of 0.5 wt.% of a polycaprolactone (PCL) into the PLA that exhibits melt fracture was found to be effective in eliminating
and delaying the onset of melt fracture to higher shear rates. This is due to significant interfacial slip that occurs in
the presence of PCL. 相似文献