Dynamic viscosity profiles

Figure 17. Dynamic viscosity profiles for the TGDDM/DDS neat resin including isothermal holds at 115, 135, 155, and 170 °C.

Figure 4.7 shows the steady- and dynamic-viscosity profiles as functions of shear rate for a filled reactive epoxy-resin moulding compound. Here, interestingly, the Cox-Merz rule provides a better correlation than does the modified Cox-Merz rule. 

Here, k and /jl are the thermal conductivity and dynamic viscosity of the fluid, respectively. The terms v and T denote the velocity and temperature of the fluid. The first term on the right side of Eq. (4.38) shows the entropy production due to finite temperature differences in axial z and radial r directions, while the second term shows the entropy production due to fluid friction. We may construct the entropy production profiles using Eq. (4.38) if we know the temperature and the velocity fields. 

Figure 4. Correlation of the predicted and experimental viscosity profiles for a dynamic cure including a 135 OC isothermal region.

Figure 14. Viscosity profiles for a dynamic/155 °C isothermal cure.

Figure 18. Viscosity profile for a dynamic/135 C isothermal cure.

In developing the arguments that are presented later in this review, it is necessary to keep in mind the relative scales (dimensions) at which each phase occurs. This is important because the effect of flow on localized corrosion is largely (though not totally) a question of the relative dimensions of the nucleus and the velocity profile in the fluid close to the surface. However, the velocity profile is a sensitive function of the kinematic viscosity, which in turn depends on the density and the dynamic viscosity. Because the kinematic viscosity of water drops by a factor of more than 100 on increasing the temperature from 25 °C to 300 °C, the conclusions drawn from ambient temperature studies of the effect of flow on localized corrosion must be used with great care when describing flow effects at elevated temperatures. 

Figure 3.69. Typical profiles of elastic modulus, loss modulus and dynamic viscosity versus applied frequency for a polymer melt.

The relationship between steady-shear viscosity and dynamic-shear viscosity is also a common fundamental rheological relationship to be examined. The Cox-Merz empirical rule (Cox, 1958) showed for most materials that the steady-shear-viscosity-shear-rate relationship was numerically identical to the dynamic-viscosity-frequency profile, or r] y ) = r] m). Subsequently, modified Cox-Merz rules have been developed for more complex systems (Gleissle and Hochstein, 2003, Doraiswamy et al., 1991). For example Doriswamy et al. (1991) have shown that a modified Cox-Merz relationship holds for filled polymer systems for which r](y ) = t] (yco), where y is the strain amplitude in dynamic shear. 

Section 4.2.1) gives a good description of the steady-shear-dynamic-shear relationship. They found that the following general relationship is a good representation of the chemo-viscosity profile ... 

A brief derivation of the turbulent velocity profile for Newtonian fluids in smooth pipes will first be presented and then extended to power-law fluids. The shear stress at any point in the fluid, at a distance y Irom the wall, is made up of viscous and turbulent contributions, the magnitudes of which vary with distance irom the wall. Expressing shear stress in terms of a dynamic viscosity and an eddy momentum diflnsivity (or eddy kinematic viscosity), E,... 

Figures Illustration of common shear rheology measurements for photopolymerization reactions, (a) Evolution of dynamic viscosity with exposure time for HEMA, HEMA MMA, and MMA monomers photo-polymerized with Darocur 1173. The gel point is defined as the time at which viscosity goes to infinity, (b) Typical profile for modulus change in photopolymerizable gels. G and G" denoting shear (storage) and loss (viscous) moduli. Gel point is defined as when G -G".

Computation of shear viscosity of hard spheres has been attempted using NEMD [11], Modified non-equilibrium molecular dynamics methods have also been developed for study of fluid flows with energy conservation [12], NEMD simulations have also been recently performed to compare and contrast the Poiseuille and Electro-osmotic flow situations. Viscosity profiles obtained from the two types of flows are found to be in good mutual agreement at all locations. The simulation results show that both type of flows conform to continuum transport theories except in the first monolayer of the fluid at the pore wall. The simulations further confirm the existence of enhanced transport rates in the first layer of the fluid in both the cases [13, 14]. 

A study using confocal Raman spectrometry was carried out to determine the concentration profile within the extrudate of rubbery particles in a polyethylene matrix during capillary flow (Chartier et al. 2010). Chartier et al. reported that the effect of the concentration of particles on the apparent viscosity of polymer melts measured using capillary flow was the opposite of that based on observations made using linear dynamic viscosity measurements (Fig. 7.41). Shear-induced migration can be detected from the concentration profile of the components of the... 

Using a Rheometrics mechanical spectrometer and powdered polymer samples, the authors compared the rheological behaviour of two polymers with similar chemical compositions but different structures. The rheological profiles of polymers 21 and 22 were determined between 140 and 400°C by increasing the temperature at 10°C min from 140 to 190°C and from 300 to 400°C. In the predominant region of isoimide-imide conversion (190-300°C), the temperatme was raised by 2 or 5°C increments, the dynamic viscosity rj being measured at each temperature step. At 190°C, the viscosity of poly(isoimide) 21 was approximately 5 X 10 Pas and decreased to a minimum value of 10 Pas at 243°C as the polymer softened and melted. Thermal conversion to polyimide 22 concurrently... 

The flux between two lateral walls caused by the nonuniformity of the ion concentration profiles in the layers adjacent to the electrodes is of the same nature as the heat convection arising while the bottom wall is heated [2]. In the latter case a disturbance of the steady state occurs if the Rayleigh number reachs a certain (critical) value (Ra = gPd AT/vx, where P is the coefficient of bulk heat expansion, d is the distance between the walls, AT the increment of temperature, v the dynamic viscosity, and X the thermal diffusivity) the liquid transforms into a new state with a periodic cell structure in such a way that the circulation in the interior of each cell has an opposite direction compared to that of the adjacent one. According to previous evaluations [53] the critical Rayleigh number in the case of lateral rigid walls is about 1700. 

In reactor tubes in which the flow velocity is low, the flow profiles deviate from that of the plug flow. The reason is that the Reynolds number, Re = wd/v (where w denotes the flow velocity in m/s, d is the diameter of the tube, and v is the kinematic viscosity), yields values that are typical for a laminar flow. The kinematic viscosity, v, is obtained from the dynamic viscosity, x, and density, p, of the flowing media (v = x/p). A typical boundary value for the Reynolds number is 2000 values below this indicate that the flow with a... 

Figure A6.1 Thermophysical property profiles vasus temperature of selected gases at 0.1 MPa (a) density, (b) thermal conductivity, (c) dynamic viscosity, (d) specific heat at constant pressure, (e) Prandtl number, and (f) volumetric expansivity.

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