Couette type flow

Criado-Sancho et al. [38] (CSJCV) extended the DO and CM formulism, but also assumed that Tr a 0, arguing that such an assumption is valid for Couette type flows, if not cone and plate type flows, hi addition they included an isotropic stress as a direct contribution to the free energy, and hence the chemical potential, in an analogous way to the theory of Wolf [23] discussed earher, but within the framework of EIT. Their excess free energy took the form. 

Ti and Nei in Eq. (13) are valid for the case of the Searle type and T2 and Ne2 for the Couette type. The shear stress from Eq. (13) is the maximum shear which occurs in the gap close to the rotating cylinder. The uniformity of stress inside the gap decrease with increasing Re number. If the particles have the tendency to flow close to the moving wall, they will be subjected to the maximum shear. 

Flow birefringence of polymer solutions is, in general, measured with the aid of an apparatus of the Couette type, containing two coaxial cylinders. One of these cylinders is rotated at constant speed, the other is kept in a fixed position. The light beam for the birefringence measurement is directed through the annular gap between these cylinders, in a direction parallel with the axis of the apparatus. In this way, the difference of principal refractive indices An is measured just in the above defined plane of flow (1—2 plane). 

In order to model the flow behavior of molten silicate suspensions such as magmas and slags, the rheological behavior must be known as a function of the concentration of suspended crystals, melt composition, and external conditions. We have determined the viscosity and crystallization sequence for a Kilauea Iki basalt between 1250°C and 1149°C at 100 kPa total pressure and f02 corresponding to the quartz-fayalite-magnetite buffer in an iron-saturated Pt30Rh rotating cup. viscometer of the Couette type. The apparent viscosity varies from 9 to 879 Pa.s. The concentration of suspended crystals varies from 18 volume percent at 1250°C to 59 volume percent at 1149 C. The molten silicate suspension shows power-law behavior ... 

However, the effect of a small perturbation in action-action-angle type flows is quite different. The two-parameter family of invariant cycles coalesce into invariant tori that are connected by resonant sheets defined by the u(h,l2) = 0 condition. The consequence of this is that contrary to action-angle-angle flows in this case a trajectory can cover the whole phase space and no transport barriers exist. Thus, in this type of flows global uniform mixing can be achieved for arbitrarily small perturbations. This type of resonance induced dispersion has been demonstrated numerically in a low-Reynolds number Couette flow between two rotating spheres by Cartwright et al. 

The fluid path in a screw pump is therefore of a complex hehcal form within the channel section. The velocity components along the channel depend on the pressure generated and the resistance at the discharge end. If there is no resistance, the velocity profile in the direction of the channel will be of the Couette type, as depicted in Figure 3.39a. With a totally closed discharge end, the net flow would be zero, but the velocity components at the walls would not be affected. As a result, the flow field necessarily would be of the form shown in Figure 3.39b. 

Rotating cone viscometers are among the most commonly used rheometry devices. These instruments essentially consist of a steel cone which rotates in a chamber filled with the fluid generating a Couette flow regime. Based on the same fundamental concept various types of single and double cone devices are developed. The schematic diagram of a double cone viscometer is shown in... 

Figure 11 shows the reference floe diameter for viscometers as a function of shear stress and also the comparison with the results for stirred tanks. The stress was determined in the case of viscosimeters from Eq. (13) and impeller systems from Eqs. (2) and (4) using the maximum energy density according to Eq. (20). For r > 1 N/m (Ta > 2000), the disintegration performance produced by the flow in the viscosimeter with laminar flow of Taylor eddies is less than that in the turbulent flow of stirred tanks. Whereas in the stirred tank according to Eq. (4) and (16b) the particle diameter is inversely affected by the turbulent stress dp l/T, in viscosimeters it was found for r > 1.5 N/m, independently of the type (Searle or Couette), the dependency dp l/ pi (see Fig. 11). 

The first mode may occur when a droplet is subjected to aerodynamic pressures or viscous stresses in a parallel or rotating flow. A droplet may experience the second type of breakup when exposed to a plane hyperbolic or Couette flow. The third type of breakup may occur when a droplet is in irregular flow patterns. In addition, the actual breakup modes also depend on whether a droplet is subjected to steady acceleration, or suddenly exposed to a high-velocity gas stream.[2701[2751... 

Two common types of one-dimensional flow regimes examined in interfacial studies Poiseuille and Couette flow [37]. Poiseuille flow is a pressure-driven process commonly used to model flow through pipes. It involves the flow of an incompressible fluid between two infinite stationary plates, where the pressure gradient, Sp/Sx, is constant. At steady state, ignoring gravitational effects, we have... 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

The Couette rheometer. Another rheometer commonly used in industry is the concentric cylinder or Couette flow rheometer schematically depicted in Fig. 2.48. The torque, T, and rotational speed, 0, can easily be measured. The torque is related to the shear stress that acts on the inner cylinder wall and the rate of deformation in that region is related to the rotational speed. The type of flow present in a Couette device is analyzed in detail in Chapter 5. 

One important aspect of wire-coating is the thickness distribution of the polymer on the surface of the wire as well as the velocity distribution within the die. A simplified wire coating process is presented in the Fig. 6.37, where the wire radius is defined by R and the annulus radius by kR. This type of flow is often referred to as an axial annular Couette flow. 

Stresses Generated by CEF Fluids in Various Viscometric Flows What stresses are necessary to maintain a CEF fluid flowing in the following flows (a) parallel-plate drag flow (b) Couette flow with the inner cylinder rotating and (c) parallel-plate pressure flow. Assume the same type of velocity fields that would be expected... 

Dynamic filtration modules are basically of two types rotating disc filter (RDF) and vortex flow filter (VFF). In the latter, the filtration module has a cylindrical shape and has a rotating concentric cylindrical mesh in its interior. The rotational movement of the internal cylinder generates a Taylor-Couette flow in the annular gap (Roth et al., 1997), creating Taylor vortices that minimize concentration polarization and mesh fouling. Continuous perfusion processes based on this type of filter and operating continuously for up to 100 days have been reported (Mercille et al., 1994). 

FIG. 15.2 Types of simple shear flow. (A) Couette flow between two coaxial cylinders (B) torsional flow between parallel plates (C) torsional flow between a cone and a plate and (D) Poisseuille flow in a cylindrical tube. After Te Nijenhuis (2007). 

The simplest type of flow of a medium that yields itself to an analytical description within the framework of the precise hydrodynamical equations of viscous liquids (Navier-Stocks equations) is the Couette flow. This flow occurs under the impact of tangential stresses generated in a viscous liquid by a solid surface moving in it. The magnitude of the force that has to be applied to this surface to securse its movement in the viscous medium characterizes the tangential stresses and the velocity of its movement — the shear velocity. 

In [62] Renardy proves the linear stability of Couette flow of an upper-convected Maxwell fluid under the 2issumption of creeping flow. This extends a result of Gorodtsov and Leonov [63], who showed that the eigenvalues have negative real parts (I. e., condition (S3) holds). That result, however, does not allow any claim of stability for non-zero Reynolds number, however small. Also it uses in a crucial way the specific form of the upper-convected derivative in the upper-convected Maxwell model, aind does not generalize so far to other Maxwell-type models. 

Nonlinear stability results for viscoelastic fluids are very few. They essentially concern Jeffreys-type fluids. We have already mentioned those of [47] for the one-dimensional stability of Couette flows (see Section 5.3), and for the stability of flows of Jeffreys-type fluids which are small perturbations of the rest state (see Corollary 4.1). 

Renardy and Renardy [66,73] have investigated the stability of plane Couette flows for Maxwell-type models involving the derivative (2). The flow lies between parallel plates at a = 0 euid x = 1, which are moving in the j/-direction with velocities 1, such as in Figure 6. 

---