Wall-slip techniques

There is also a variety of wall-slip techniques used in rheological analysis (Gupta, 2000). The methods described here are flow visualization, capillary flow and torsional flow. 

Figure 4.6 shows that all wall-slip techniques can be used successfully to determine the wall slip of a material over a wide range of shear stresses. Once again, for full characterization of wall slip in reactive systems the effects of temperature and extent of cure on wall slip should be determined. 

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

The discussion above that led to Eqs. (4.2.6 and 4.2.7) assumes that the no-slip condition at the wall of the pipe holds. There is no such assumption in the theory for the spatially resolved measurements. We have recently used a different technique for spatially resolved measurements, ultrasonic pulsed Doppler velocimetry, to determine both the viscosity and wall slip velocity in a food suspension [2]. From a rheological standpoint, the theoretical underpinnings of the ultrasonic technique are the same as for the MRI technique. Flence, there is no reason in principle why MRI can not be used for similar measurements. 

The effectiveness of the marker line technique to detect wall-slip is a function of the thickness of the slip layer. For polymer solutions for which the slip layer could be of the order of microns or less, more sophisticated techniques have been applied. 

G.H. Meeten and J.D. Sherwood, Vane Technique for Shear-sensitive and Wall-slipping Fluids, Theoretical and Applied Rheology, P. Moldenaers and R. Kennings (eds.), Elsevier Science B.V., 1992, pp. 935-937. 

Schowalter and coworkers [49-51 ] developed a hot film anemometer to measure wall slip [49]. This particular experimental technique attempted to correlate the pressure and hot film oscillation with the alternation of boundary condition in slit capillary flow of monodisperse polybutadiene (PB). 

On the other hand, the heat fransfer literatiue of the last decade has demonstrated a vivid and growing interest in thermal analysis of flows in micro-channels, botii tiirough experimental and analytical approaches, in connection with cooling techniques of micro-electronics and witii tiie development of micro-electromechanical sensors and actuators (MEMS), as also pointed out in recent reviews [12-16]. Since tiie available analytical information on heat fransfer in ducts could not be directly extended to flows witiiin microch mels with wall slip, a number of contributions have been recentiy directed towards the analysis of internal forced convection in the micro-scale. In the paper by Barron et al. 

Capillary rheometry and parallel-plate rheometry use the fact that wall slip will manifest itself as a geometry-dependent phenomenon. That is, wall slip will appear as a geometric effect on apparent rheological properties. In the capillary-rheometer technique, slip will manifest itself as an effect of capillary diameter ( )) on the shear stress (t, ). Wall slip in capillary rheology can be calculated from an analysis that involves the following ... 

An overview of rheological measurements coupled with magnetic resonance is provided by Callaghan [67], Rheo-NMR of emulsified systems has been studied, the systems including formulations with yield stress exhibiting wall slip [68], Comparisons are provided between conventional rheological techniques and Rheo-NMR characterization. 

Stirring Paddle Devices. In an attempt to overcome these problems as well as the temperature limitation (85 °C) of standard oil field equipment, other devices, similar to the equipment used to measure the thickening time, have been developed (20). The cement slurry contained in a cylindrical cup is usually stirred with a paddle under pressure and temperature. This allows the simulation of the shear history encountered by the fluid during placement. Then, the rotational speed is reduced to a very low value—typically 0.003 rpm—and the torque on the paddle is measured as a function of time. The main advantages of such a technique is that measurements are performed under realistic conditions of pressure, temperature, and shear history. On the other hand, the analysis of the data is not straightforward as the stress distribution in these devices is not known, and it is not clear whether or not measurements are affected by wall slip layers. 

If twin screws are fitted to enhance storage volume, rather than providing a wide outlet for flow, then the capacity can he further enhanced by the use of a central insert ridge between the two, to give a wider base to the hopper section, Fig. 3.7. Although the feeder outlet port is made wider by this technique, the discharging material can be focused by means of an inclined chute at a much lower inclination than that required to stimulate wall slip in the confined flow circumstances within the hopper. This is because flow in the discharge chute is unconfined. 

Characterization of the flow properties of aggregated suspensions is difficult due to long relaxation times and the potential for wall slip in a standard rheometer. A variety of techniques have been developed to reduce wall slip (Walls, 2003 Yoshimura, 1987) including roughening the rheometer tool walls and using a vane such that failure is cohesive as opposed to adhesive (i.e., between particles as opposed to between the slurry and the rheometer wall). As a result of these difficulties, measurements of parameters characterizing flow properties may suffer from poor reproducihiUty (BuscaU, 1987). 

At this point, it is important to remark that there are needed corrections for end effects and wall slip. A discussion on Bagley and Mooney correction techniques is given in reference [2]. 

Slip casting of metal powders closely follows ceramic slip casting techniques (see Ceramics). SHp, which is a viscous Hquid containing finely divided metal particles in a stable suspension, is poured into a plaster-of-Paris mold of the shape desired. As the Hquid is absorbed by the mold, the metal particles are carried to the wall and deposited there. This occurs equally in all directions and equally for metal particles of all sizes which gives a uniformly thick layer of powder deposited at the mold wall. 

Applying Immersed or Embedded Boundary Methods (Mittal and Iaccarino, 2005) circumvents the whole issue of the friction between the more or less steady overall flow in the bulk of the vessel and the strongly transient character of the flow in the zone of the impeller. These methods are introduced below. In the context of a LES, Derksen and Van den Akker (1999) introduced a forcing technique for both the stationary vessel wall and the revolving impeller. They imposed no-slip boundary conditions at the revolving impeller and at the stationary tank wall (including baffles). To this purpose, they developed a specific control algorithm. 

However, in the case of large Kn, the no-slip approximation cannot be applied. This implies that the mean free path of the liquid is on the same length scale as the dimension of the system itself. In such a case, stress and displacement are discontinuous at the interface, so an additional parameter is required to characterize the boundary condition. A simple technique to model this is the one-dimensional slip length, which is the extrapolation length into the wall required to recover the no-slip condition, as shown in Fig. 1. If we consider... 

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