Elongation flow, types

In transient elongational flow degradation, it was determined in the authors laboratory, by a detailed mass balance, that main chain scission accounted for >95% of the degradation in dilute solution. Any other type of depolymerization, if present, should then be of minor importance. 

The degree of deformation and whether or not a drop breaks is completely determined by Ca, p, the flow type, and the initial drop shape and orientation. If Ca is less than a critical value, Cacri the initially spherical drop is deformed into a stable ellipsoid. If Ca is greater than Cacrit, a stable drop shape does not exist, so the drop will be continually stretched until it breaks. For linear, steady flows, the critical capillary number, Cacrit, is a function of the flow type and p. Figure 14 shows the dependence of CaCTi, on p for flows between elongational flow and simple shear flow. Bentley and Leal (1986) have shown that for flows with vorticity between simple shear flow and planar elongational flow, Caen, lies between the two curves in Fig. 14. The important points to be noted from Fig. 14 are these ... 

Figure 12 shows the estimated liquid flow rate versus the actual liquid flow rate. The tests for Qa — 0.6 m3/h are of the stratified flow type. The tests of 1.8 < Qa < 7.5 m3/h are of the elongated bubble and slug flow type (Brennen, 2005 Govier and Aziz, 1972). In this study, the flow conditions are compared with the flow regime charts of Govier and Omer (1962 in Govier and Aziz, 1972) and Mendhane (1974 in Brennen, 2005). 

Second, a peak-intensity ultrasound echo can be used to detect the gas-liquid interface, but in this case the aim is the development of a flow meter capable of estimating the ratio of component phases accurately and in real time. Our results are promising for the estimation of the liquid flow rate of gas-liquid two-phase flow further research will produce valuable data that will allow the estimation of flow rates for the two phases simultaneously. The results presented here show the liquid flow rate estimated by the peak echo intensity method can provide an accurate estimate of the actual liquid flow rate. This method can be applied to pure liquid as well as to a two-phase flow where the void fraction is as high as 50%. The flows tested are of the stratified, elongated bubble, and slug flow types. Other types of flow such as wave flow and dispersive flow were not tested the present experimental setup does not provide the gas and liquid flow rates needed to achieve such flows. 

Deformation of a Sphere in Various Types of Flows A spherical liquid particle of radius 0.5 in is placed in a liquid medium of identical physical properties. Plot the shape of the particle (a) after 1 s and 2 s in simple shear flow with y 2s1 (b) after 1 s and 2 s in steady elongational flow with e = 1 s 1. (c) In each case, the ratio of the surface area of the deformed particle to the initial one can be calculated. What does this ratio represent ... 

Part 2 presents a summary of the theoretical considerations and basic assumptions that lead to the model equations. Part 3 discusses some experimental aspects and focuses on the measmements in various shear and uniaxial elongational flow situations. Part 4 and 5 are devoted to the comparisons between experimental and predicted rheological functions. Problems encountered in the choice of correct sets of parameters or related to the use of each type of equation will be discussed in view of discrepancies between model and data. 

Polymer Melts. Polymer melts are an extremely important field of study for molecular simulation researchers. Melts play an important role in the processing of polymers into products it is only in the melt phase that they can be suitably shaped. The processing of melts also involves a number of different types of flow geometries, often combining both shear and elongational flow. We briefly report on some studies of melts in equilibrium, under shear and elongational flow. 

The magnitude of most of the effects mentioned also depends on flow type. In elongational flow, for instance, rodlike particles may obtain a parallel orientation in the direction of flow, which tends to decrease the viscosity increase caused by the particles. In turbulent flow, the relations are more complicated. 

Hydrodynamic Retardation. Smoluchowski assumed in the derivation of his equations that )pair = Z)1+Z)2, but this is not true if the diffusing particles are relatively close to each other. When two particles come close, the liquid between them has to flow out of the gap, and this means that (a) the local velocity gradient is increased and (b) the flow type becomes biaxial elongation rather than simple shear (see Section 5.1). Both factors cause the effective viscosity to be increased, which means in turn that the mutual diffusion coefficient of the particles is decreased, the more so as the particle separation (h) is smaller. The phenomenon is called the Spielman-Honig effect. 

Other flow types, especially elongational flow, give other results. Equation (13.8) will not alter very much, but the capture efficiency may be greatly affected. Elongational flow exerts greater stress on a particle pair than simple shear flow (Section 5.1). 

It should further be understood that the deformation will often be of an intermediate type, although elongational components tend to be dominant. Pure biaxial elongation occurs around a gas bubble that expands in a semisolid food. Also the flow of material between two approaching particles is largely biaxial elongation. For undefined flow types, we will use E for modulus and s for strain. 

---