The slow viscous flow of liquids

At this stage, one has to take into account the volume compressibility of the material, since upon feed-up the hold-on time of material under pressure is determined by compressibility and slow viscous flow. If the pressure of injection PQ is sufficiently high, then at this stage a liquid may be considered to be Newtonian with viscosity q ,. Keeping this in mind, we may state that the calculation given below will be applicable to various plastisols (of types I and II) with the only difference that for plastisol I q = const, while for plastisol II q = q. For the sake of simplicity, the analysis will be performed for the case of a flat mould filled through a slit runner (Fig. 10 a). 

Small Reynolds Number Flow, Re < 1. The slow viscous motion without interfacial mass transfer is described by the Hadamard (66)-Rybcynski (67) solution. For infinite liquid viscosity the result specializes to that of the Stokes flow over a rigid sphere. An approximate transient analysis to establish the internal motion has been performed (68), Some simplified heat and mass transfer analyses (69, 70) using the Hadamard-Rybcynski solution to describe the flow field also exist. These results are usually obtained through numerical integration since analytical solutions are usually difficult to obtain. 

Langlois WE (1964) Slow Viscous Flow. Macmillan, New York Laux H (1998) Modeling of dilute and dense dispersed fluid-particle flow. Dr Ing Thesis, Norwegian University of Science and Technology, Trondheim, Norway Lawler MT, Lu P-C (1971) The role of lift in radial migration of particles in a pipe flow. In Zandi 1 (ed) Advances in Solid-Liquid Flow in Pipes and its Apphcations. Pergamon Press, Oxford, Chap 3, pp. 39-57 Lee SL (1987) Particle drag in a dilute turbulent two-phase suspension flow. Int J Multiphase Flow 13(2) 247-256... 

Emulsoids differ in several ways from suspensoids they are usually more viscous, not easily precipitated by electrolytes, and usually their surface tension is markedly lower than that of the solvent. They also protect suspensoids from precipitation. Graham (V) said the flow of liquid colloids through a capillary tube is always slow compared with the flow of crystalloid solutions, so that a liquid-transpiration tube may be employed as a colloidoscope. The precipitation of emulsoids by electrolytes follows a different course from that... 

At low values of the Reynolds number, less than about 10, a laminar or viscous zone exists and the slope of the power curve on logarithmic coordinates is — 1, which is typical of most viscous flows. This region, which is characterised by slow mixing at both macro-arid micro-levels, is where the majority of the highly viscous (Newtonian as well as non-Newtonian) liquids are processed. 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

The final main category of non-Newtonian behaviour is viscoelasticity. As the name implies, viscoelastic fluids exhibit a combination of ordinary liquid-like (viscous) and solid-like (elastic) behaviour. The most important viscoelastic fluids are molten polymers but other materials containing macromolecules or long flexible particles, such as fibre suspensions, are viscoelastic. An everyday example of purely viscous and viscoelastic behaviour can be seen with different types of soup. When a thin , watery soup is stirred in a bowl and the stirring then stopped, the soup continues to flow round the bowl and gradually comes to rest. This is an example of purely viscous behaviour. In contrast, with certain thick soups, on cessation of stirring the soup rapidly slows down and then recoils slightly. 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

Preparation of Antimony Trifluorodichloride (SbF3Cl2). This is made in the steel reaction vessel, described on p. 59. A known quantity of antimony fluoride is placed in the vessel the vessel is evacuated, the needle valve is closed, and the whole is weighed. Connection is established to a chlorine cylinder, and the needle valve is opened to permit qhlorine to fill the vessel. Part of it is absorbed rapidly by the salt, with evolution of heat. Soon the reaction slows down as indicated by the rate of pressure fall when the needle valve is dosed. Weighing indicates the amount of chlorine present in the vessel. When the absorption practically ceases, the valve is closed, and the connection with the chlorine tank is removed. The reaction vessel is alternately heated gently, then allowed to cool in order to permit SbFsCl2, which is a viscous liquid, to flow and expose fresh surfaces of crystalline antimony trifluoride. The operation is ended after the absorption of the desired quantity of chlorine. 

Abstract Macromolecular coils are deformed in flow, while optically anisotropic parts (and segments) of the macromolecules are oriented by flow, so that polymers and their solutions become optically anisotropic. This is true for a macromolecule whether it is in a viscous liquid or is surrounded by other chains. The optical anisotropy of a system appears to be directly connected with the mean orientation of segments and, thus, it provides the most direct observation of the relaxation of the segments, both in dilute and in concentrated solutions of polymers. The results of the theory for dilute solutions provide an instrument for the investigation of the structure and properties of a macromolecule. In application to very concentrated solutions, the optical anisotropy provides the important means for the investigation of slow relaxation processes. The evidence can be decisive for understanding the mechanism of the relaxation. 

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