Rheologically complex liquids pseudoplastic

Keywords Capillary instability of liquid jets Curvature Elongational rheology Free liquid jets Linear stability theory Nonlinear theory Quasi-one-dimensional equations Reynolds number Rheologically complex liquids (pseudoplastic, dilatant, and viscoelastic polymeric liquids) Satellite drops Small perturbations Spatial instability Surface tension Swirl Temporal instability Thermocapillarity Viscosity... 

Abstract This chapter deals with capillary instability of straight free liquid jets moving in air. It begins with linear stability theory for small perturbations of Newtonian liquid jets and discusses the unstable modes, characteristic growth rates, temporal and spatial instabilities and their underlying physical mechanisms. The linear theory also provides an estimate of the main droplet size emerging from capillary breakup. Formation of satellite modes is treated in the framework of either asymptotic methods or direct numerical simulations. Then, such additional effects like thermocapiUarity, or swirl are taken into account. In addition, quasi-one-dimensional approach for description of capillary breakup is introduced and illustrated in detail for Newtonian and rheologically complex liquid jets (pseudoplastic, dilatant, and viscoelastic polymeric liquids). 

As discussed earlier, LADDs are complex, multicomponent mixtures consisting of both organic and inorganic compounds dispersed in a liquid matrix. Such compositions can exhibit a broad range of rheological characteristics from simple Newtonian to complex pseudoplastic flow. Shown in Figure 9.6 and Figure 9.7 are flow and viscosity profiles of Newtonian and non-Newtonian fluids as a function of applied shear rate. A number of mathematical models have been proposed [76] to describe the flow characteristics of various systems. These equations are called constitutive equations and are used to predict flow behavior in complex systems. 

In most cases, the flow properties of polymers in solution or in a molten state are Newtonian, pseudoplastic, or a combination of both. In the case of liquid crystal polymer solutions, the flow behavior is more complex. The profound difference in the rheological behavior of ordinary and liquid crystalline polymers is due to the fact that, for the flrst ones, the molecular orientation is entirely determined by the flow process. The second ones are anisotropic materials already at equilibrium (Acierno and Brostow 1996). The spontaneous molecular orientation is already in existence before the flow and is switched on, varying in space, over distances of several microns or less (polydomain). If one ignores the latter, one can discuss the linear case (slow flow) as long as the rate of deformation due to flow (the magnitude of the symmetric part of the velocity gradient) is lower than the rate at which molecules rearrange their orientational spread by thermal motions. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

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