Design of Atomizers and Burners for Coal-water Slurry

A novel extensional viscometer was developed to measure the extensional properties of aqueous solutions of polymeric material and coal water slurries (CWS) containing additives. When a drop of viscoelastic liquid or CWS containing additives is allowed to form at the end of a capillary tube, it starts to fall once its weight exceeds the retaining force exerted by surface tension. In experiments with aqueous solutions of Polyacrilamide it was observed that a long filament of fluid connected the droplet to the end of the capillary tube. The filament partially supported the droplet slowing its rate of fall. The falling droplet technique is used to determine the extensional properties of polymeric solutions and coal-water slurries. Nine different aqueous solutions of Polyacrilamide E10 were tested spanning a wide range of polymer concentration (1.0%, OS%, 0.25%, 0.125%, 0.0625%, 0.03 125%, 0.015625%, 0.0078 125% and 0.003906% by weight). The extensional viscosity for all solutions was found to be orders of magnitude larger than the shear viscosity. The extensional viscosity increases rapidly with time after the start of stretching. It was also shown that there is a linear relationship between the stress and the strain in the fluid filament, indicating that the fluid behaves like an elastic solid. The modulus of elasticity of the fluid was found to increase with polymer concentration. INTRODUCTION Currently available methods to measure the extensional viscosity are limited to highly viscous liquids. Low viscosity liquids present a special difficulty. Many of the difficulties in the measurement of the extensional viscosity of low viscosity liquids have been described by Walters (1992). In order to measure the steady state extensional viscosity, the fluid must be subjected to a constant rate of extension for a time that is sufficient for the stress to reach a constant value, or alternatively subjected to a constant stress for the rate of extension to become constant. Most reported cases in which it is certain that a steady state was reached involve fluids of very high viscosity and rates of extension not greater than 0.1 sec-1. In this limited range the Trouton Viscosity has invariably been found to be either nearly constant or, at the highest rates of extension, an increasing function of the stretch rate E. With decreasing viscosity it becomes more difficult to control these transient experiments because the limits of the apparatus are exceeded before a steady state shear viscosity is achieved. Then an instantaneous elongational viscosity which depends upon both the deformation rate and the complete defoiirtation history can be evaluated. Only in the case of quasi-steady elongation or elongations which have essentially the same history, can this instantaneous elongational viscosity be used for a unique characterization of the material behavior (Weinberger et al., 1974). Otheiwise the instantaneous rate of stress to strain rate still represents a convenient parameter for practical comparison (Schummer et al. 1983). In this study, we have developed a technique for measurement of the extensional viscosity of polymer solutions and coalwater slunies. The technique is based on the uniaxial extension of a viscoelastic filament by a falling droplet. The technique was capable of yielding satisfactory results for very dilute polymer solutions having very low shear viscosities. In future work, the technique will be applied to coalwater slurries. THEORETICAL BACKGROUND In order to measure the extensional viscosity of polymeric solutions and coal water slurries (CWS) a novel free-fall extensional device was developed. The drip mode of breakup is used to extract information on the extensional properties of polymer solutions and CWS. Figure 1 shows a droplet during its initial stages of fall. The most important feature shown in Fig. 1 is that the fluid necks rapidly and is essentially cylindrical over most of the t id ing filament. The geometry thus appears to provide a means of implementing unifoiin uniaxial extension. The filament is assumed to be in cylindrical foi-m undergoing uniaxial extension, with one end fixed and the other end moving with a velocity V. The initial length and radius are LO and 1-0, and after a time t they are L and r. The length of the specimen at time t is given by L(t) = Lo + V(t') dt' The strain for uniaxial extension is E = II?.(UL,) so the strain rate is € = d [ln(LIL,)] = 1 d L v dt L dt L (3) Assuming that the volume of the filament remains constant during the stretching, then the strain rate can also be defined as where d is the diameter of the filament (d = 2 r). Provided that there are no extreme conditions imposed by the geometry, the balance of the drop weight and surface tension determines the size of € = -2 iuu! (4). the drops. The subsequent fall of h e drop is determined by inertia, surface tension, viscosity, elasticity, gravity and drag. The total stress TZz in the axial direction is given by: where G is the surface tension, m is the mass of the suspended droplet, g is the gravitational acceleration, a is the droplet acceleration and Dr is a correction for the aerodynamic drag on the droplet. Due to the presence of surface tension, the total stress in the radial direction Tn within the filament is T,.,, = 0 r The extensional viscosity (effective) growth function q~ of the fluid in the extending filament is defined by Thus, TZ, Ti-,. = 7 7 ~ & (7)