Viscous sheets

In practical fan sheet breakup processes, sheet thickness diminishes as the sheet expands away from the atomizer orifice, and liquid viscosity affects the breakup and the resultant droplet size. Dombrowski and Johns[238] considered these realistic factors and derived an analytical correlation for the mean droplet diameter on the basis of an analysis of the aerodynamic instability and disintegration of viscous sheets with particular reference to those generated by fan spray atomizers ... 

England P, McKenzie D (1982) A thin viscous sheet model for continental deformation. Geophys J R Astr Soc 70 295-321... 

Skorobogatiy M. Mahadevan, L. Folding of viscous sheets and filaments. Europhys. Lett. 52, 532-538 (2000). 

Keywords Liquid sheet instability Nonlinear sheet instability Sinuous and dilational disturbances of a liquid sheet Thinning liquid sheet Three dimensional instability of liquid sheets Viscous sheets... 

Arai and Hashimoto [19] reported the following correlation for the sheet breakup length of a viscous sheet ... 

J. Sebilleau, L. Lebon, L. Limat, L. Quartier, and M. Receveur, The dynamics and shapes of a viscous sheet spreading on a moving liquid bath, FPL, 92,14003 [2010]. 

The burden must have a definite sohdification temperature to assure proper pickup from the feed pan. This limitation can be overcome by side feeding through an auxiliary rotating spreader roll. Apphcation hmits are further extended by special feed devices for burdens having oxidation-sensitive and/or supercoohng characteristics. The standard double-drum model turns downward, with adjustable roll spacing to control sheet thickness. The newer twin-drum model (Fig. ll-55b) turns upward and, though subject to variable cake thickness, handles viscous and indefinite solidification-temperature-point burden materials well. 

In the deaeration of high-viscosity fluids such as polymers, the material is flowed in thin sheets along solid surfaces. Vacuum is apphed to increase bubble size and hasten separation. The Versator (Cornell Machine Co.) degasses viscous liquids by spreading them... 

Dry filters are usually deeper than viscous filters. The dry filter media use finer fibers and have much smaller pores than the viscous media and need not rely on an oil coating to retain collected dust. Because of their greater resistance to air flow, dry filters must use lower filtration velocities to avoid excessive pressure drops. Hence, dry media must have larger surface areas and are usually pleated or arranged in the form of pockets (Fig. 17-64), generally sheets of cellulose pulp, cotton, felt, or spun glass. 

Second, the creep modulus, also known as the apparent modulus or viscous modulus when graphed on log-log paper, is normally a straight line and lends itself to extrapolation for longer periods of time. The apparent modulus should be differentiated from the modulus given in the data sheets, which is an instantaneous or static value derived from the testing machine, per ASTM D 638. 

Sundaraj, U., Dori, Y., and Macosko, C. W., Sheet formation in immiscible polymer blends model experiments on an initial blend morphology. Polymer 36,1957-1968 (1995). Swanson, P. D., and Ottino, J. M., A comparative computational and experimental study of chaotic mixing of viscous fluids, J. Fluid Mech. 213, 227-249 (1990). 

Taylod205 also conducted mathematical analysis of the generation of ripples by wind blowing over a viscous fluid. Using a relationship between the growth of the amplitude of disturbance waves and the surface stress, Taylor derived a criterion for the instability of waves. In Taylor s instability theory, the disintegration of a liquid sheet/film is visualized as a process in which droplets are detached from the liquid surface with a wave of optimum amplitude. The diameter of the most frequent droplets is then formulated as a function of air velocity over the liquid surface, liquid density, surface tension and viscosity, as well as air density. 

Flat Sheets. Generally, the interface between a liquid sheet and air can be perturbed by aerodynamic, turbulent, inertial, surface tension, viscous, acoustic, or electrical forces. The stability of the sheet and the growth rate of unstable disturbances are determined by the relative magnitude of these forces. Theoretical and experimental studies 255112561 on disintegration mechanisms of flat sheets showed that the instability and wave formation at the interface between the continuous and discontinuous phases are the maj or factors leading to... 

Weiss and Worsham 259 indicated that the most important factor governing mean droplet size in a spray is the relative velocity between air and liquid, and droplet size distribution depends on the range of excitable wavelengths on the surface of a liquid sheet. The shorter wavelength limit is due to viscous damping, whereas the longer wavelengths are limited by inertia effects. 

For the transition from Ligament to Film/Sheet Formation regime or the reverse transition, the equation of Hinze and MilbornJ112 QX = 0.340 Re2/3/We° 883, may be used to predict the dimensionless transition flow rate for liquids of low viscosities (less than a few poises). For more viscous liquids, the equation derived by Tanasawa et al.,[48°l QX = 0.297 Re6/5/We, is applicable for the calculation of the dimensionless transition flow rate. 

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