Vortex growth

Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. 

An illustrative example of the previous considerations may be given for polyethylene melts. It is admitted that low density polyethylene (LDPE) melts develop rapid vortex growth in an abrupt contraction, and that high density polyethylene (HDPE) and linear low density polyethylene (LLDPE) melts do not. However, in exit flows, all these polyethylene melts can swell notably, and, for many years, there has been no clear understanding about differences in entry and exit flows of these polymer melts. 

Vortex Growth The formation and growth of the vortex upstream of the contraction is proportional to the De value, which increases with an increase in flow rate (see Eq. 3). This implies that the elastic forces become more dominant as the flow rate increases. When the elastic effects are large enough to suppress the inertial effects, a viscoelastic fluid undergoes transitions from the Newtonian-like behavior (low flow rate structure) to regimes with vortex formation and... 

Less research has been performed on the exit behavior of fluids from the contraction. Generally, the elasticity of a viscoelastic fluid has the opposite effects to fluid inertia. As a result, the large viscoelastic forces that generate vortex behavior upstream work in an opposite fashion downstream of the contraction and thus suppress downstream vortex growth. These flow behaviors were reported by Townsend and Walters [14]. 

Stable flow with strong vortex growth [31]. Obviously, any steady-state, two-dimensional, axisymmetric simulations are incapable of reproducing three-dimensional, time-dependent effects, such as the pulsating flow patterns exhibited by some polymer solutions in contractions. 

Luo, X, L, and Mitsoulis, E. (1990) A Numerical Study of the Effect of Elongational Viscosity on Vortex Growth in Contration Flows of Polyethylene Melts/, Rheol, 34, 309-342. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

Winant, D., and F. K. Browand. 1974. Vortex pairing, the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mechanics 63 237-55. 

With forcing, the air vortices are reinforced. In Fig. 20.3a, one can see the growth of an air vortex at four instances of time. At time 0, the vortex begins to form at the nozzle exit. At times 7t/2, tt, and 37t/2, the air vortex continues its roll-up until it is fully developed. 

Kurita, Y. and Sekiguchi, L, Effect of vortex orifice air distributor on granule growth in conical fluidized bed granulation with bottom entry spray, /. Ghent. Eng. Japan, 33 (2000) 57-66. 

Suspension cells should be transfected when they are in the logarithmic growth phase which is generally, 106-107 cells per mL. It is important to avoid extra pipetting or unnecessary washing steps. Do not vortex cells. 

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