Drag force spherical drop

The term mist generally refers to liquid droplets from submicron size to about 10 /xm. If the diameter exceeds 10 /xm, the aerosol is usually referred to as a spray or simply as droplets. Mists tend to be spherical because of their surface tension and are usually formed by nucleation and the condensation of vapors (6). Larger droplets are formed by bursting of bubbles, by entrainment from surfaces, by spray nozzles, or by splash-type liquid distributors. The large droplets tend to be elongated relative to their direchon of mohon because of the action of drag forces on the drops. 

By equating the drag force F of the sphere with the difference wa gAp between the gravity and buoyancy forces, one can estimate the steady-state velocity of relative motion of phases (the velocity at which a spherical drop falls or rises) as... 

The Stokes experiment consists in dropping a spherical particle of diameter D where Ps>Pf The ball rapidly reaches a constant fall velocity Wc parallel to the gravitational acceleration g. When steady-state velocity is reached, the equilibrium of the forces applied on the ball reduces to the equilibrium between the reduced weight Fg (difference between the weight and Archimedes force) and the hydrodynamic drag force Fr exerted by the fluid flow on the particle. 

The drop deformation is modeled by Taylor s drop oscillator [56], as introduced by O Rourke and Amsden [37] into the context of sprays. In this approach, the drop distortion is described by a forced, damped, harmonic oscillator in which the forcing term is given by the aerodynamic drag, the damping is due to the liquid viscosity, and the restoring force is supplied by the surface tension. More specifically, the drop distortion is described by the deformation parameter, y = 2x/r, where x denotes the maximum radial distortion from the spherical equilibrium surface, and r is the drop radius. The deformation equation in terms of the normalized distortion parameter, y, is... 

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