Viscous limit scaling laws

Roy and Davidson (1989) considered the validity of the Ml and viscous limit scaling laws at elevated pressures and temperatures. The nondimensional dominant frequency and amplitude of the pressure drop fluctuations were used as the basis of the comparison. They concluded that when the full set of scaling parameters is matched, similarity is achieved. They also suggested that it is not necessary to match the density ratio (ps/pf) and dp/D, the simplification for viscous limit scaling, for particle Reynolds numbers (Re ) less than 30. Although the only run with Redp near 30 which was similar to the low Reynolds number test had the same density ratio as the lowRedp runs. These conclusions may be open to different interpretations. As shown in Table 6, the scaling parameters neither matched closely nor varied in a systematic manner. 

Roy and Davidson (1989) considered the validity of the full and viscous limit scaling laws at elevated pressures and temperatures. The nondimensional dominant frequency and amplitude of the pressure drop fluctuations were used as the basis of the comparison. They concluded that when the full set of scaling parameters is matched, similarity is achieved. 

The characteristic relaxation time t = 1 /(Hp was found to be insensitive to the droplet size a, weakly dependent on the continuous-phase viscosity, and perhaps weakly dependent on r and M also. Although the complete scaling law for r cannot be deduced from this limited set of data, it is evidently influenced by lubrication flow of liquid in the thin films between the deformed droplets, and perhaps also by the circulatory flow in the viscous droplets. 

A model for electrically pulsed jets has been described (26). The viscous drag in a thin nozzle limits the flow rate and leads to intrinsic pulsations of the cone jet. Scaling laws for intrinsic cone jet pulsations have been derived to establish the operating regime for drop deployment. The scaling laws are applicable to similar electro-hydrodynamic processes in miniaturized electrospraying systems. 

Scaling Laws for the Droplets Emitted from Cone-Jets. Recent studies on the laws governing the size of electrosprayed drops have made it possible in some cases to control their initial diameter d at will. Experiments show that relatively inviscid liquids (water, methanol, formamide, etc.) exhibit electrospray regimes where they tend to produce fairly uniform drops. In contrast, highly viscous liqmds such as glycerol tend to break up into more complex sprays which have been studied only to a limited degree. We shall therefore restrict the discussion to solutions with relatively small viscosities. Likewise, we will deal exclusively with polar liquids, which are best suited to form electrosprays of nanodroplets. A limited discussion on alternative situations is available for nonpolar liquids,(75) and on viscous effects (14, 75). 

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