Current and droplet size in the electrospraying of liquids. Scaling laws

Measurements of the current and size of the primary droplets of sprays generated by electrostatic atomization of a variety of liquids with different electrical conductivities, permittivities, liquid-gas surface tensions, densities and viscosities have been carried out. Scaling laws of the spray current as well as the charge and size of the droplets have been obtained from a theoretical model of the charge transport. Comparisons between experimental and theoretical results are good. We have found that there are two different behaviours strongly related to the viscosity and electrical conductivity of the liquid. The separation between both behaviours is governed by the dimensionless parameter δμδ1/3=[ɛ02γ3/(K2μ3Q)]1/3; Q, μ, K, γ, and ɛ0 are the flow rate, viscosity, electrical conductivity, surface tension of the gas-liquid interface and vacuum permittivity, respectively. For liquids with high enough conductivities and viscosities (δμδ1/3 ≪ 1), the spray current and droplet size are approximately given by I/I0 = 6.2[Q/(β-1)1/2Q0]1/2 - 2.0 and d/(β-1)1/3d0 = 1.6[Q/ (β - 1)1/2Q0]1/3 - 1.0, where βɛ0 is the liquid permittivity and I0 = (ɛ0γ2/ρ)1/2,d0 = [γɛ02/(ρK2)]1/3 and Q0 = γɛ0/ρK are a reference intensity, droplet size and flow rate, respectively. In the opposite limit, we have found I/I0= 11.0(Q/Q0)1/4 - 5.0 and d/d0 = 1.2(Q/Q0)1/2 -0.3. Comparisons with experimental data reported in the literature are also satisfactory