Evaporation Model, Kohler modification and Surface Phenomena
The process of microdroplet evaporation is associated with the mass and heat transport through the microdroplet surface [1,2] .
[2]:
[ 1]
Where a is the droplet radius, Pa and Pcc are the saturated vapor pressures near the droplet surface and far from the droplet respectively. Ta and Tcc are the temperatures at the microdroplet surface and the reservoir. D is the diffusion constant of vapor in the ambient gas. M and are the molecular weight and density respectively. R is the universal gas constant. The vapor pressure at the surface of the droplet is given by [2,3] :
Where is the volume equivalent dry radius or the effective surface volume concentration, is the …show more content…
P3 is the initial volume equivalent dry radius. P4 and P5 are correction parameters accounting for the effect of the growing effective surface concentration of the droplet surface. When P4=0, equation 5 takes the form of equation 4. A comparison of fit of equation 4 and 5 to experimentally determined speed of evaporation aa ̇ is shown in Figure 1 and the insert. The magnified noise present in the experimental data aa ̇ is due to differentiation and uncertainties mentioned in for e.g. [3]. It is worth noticing that the use of the unmodified Raoult term in the Köhler parts of the evaporation model with P2 = -0.17441 and P3 = 2.0509 fails to fit the experimental aa’ in the region when the SDS surfactant starts to appear and populate the surface of the droplet. The deviation of the Köhler term in the evaporation model as result of the presence of SDS inclusions is clearly seen in the insert. Parameterization of the Köhler term to account for such influence for e.g., solute in mixtures for microdroplet activation have been reported in [5–7] with different approaches. Here we try to model the effect of the soluble SDS surfactant inclusions growing surface volume concentrations on an evaporating suspension microdroplet. Figure 1b shows the temporal evolution of the microdroplet radius obtained from droplet sizing with whispering gallery modes and the evolution of the growing effective surface concentration of SDS obtained from equation 5. It could be seen in Figure 1(right) that, the effective surface concentration of SDS is constant from the beginning of the droplet evaporation until it reaches about 298s. At this point, the inclusions were still dispersed within the volume of the microdroplet and beneath the surface of the microdroplet and hence their effect could not be felt. As the evaporation continues, the inclusions begin to appear on the droplet
The process of microdroplet evaporation is associated with the mass and heat transport through the microdroplet surface [1,2] .
[2]:
[ 1]
Where a is the droplet radius, Pa and Pcc are the saturated vapor pressures near the droplet surface and far from the droplet respectively. Ta and Tcc are the temperatures at the microdroplet surface and the reservoir. D is the diffusion constant of vapor in the ambient gas. M and are the molecular weight and density respectively. R is the universal gas constant. The vapor pressure at the surface of the droplet is given by [2,3] :
Where is the volume equivalent dry radius or the effective surface volume concentration, is the …show more content…
P3 is the initial volume equivalent dry radius. P4 and P5 are correction parameters accounting for the effect of the growing effective surface concentration of the droplet surface. When P4=0, equation 5 takes the form of equation 4. A comparison of fit of equation 4 and 5 to experimentally determined speed of evaporation aa ̇ is shown in Figure 1 and the insert. The magnified noise present in the experimental data aa ̇ is due to differentiation and uncertainties mentioned in for e.g. [3]. It is worth noticing that the use of the unmodified Raoult term in the Köhler parts of the evaporation model with P2 = -0.17441 and P3 = 2.0509 fails to fit the experimental aa’ in the region when the SDS surfactant starts to appear and populate the surface of the droplet. The deviation of the Köhler term in the evaporation model as result of the presence of SDS inclusions is clearly seen in the insert. Parameterization of the Köhler term to account for such influence for e.g., solute in mixtures for microdroplet activation have been reported in [5–7] with different approaches. Here we try to model the effect of the soluble SDS surfactant inclusions growing surface volume concentrations on an evaporating suspension microdroplet. Figure 1b shows the temporal evolution of the microdroplet radius obtained from droplet sizing with whispering gallery modes and the evolution of the growing effective surface concentration of SDS obtained from equation 5. It could be seen in Figure 1(right) that, the effective surface concentration of SDS is constant from the beginning of the droplet evaporation until it reaches about 298s. At this point, the inclusions were still dispersed within the volume of the microdroplet and beneath the surface of the microdroplet and hence their effect could not be felt. As the evaporation continues, the inclusions begin to appear on the droplet