# Evaporation Model, Kohler Motification And Surface Phenomena

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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

This means that the effect of density and surface modification from the inclusions during suspension microdroplet evaporation is not considered. To account for the effect of growing concentration of the inclusions on the droplet surface (soluble surfactant (SDS) and the insoluble SiO2 nanospheres), the Köhler term in has to be taken into account. To model equation 4 to account for the effects of the inclusions in the evaporating suspension microdroplet, we considered that: the insoluble inclusions in the microdroplet are perfectly insoluble; the interaction between the totally submersed SiO2 inclusions, the SDS surfactant molecules and the evaporating molecules of dispersing liquid is perfectly negligible. The modification of the Kohler term (Raoult effect) is purely due to the influence of the SDS surfactant addition to the suspension droplet due to their [5]. We also introduce an average microdroplet surface temperature T_ave such that T_a=T_ave=const for the slowly evaporating liquid microdroplet of suspension. This behavior allows us to investigate the modification of the Köhler term in equation 4 as result of the influence of the SDS surfactant growing concentration on the microdroplet surface. In doing so, we introduce correction parameters P4 and P5 accounting for the evolving effective surface

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 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…*This means that the effect of density and surface modification from the inclusions during suspension microdroplet evaporation is not considered. To account for the effect of growing concentration of the inclusions on the droplet surface (soluble surfactant (SDS) and the insoluble SiO2 nanospheres), the Köhler term in has to be taken into account. To model equation 4 to account for the effects of the inclusions in the evaporating suspension microdroplet, we considered that: the insoluble inclusions in the microdroplet are perfectly insoluble; the interaction between the totally submersed SiO2 inclusions, the SDS surfactant molecules and the evaporating molecules of dispersing liquid is perfectly negligible. The modification of the Kohler term (Raoult effect) is purely due to the influence of the SDS surfactant addition to the suspension droplet due to their [5]. We also introduce an average microdroplet surface temperature T_ave such that T_a=T_ave=const for the slowly evaporating liquid microdroplet of suspension. This behavior allows us to investigate the modification of the Köhler term in equation 4 as result of the influence of the SDS surfactant growing concentration on the microdroplet surface. In doing so, we introduce correction parameters P4 and P5 accounting for the evolving effective surface

*…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