Calculating Solubility

From Equation (7), s_{c} scales with d^{-3/2} for completely soluble CCN . However, if it the aerosol is composed of sparingly soluble material, s_{c} will change its dependence with d at a specific dry diameter, d^{*} (Figure 1). This is because when d < d^{*}, the amount of water available at the point of activation is not enough to dissolve the solute core (giving a much steeper dependence of s_{c} on d). But when d > d^{*}, all the solute dissolves and s_{c} scales with d^{-3/2}. Therefore the solubility limit of the solute, C_{eq}, occurs at the point where d = d^{*} and can be expressed as:

(10)

where s_{c}^{*} is the critical supersaturation of the particle with dry diameter d^{*}.