A new numerical method for the solution of an internally mixed spatially homogeneous sectional model for aerosol nucleation and condensation is proposed. The characteristics method is used to predict droplet sizes within a discrete time step. The method is designed such that 1) a pre-specified number of moments of the droplet size distribution may be preserved, 2) there exists no time step stability restriction related to the condensation rate and section size, 3) highly skewed fixed sectional distributions may be used and 4) it is straightforward to extend to spatially inhomogeneous settings and to incorporate droplet coagulation and break-up. We derive, starting from mass conservation, a consistent internally mixed multi-species aerosol model. For certain condensational growth laws analytical solutions exist, against which the method is validated. Using two-moment and four-moment-preserving schemes, we find first order convergence of the numerical solution to the analytical result, as a function of the number of sections. As the four-moment-preserving scheme does not guarantee positivity of the solution, a hybrid scheme is proposed, which, when needed, locally reverts back to two-moment preservation, to prevent negativity. As an illustration, the method is applied to a complete multi-species homogeneous nucleation and condensation problem.
PMIScience.com is operated by Philip Morris International for the purpose of publishing and disseminating scientific information about Philip Morris International’s efforts in support of its smoke-free product portfolio. This site is a global site for use by scientists, the public health and regulatory communities, and other stakeholders with an interest in tobacco policy. The purpose of this site is not advertising or marketing, nor is it directed at any specific market. It is not intended for use by consumers. New tobacco products sold in the United States are subject to FDA regulation; therefore the content of this site is not intended to make, and nor should it be construed as making, any product related claims in the United States without proper FDA authorization.
Reduced Risk Products ("RRPs”) is the term we use to refer to products that present, are likely to present, or have the potential to present less risk of harm to smokers who switch to these products versus continuing smoking. PMI has a range of RRPs in various stages of development, scientific assessment and commercialization. All of our RRPs are smoke-free products that deliver nicotine with far lower quantities of harmful and potentially harmful constituents than found in cigarette smoke.