**5. Summary**

hence, surface forces such as drag force and lift force, as well as interaction force between particles can be directly integrated from the shear stress and pressure distribution along the

Compared with CFPD models which are based on Euler-Euler or Euler-Lagrange methods, CNS is a mesoscale model that can accurately describe motions of particles with arbitrary shapes. As such, CNS of multiphase flows can promote fundamental understanding of the underlying physics, e.g., the nonlinear and geometrically complicated phenomena of particle-

With the enhancement of the computational power in the future, CFPD models will be replaced by DNS and CNS methods to simulate unconventional lung aerosol dynamics. However, the computational cost of DNS and CNS methods is still too high for engineering application. Applying these methods to a large number of particles is not realistic according to the current

Discrete element method (DEM) can provide transient forces and torques acting on individual particles. DEM was first proposed by Cundall and Strack [81] based on molecular dynamics. The most attractive feature of DEM method is its relatively efficient algorithms for the contact detection and contact force calculation between arbitrary shaped particles [82]. Soft-sphere models are the most common type of models used in DEM, which simplify particle-particle interaction force with spring-dashpot-slider systems [27]. Determinations of the stiffness coefficients and damping coefficients are essential in DEM interaction models. Contact forces

**2.** Contact resolution: the actual contact forces are calculated. This step involves the accurate calculation of the contact geometry and kinematics, typically characterized by the overlap

Additionally, for nonspherical particles, representation of the particle shape is also essential in DEM simulations. Two major treatments of the particle shape representation are widely used for the contact detection and contact force calculation between nonspherical particles [84]: superquadric method and multisphere method. The algorithm to integrate DEM with Euler-Euler and Euler-Lagrange models (see **Figure 12** for a standard flow chart) for dense particulate

**1.** Spring-dashpot-slider systems are not designed for micro-/nano-particles. Coefficients, i.e., equivalent stiffness and damping coefficient, need to be determined via experiments specifically for ultrafine particles. Or else, the validity of using soft-sphere models needs

**2.** DEM is not computationally efficient on handling aerosol transport and deposition in human respiratory systems, in which the difference in characteristic dimensions between

particle surfaces. This avoids empirical correlations, such as drag and lift coefficients.

particle and particle-wall interactions.

computational resources [79].

76 Aerosols - Science and Case Studies

to be tested.

*4.4.2. Discrete element method (DEM)*

are calculated in two steps in DEM methods [83]:

**1.** Contact detection: identify which particles are contacting;

depth/separation and sometimes also relative tangential motion.

flow is straightforward [38]. However, there are two key challenges:

In this chapter, CFPD models have been systematically overviewed, with emphases on simulating the transport and deposition of unconventional ultrafine aerosol particles in human upper airways. Compared to other numerical models for inhaled aerosol dose [1], CFPD models provide more detailed characterizations of airflow and aerosol deposition patterns with a reasonable degree of accuracy and computational cost.

However, in order to provide comprehensive tissue and delivered dosage data for risk assessment or drug delivery efficacy evaluation, it is necessary to improve current CFPD models and extend lung deposition calculation by integrating with other simulation techniques to build a multiscale dosimetry model (see **Figure 11** for the framework). This multidisciplinary effort requires expertise in medical imaging, airway geometric reconstruction, computational techniques, pulmonary physiology and medicine, fluid mechanics, etc. From a physics viewpoint, the future numerical models for lung aerosol dynamics will provide comprehensive analysis of the fate of inhaled particulate matter under realistic conditions, namely, actual particle characteristics, inhalation flow rates, and human respiratory systems. The anticipated results will greatly increase understanding of distinct particle transport/ deposition phenomena under realistic inhalation conditions as well as quantify the knowledge base for dosimetry and health-effect studies in the case of toxic particles, and optimal drugaerosol targeting in the case of therapeutic particles. Relevant numerical researches will lead to understanding and quantification of dosimetry effects of inhalation hazards, more accurate evaluation of toxic particle fate in the human lung, and improved estimates of drug delivery points for treating lung and other diseases.
