Engineered nanomaterials (ENMs) possess unique characteristics affecting their interactions in biological media and biological tissues. Systematic investigation of the effects of particle properties on biological toxicity requires a comprehensive modeling framework which can be used to predict ENM particokinetics in a variety of media. The Agglomeration-diffusion-sedimentation-reaction model (ADSRM) described here is stochastic, using a direct simulation Monte Carlo method to study the evolution of nanoparticles in biological media, as they interact with each other and with the media over time. Nanoparticle diffusion, gravitational settling, agglomeration, and dissolution are treated in a mechanistic manner with focus on silver ENMs (AgNPs). The ADSRM model utilizes particle properties such as size, density, zeta potential, and coating material, along with medium properties like density, viscosity, ionic strength, and pH, to model evolving patterns in a population of ENMs along with their interaction with associated ions and molecules. The model predictions for agglomeration and dissolution are compared with in vitro measurements for various types of ENMs, coating materials, and incubation media, and are found to be overall consistent with measurements. The model has been implemented for an in vitro case in cell culture systems to inform in vitro dosimetry for toxicology studies, and can be directly extended to other biological systems, including in vivo tissue subsystems by suitably modifying system geometry.