New expression for collision efficiency of spherical nanoparticles in Brownian coagulation

Abstract

The collision efficiency of dioctyl phthalate nanoparticles in Brownian coagulation has been studied. A set of collision equations is solved numerically to find the relationship between the collision efficiency and the particle radius varying in the range of 50 nm to 500 nm in the presence of Stokes resistance, lubrication force, van der Waals force, and elastic deformation force. The calculated results are in agreement with the experimental data qualitatively. The results show that the collision efficiency decreases with the increase of the particle radii from 50 nm to 500 nm. Based on the numerical data, a new expression for collision efficiency is presented.

Clearance of nanoparticles from blood: effects of hydrodynamic size and surface coatings

“…Collision theory is widely used to describe the aggregation of particles, facilitating its applications in industry, 73 materials 74 and environmental science. 75 In the field of biology, collisions between particles and organisms (protein corona) 76 are also relevant.…”

“…48 We implemented a term (e − E a /( k B · T ) ) (eqn (6)) for statistical thermodynamics that uses van der Waals surface energies 27,84 of NP coatings expanding the generic phagocytosis-based model in the ESI †. In ESI† Methods 1.2, the van der Waals energy 73 (Δ G LW ( h )), being part of the activation energy E a ( E a = δ ·Δ G LW ( h )), was used to replace E a . The van der Waals free energies of NPs ( e.g.…”

“…48 We implemented a term (e −Ea/(kB•T) ) (eqn ( 6)) for statistical thermodynamics that uses van der Waals surface energies 27,84 of NP coatings expanding the generic phagocytosis-based model in the ESI. † In ESI † Methods 1.2, the van der Waals energy 73 (ΔG LW (h)), being part of the activation energy E a (E a = δ•ΔG LW (h)), was used to replace E a . The van der Waals free energies of NPs (e.g., the Lifshitz-van der Waals, γ np LW ) and macrophages (γ m LW ) were calculated or collected to obtain the van der Waals energy (Eqn (S5 †), ΔG LW (h), h is the separation distance between the interacting surfaces).…”

Attachment Efficiency of Polydisperse Nanoparticles Wall-Deposition

“…Wang et al [27][28][29] extended Feng and Lin s work to the oblique collision of two nanoparticles with different diameter by taking the electrostatic force into account. Chen and You 30) used another method to calculate the collision efficiency in the presence of hydrodynamic interactions. However, the research on the elastic collision between nanoparticles and wall as well as the attachment efficiency has yet not been found in literature.…”