Research Paper: Investigation of Fluid around Nanoparticles via Stokes Method and Calculation of Hydrodynamic Radius of Gold Nanoparticles Synthesized by Reduction Method

In this paper, we are going to study the fluid around nanoparticles and their hydrodynamic size, completely. First, we obtain the complete set of relations of the velocity equations and the velocity vector field around a spherical nanoparticle. For this, we use Stokes' analytical method with boundary conditions. Using the velocity vector field equations, we obtain the stress tensor components on the sphere surface and the fluid resistance force on the nanoparticle. In the next step, we consider the hydrodynamic diameter of the particle to be the diameter at which the fluid no longer moves effectively with the particle, and we obtain a description for this quantity from the equations of velocity. We will examine and find a significant correlation between these values. In the experimental part, gold nanoparticles with a diameter of 12 nm are synthesized and characterized by the Turkevich method. The diameter and hydrodynamic diameter of particles are measured using an electron microscope (TEM) and dynamic light scattering (DLS). By numerical fitting the Fortran 90 programming code and using experimental data, we were able to estimate the relative velocity of the particles relative to the fluid. These studies can be a useful method for the experimental and theoretical study of resistance force and dispersion of nanoparticles in colloidal media and have many applications in experimental applications of nano colloids such as nanoparticle drug delivery.