Transient dynamics of a complex nano-particle in a viscous fluid

This dissertation investigates the transient dynamics of a complex nanoparticle immersed in a viscous fluid, focusing on the unsteady translational motion of a porous sphere with a slip-surface. The particle's characteristics include radius a, density ρs , permeability parameter 𝛾, slip-length 𝑙, and effective viscosity-ratio 𝜖. The study assumes a low Reynolds number regime, ensuring negligible convective contributions, while considering transient inertia comparable to viscous forces for both liquid and solid phases. The linearized unsteady flow equations, formulated in the time-invariant frequency domain, are solved by adhering to appropriate boundary conditions, resulting in frequency-dependent hydrodynamic friction for the suspended particle. The frictional coefficient is computed under low and high-frequency limits for various 𝛾, 𝑙, and 𝜖, facilitating comparison with known results for impermeable surfaces. Parametric exploration reveals that the sphere behaves like a no-slip body even with non-zero slip-length 𝑙 if 𝑎𝛾≫1/𝜖, an observation explained through a novel boundary layer theory. Incorporating computed fluid resistance into the particle's equation of motion allows for determining its time-dependent velocity response to a force impulse. This transient response varies significantly with 𝜌, 𝛾, 𝑙, and 𝜖, highlighting the study's relevance. Moreover, the dissertation addresses the variability in Brownian diffusivity among nanoparticles of identical size, shape, and mass, attributing such differences to nano-scale dynamic features. These variabilities, influenced by interfacial and bulk properties, can result in order-of-magnitude fluctuations in diffusivity. The findings elucidate several unresolved issues in submicron systems, including the anomalous thermal properties of nano-fluids and the varying transmittivities of biologically originated particulate droplets. The study concludes that slip and permeability are critical features for understanding and predicting the behavior of submicron particles in nano-fluidic applications and viral transmission phenomena.