Ballistic Brownian motion of supercavitating nanoparticles

Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic diffusion

Using an approach based on the diffusion analog of the Cattaneo-Vernotte differential model, we find the exact analytical solution to the corresponding time-dependent linear hyperbolic initial boundary value problem, describing irreversible diffusion-controlled reactions under Smoluchowski's boundary condition on a spherical sink. By means of this solution, we extend exact analytical calculations for the time-dependent classical Smoluchowski rate coefficient to the case that includes the so-called inertial effects, occurring in the host media with finite relaxation times. We also present a brief survey of Smoluchowski's theory and its various subsequent refinements, including works devoted to the description of the short-time behavior of Brownian particles. In this paper, we managed to show that a known Rice's formula, commonly recognized earlier as an exact reaction rate coefficient for the case of hyperbolic diffusion, turned out to be only its approximation being a uniform upper bound of the exact value. Here, the obtained formula seems to be of great significance for bridging a known gap between an analytically estimated rate coefficient on the one hand and molecular dynamics simulations together with experimentally observed results for the short times regime on the other hand. A particular emphasis has been placed on the rigorous mathematical treatment and important properties of the relevant initial boundary value problems in parabolic and hyperbolic diffusion theories.

Optically Driven Gold Nanoparticles Seed Surface Bubble Nucleation in Plasmonic Suspension

Photothermal surface bubbles play important roles in applications like microfluidics and biosensing, but their formation on transparent substrates immersed in a plasmonic nanoparticle (NP) suspension has an unknown origin. Here, we reveal NPs deposited on the transparent substrate by optical forces are responsible for the nucleation of such photothermal surface bubbles. We show the surface bubble formation is always preceded by the optically driven NPs moving toward and deposited to the surface. Interestingly, such optically driven motion can happen both along and against the photon stream. The laser power density thresholds to form a surface bubble drastically differ depending on if the surface is forward- or backward-facing the light propagation direction. We attributed this to different optical power densities needed to enable optical pulling and pushing of NPs in the suspension, as optical pulling requires higher light intensity to excite supercavitation around NPs to enable proper optical configuration.