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Self-Propelled Nanomotors
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Another important effect is caused by Brownian motion. The translational diffusion constant is inversely proportional to the size of the particle from the Stokes–Einstein relationD=kBT6πηR. Rotational Brownian motion dominates over ballistic motion as particles become smaller (the rotational diffusion constant scales as D ∝ R–3). This makes particles lose orientation at a very short time scale (e.g., a 1 μm swimmer loses orientation in 3 s, while a 5 nm particle randomizes its orientation in 1 μs.).
Rotational Brownian Motion and Diffusion
Published in Gregory S. Chirikjian, Alexander B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, 2021
Gregory S. Chirikjian, Alexander B. Kyatkin
In this chapter we reviewed the classical theories of rotational Brownian motion and their generalizations. Diffusion processes on the rotation group are associated with a diverse array of scenarios ranging from chemical physics and the analysis of liquid crystals to estimation problems. Fokker-Planck equations describing the time evolution of probability density functions in rotational Brownian motions are derived. In the non-inertial theory of rotational Brownian motion, a PDF governed by the Fokker-Planck equation is a function of rotation. In the inertial theory of rotational Brownian motion these PDFs are functions of both rotation and angular velocity.
Magnetic Nanoparticles for Drug Delivery
Published in Claudia Altavilla, Enrico Ciliberto, Inorganic Nanoparticles: Synthesis, Applications, and Perspectives, 2017
Rotational Brownian motion (observed also in multidomain nanoparticles) within a carrier liquid (blood) is due to the torsion exerted by the external AC magnetic field on the magnetic moment that produces the rotation of particle as a whole and determines the friction with the surrounding liquid. The Brown relaxation time, tB, is correlated with the viscosity of the liquid (η) and the hydrodynamic volume of the particles (V) through the equation
One-dimensional displacement of active matter on curved substrates
Published in Molecular Physics, 2020
Pedro Herrera, Leonardo Apaza, Mario Sandoval
In the present research, a one-dimensional model of a Brownian self-propelled particle moving on a curved substrate is examined. Since the active particle is immersed in a liquid, its propulsion direction is subject to rotational Brownian motion. Given the fact that the particle is confined to a channel, only the projection along the channel's long section of its propulsion force will be responsible for its autonomous motion. This propulsion force is restricted to rotate in the instantaneous tangential plane to the substrate. This study generalises the work in [19] for the following reasons: First, the effect of substrate curvature on the particle's diffusion is now elucidated. Second, this work presents general overdamped Langevin equations valid for any one-dimensional channel shape as long as the channel's shape is equipped with a metric; and finally, by neglecting the activity in the actual system, our findings also apply to classic (passive) Brownian particles whose motion is constrained to any curved geometries equipped with a metric.
Trapping characteristics of magnetic rod-like particles flowing in a cylindrical pipe by means of a non-uniform magnetic field (Brownian dynamics simulations)
Published in Molecular Physics, 2020
Takeru Yamanouchi, Akira Satoh
In Brownian dynamics simulations, the translational and rotational Brownian motion of the particles is generated according to Equations (19) and (20) and their motion in the flow field is used to evaluate the characteristics of the physical quantities of interest.