Fig. 7.1 — Brownian motion

Chapter 7 — Brownian Motion

An important aspect of optical trapping and manipulation is the ubiquitous presence of Brownian motion. In fact, as shown in Fig. 7.1, microscopic particles undergo a perpetual random motion due to collisions with the molecules of the fluid where they are immersed. The motion of an optically trapped particle is, therefore, the result of the interplay between this random motion and the deterministic optical forces we have studied in the previous Chapters: eventually the particle settles down near an equilibrium position in the optical force field, but never completely, as instead it keeps on jiggling because of Brownian motion. In this Chapter, we will review the main properties of Brownian motion that come into play when dealing with optical trapping and manipulation.

7.1  The physical picture

7.2  Mathematical models
7.2.1  Random walk
7.2.2  Langevin equation
7.2.3  Free diffusion equation
7.2.4  Fokker–Planck equation

7.3  Fluctuation–dissipation theorem, potential and equilibrium distribution
7.4  Brownian dynamics simulations
7.4.1  White noise
7.4.2  Optically trapped particle

7.5  Inertial regime

7.6  Diffusion gradients

7.7  Viscoelastic media

7.8  Non-spherical particles and diffusion matrices
7.8.1  Free diffusion
7.8.2  External forces



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