Broadband boundary effects on Brownian motion

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.Sid W. Richardson FoundationR. A. Welch Foundation F-1258Physic

Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. 2005, 2009b) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework has an inconsistency which we address in this work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature of the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation, and the method of reflections. We show that our modifications to Felderhof's framework would become significant for systems of metallic nanoparticles in liquids.Comment: 40 page draft submitted for review to the Journal of Fluid Mechanic

Short timescale Brownian motion and applications

textThis dissertation details our experiments and numerical calculations on short timescale Brownian motion and its applications. We test the Maxwell-Boltzmann distribution using micrometer-sized spheres in liquids at room temperature. In addition to that, we use Brownian particles as probes to study boundary effects imposed by a solid wall, viscoelasticities of complex fluids, slippage at solid-fluid interfaces, and fluid compressibility. The experiments presented in this dissertation relies on the use of tightly focused laser beams to both contain and probe the Brownian motion of microspheres in fluids. A dielectric sphere near the focus of a laser beam scatters some of the incident photons in a direction which depends on the particle's position. Changes in the particle's position are encoded in the spatial distribution of the scattered beam, which can be measured with high sensitivity. It is important to emphasize that the Brownian motion in this dissertation is exclusive for translational Brownian motion. We have reported shot-noise limited measurements of the instantaneous velocity distribution of a Brownian particle. Our system consists of a single micron-sized glass sphere held in an optical tweezer in a liquid in equilibrium at room temperature. We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and a modified energy equipartition theorem that account for the kinetic energy of the liquid displaced by the particle. Our measurements con rm the distribution over a dynamic range of more than six orders of magnitude in count-rate and five standard deviations in velocity. We have reported high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately at wall. At short distances, we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of particle in a bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes at at low frequencies. We have numerically studied Brownian motion of a microsphere in complex fluids. We show that Brownian motion of immersed particles can be dramatically affected by the viscoelastic properties of the host fluids. Thus, this fact can be used to extract the properties of complex fluids via observing the motion of the embedded particles. This will be followed by two experimental demonstrations of obtaining the viscosities of water and acetone. We also study Brownian motion with partial and full slip boundary conditions both on the surface of a sphere and a boundary. We show that the motion of particles can be significantly altered by the boundary condition of fluid flow on a solid surface. We suggest that this fact can be used to measure the slippage, namely the slip length. Lastly, I will discuss the efforts to study fluid compressibility and nonequilibrium physics using a short duration pulsed laser. We expect to increase the postion sensitivity from current 10⁻¹⁵ m/[square root of Hz] to about 10⁻¹⁹ m/[ square root of Hz] by using a pulsed laser with a peak power of 10^8 W. With such a high position sensitivity, we expect to be able to resolve the compressibility of fluids. We will also discuss a few future experiments studying non-equilibrium physics.Physic