On interpretation of force measurements in fluids: regular and thermal forces
The paper is devoted to the problem of the determination of regular and thermal forces acting on microscopic and smaller objects in fluids. One of the methods how regular forces are determined is the measurement of the drift velocity of Brownian particles. We have obtained an exact expression for this velocity within the hydrodynamic theory of the Brownian motion. It is shown that the influence of the inertial and memory effects can be significant in the force determination when the experimental times are sufficiently short. In the second part of the work, within the same theory, we study the properties of the thermal force driving the particles in incompressible fluids. We show that the usual assumption for the Kubo's generalized Langevin equation (called the "fundamental hypothesis") that the thermal force at a time t and the velocity of the particle in preceding times are uncorrelated, leads to an unexpected super-diffusion of the particle. To obtain the Einstein diffusion at long times, the mentioned hypothesis must be abandoned, which however does not contradict to causality. Finally, we consider the "color" of thermal noise, recently measured experimentally [Th. Franosch et al., Nature 478, 85 (2011)], and correct the interpretation of these experiments.