Brownian motion of rigid bodies in compressible fluids under nonisothermal conditions

In the present thesis a microhydrodynamic theory for Brownian multi-particle dynamics in an isolated colloidal suspension is developed that takes account of all hydrodynamic degrees of freedom of the solvent in which the rigid particles are suspended, inner structure of the particles (i.e. inhomogenous mass density, thermal properties), their mutual hydrodynamic interaction as well as hydrodynamic memory-effects. The whole system is treated as nonisothermal. This theory represents a systematic advancement of a singleparticle theory due to E.H. Hauge and A. Martin-Löf that was published in 1973. From local conservation laws for mass, momentum and energy as well as the local balance of entropy, linear governing equations and appendant boundary conditions for field variables and kinematical variables of the particles are derived that describe the average regression of a perturbation of equilibrium of the isolated colloidal suspension. To be specific, the field variables are perturbations of local velocity and local mass density in the fluid as well as perturbations of local temperature in the whole system. The kinematical variables of the particles are their rotational and translational velocities. By constructing random force fields under reference to perturbations of the total entropy of the system and supplementing these random force fields into the equations for the average dynamics, one obtains linear Langevin equations that describe the random dynamics of field variables and kinematical variables of the particles as long as the particles stay close to a certain (time-independent) reference configuration which is incorporated into the linear Langevin equations. Since for Brownian motion only the kinematical variables of the particles are of interest, the explicit dynamics of the field variables is eliminated from the above description. This elimination of field variables results in a generalized Langevin equation for the kinematical variables of the particles alone. This generalized Langevin equation describes random thermal motion of the particles as long as the particles stay close to the same (time-independent) reference configuration as that, which is incorporated into the linear Langevin equations from which the generalized Langevin equation results by the elimination of field variables. Mutual hydrodynamic interaction of the particles and hydrodynamic memory-effects enter into this generalized Langevin equation via the N-particle friction kernel. This friction kernel also refers to a particular reference configuration of particles and it represents a generalization of the Stokesian friction coefficient that goes beyond the single-particle treatment of retarded hydrodynamic friction used by Hauge and Martin-Löf. The N-particle friction kernel is not only the main implement for the systematic frictional forces but also for the random forces that occur in the generalized Langevin equation: A fluctuation-dissipation theorem is derived that relates the dynamical second-order correlations of the Gaussian random forces to the N-particle friction kernel. Furthermore an iterative use of such generalized Langevin equations is introduced which provides, at least qualitatively, a transition to conventional Brownian dynamics of the particles. In this way random multi-particle diffusion becomes describable. Finally, the Laplace transform of the friction kernel (spectral friction kernel) of a single homogenous sphere immersed in an unbounded fluid is calculated explicitly and thereby the impact of nonisothermal conditions and compressibility of the solvent on the spectral friction kernel is illustrated.