J.M. Rubí

Hydrodynamical fluctuations in extended irreversible thermodynamics

Starting from the generalized Gibbs equation of extended irreversible thermodynamics, we define a thermodynamic potential that provides a suitable description of the fluctuations of the hydrodynamical dissipative fluxes when it is used in an expression analogous to the classical Einstein formula for the probability of fluctuations. In the limit of vanishing relaxation times, our results coincide with those of Landau-Lifshitz. The effect of the rapid normal modes is taken into account as a stochastic noise in the evolution equations of the dissipative fluxes, and their covariance matrix is found from a fluctuation-dissipation theorem.

A generalised Gibbs equation for second-order fluids

A generalised Gibbs equation for viscous, incompressible fluids is proposed. It takes into account the dependence of the entropy on the viscous pressure tensor. When the restrictions of the objectivity principle are imposed on the phenomenological equations, the expression for the pressure tensor is seen to be equivalent to that of second-order fluids.

Heat Fluctuations and a generalized Gibbs equation

Abstract Starting from a generalized Gibbs equation and from the Einstein formula for the probability of fluctuations, we obtain the correlation function of heat fluctuations.

Brownian motion in a fluid in elongational flow

Brownian motion of a spherical particle in stationary elongational flow is studied. We derive the Langevin equation together with the fluctuation-dissipation theorem for the particle from nonequilibrium fluctuating hydrodynamics to linear order in the elongation-rate-dependent inverse penetration depths. We then analyze how the velocity autocorrelation function as well as the mean square displacement are modified by the elongational flow. We find that for times small compared to the inverse elongation rate the behavior is similar to that found in the absence of the elongational flow. Upon approaching times comparable to the inverse elongation rate the behavior changes and one passes into a time domain where it becomes fundamentally different. In particular, we discuss the modification of thet−3/2 long-time tail of the velocity autocorrelation function and comment on the resulting contribution to the mean square displacement. The possibility of defining a diffusion coefficient in both time domains is discussed.

Drag on a sphere moving slowly through a fluid in elongational flow

The friction tensor for a sphere moving slowly through a fluid which is in elongational flow is calculated using the method of induced forces to second order in an expansion in the radius of the sphere divided by the “inverse penetration length” of transverse waves. This inverse penetration length is a function of the frequency and the elongation rate and is furthermore direction dependent. The resulting friction tensor depends as a consequence also on the direction. As a consequence the sphere may experience a lift force.

Thermodynamical fluctuations of a massive Schwarzschild black hole

Abstract Starting from the Einstein-Boltzmann formula we determine classically the second moments for the fluctuations of a massive Schwarzschild black hole enclosed with thermal radiation in a rigid box.

On Brownian motion in fluids with spin

A method of induced forces and torques is employed to study brownian motion of a particle in a fluid with internal angular momentum (spin). One derives generalized Faxen theorems for the force and torque exerted on the particle. In the Landau-Lifshitz approach, one obtains fluctuation-dissipation theorems for the force and torque. The results are applied to quinoline and liquid nitrogen.

Friction, diffusion and Brownian motion in suspensions of dipolar spherical particles

The spin fluid model is applied to study suspensions of gravitatory dipoles. Faxen theorems for translational and rotational motion of a sphere through the suspension are obtained. Brownian motion is also considered. As a general feature and due to the introduction of internal degrees of freedom, friction and diffusion tensors as well as correlation functions are modified by a factor proportional to the volume fraction of suspended spheres.

Boundary conditions for interfacial fluid systems with spin

Interfacial immiscible fluid systems with hydrodynamic spin are studied within the framework of non-equilibrium thermodynamics. The energy and entropy densities and the momentum, internal angular momentum and heat currents are allowed to be singular at the interface. Balance equations in the bulk and at the surface are derived following the procedure indicated in BAM method. The interfacial entropy production leads, on the one hand, to linear laws at the surface, and on the other hand to boundary conditions for both fluids. Finally, boundary conditions in the de Groot-Mazur approximation are obtained and discussed.

Spatial correlations for temperature fluctuations from surface noise

The equal-time or static temperature correlation function from fluctuations originated at a surface is computed. Such fluctuations come from a random heat flux appearing in Newtons law of cooling. The correlation is studied in the real space and for different values of the Nusselt number.