相关论文: Partial Pressures in Liquid Mixtures and Osmotic P…
In thermal equilibrium, a colloidal particle between two parallel plates immersed in a fluid which partially wets both the particle and the plates, is attracted by the walls. However, if the particle moves parallel to the plates, a…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall…
In an unsaturated granular material, the spatial distribution of the liquid phase results from the competition between gravity and capillary forces. We show that, in the funicular regime, it can be described by a Boltzmann law, with static…
Mathematically rigorous derivation of the hadron matter equation of state within the induced surface and curvature tensions approach is worked out. Such an equation of state allows one to go beyond the Van der Waals approximation for the…
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through…
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the…
Unstable pressure and u-equilibrium states are introduced and investigated for a partially hyperbolic diffeomorphsim $f$. We define the u-pressure $P^u(f, \varphi)$ of $f$ at a continuous function $\varphi$ via the dynamics of $f$ on local…
We derive a first--principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is…
The equation of state of the osmotic pressure for linear-polymer solutions in good solvents is universally described by a scaling function. We experimentally measure the osmotic pressure of the gelation process via osmotic deswelling. We…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation…
This work is concerned with the equation $ \partial_t \rho = \Delta_x \rho^m $, $ m > 1 $, known as the porous medium equation. It shows stability of the pressure of solutions close to flat travelling wave fronts in the homogeneous…
Abundant interfacial phenomena in nature, such as water droplets on lotus leaves and water transport in plant vessels, originate from partial-wetting phenomena, which can be well described by Young's equation. It remains an intriguing…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its…