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Register a new userConsolidated theory of fluid thermodiffusion
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Added by
Alexander Van-Brunt
Publication date
2021
fields
Physics
and research's language is
English
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We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids by treating heat as a pseudo-component. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the isothermal Stefan--Maxwell equations, separating the thermodynamic forces that drive diffusion from the force that drives heat flow. The Onsager--Stefan--Maxwell transport-coefficient matrix is symmetric, and the second law of thermodynamics imbues it with simple spectral characteristics. This new approach proves equivalent to both the intuitive extension of Ficks law and the generalized Stefan--Maxwell equations popularized by Bird, Stewart, and Lightfoot. A general inversion process allows the unique formulation of flux-explicit transport equations relative to any choice of convective reference velocity. Stefan--Maxwell diffusivities and thermal diffusion factors are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and xenon. The framework is deployed to perform numerical simulations of steady three-dimensional thermodiffusion in a ternary gas.
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The traditional fluid perturbation theory is improved by taking electronic excitations and ionizations into account, in the framework of average ion spheres. It is applied to calculate the equation of state for fluid Xenon, which turns out in good agreement with the available shock data.
A physical model of a three-dimensional flow of a viscous bubbly fluid in an intermediate regime between bubble formation and breakage is presented. The model is based on mechanics and thermodynamics of a single bubble coupled to the dynamics of a viscous fluid as a whole, and takes into account multiple physical effects, including gravity, viscosity, and surface tension. Dimensionle
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We are modelling multi-scale, multi-physics uncertainty in wave-current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI; namely, the Generalised Lagrangian Mean (GLM) model and the Craik--Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom in Hamiltons principle. This is done by coupling an Euler--Poincare {it reduced Lagrangian} for the current flow and a {it phase-space Lagrangian} for the wave field. WCI in the GLM model involves the nonlinear Doppler shift in frequency of the Hamiltonian wave subsystem, which arises because the waves propagate in the frame of motion of the Lagrangian-mean velocity of the current. In contrast, WCI in the CL model arises because the fluid velocity is defined relative to the frame of motion of the Stokes mean drift velocity, which is usually taken to be prescribed, time independent and driven externally. We compare the GLM and CL theories by placing them both into the general framework of a stochastic Hamiltons principle for a 3D Euler--Boussinesq (EB) fluid in a rotating frame. In other examples, we also apply the GLM and CL methods to add wave physics and stochasticity to the familiar 1D and 2D shallow water flow models. The differences in the types of stochasticity which arise for GLM and CL models can be seen by comparing the Kelvin circulation theorems for the two models. The GLM model acquires stochasticity in its Lagrangian transport velocity for the currents and also in its group velocity for the waves. The Kelvin circulation theorem stochastic CL model can accept stochasticity in its both its integrand and in the Lagrangian transport velocity of its circulation loop.
The study reports the aspects of postimpact hydrodynamics of ferrofluid droplets on superhydrophobic SH surfaces in the presence of a horizontal magnetic field. A wide gamut of dynamics was observed by varying the impact Weber number We, the Hartmann number Ha and the magnetic field strength manifested through the magnetic Bond number Bom. For a fixed We 60, we observed that at moderately low Bom 300, droplet rebound off the SH surface is suppressed. The noted We is chosen to observe various impact outcomes and to reveal the consequent ferrohydrodynamic mechanisms. We also show that ferrohydrodynamic interactions leads to asymmetric spreading, and the droplet spreads preferentially in a direction orthogonal to the magnetic field lines. We show analytically that during the retraction regime, the kinetic energy of the droplet is distributed unequally in the transverse and longitudinal directions due to the Lorentz force. This ultimately leads to suppression of droplet rebound. We study the role of Bom at fixed We 60, and observed that the liquid lamella becomes unstable at the onset of retraction phase, through nucleation of holes, their proliferation and rupture after reaching a critical thickness only on SH surfaces, but is absent on hydrophilic surfaces. We propose an analytical model to predict the onset of instability at a critical Bom. The analytical model shows that the critical Bom is a function of the impact We, and the critical Bom decreases with increasing We. We illustrate a phase map encompassing all the post impact ferrohydrodynamic phenomena on SH surfaces for a wide range of We and Bom.
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