相关论文: Convective transport in nanofluids: the stationary…

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid…

Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…

Coherent thermal transport in nanopatterned structures is a topic of considerable interest, but whether it occurs in certain structures remains unclear due to poor understanding of which phonons conduct heat. Here, we perform the first…

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular…

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…

In this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. As the temperature gradient…

Liquids in contact with solids are submitted to intermolecular forces making liquids heterogeneous and stress tensors are not any more spherical as in homogeneous bulks. The aim of this article is to show that a square-gradient functional…

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier-Stokes equations for the fluid…

Existence of nodal (i.e., sign changing) solutions and constant sign solutions for quasilinear elliptic equations involving convection-absorption terms are presented. A location principle for nodal solutions is obtained by means of constant…

We prove some theorems on the existence, uniqueness, stability and compactness properties of solutions to inhomogeneous transport equations with Sobolev coefficients, where the inhomogeneous term depends upon the solution through an…

Observations of an enhanced mass transfer in nanofluids have led to several propositions for the underlying cause, but none of them have been clearly established. Here, we reproduce the enhancement phenomenon within a glass capillary…

The phenomenon of convection is found in a wide variety of settings on different scales -- from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing…

This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…

Thermophoresis (thermodiffusion, Soret effect) moves molecules along thermal gradients. We measure its phenomenological linear drift relation by single particle tracking in convection-free settings. For moderate thermal gradients, drift…

We use a hydrodynamic reciprocal approach to phoretic motion to derive general expressions for the electrophoretic and thermophoretic mobility of weakly charged colloids in aqueous electrolyte solutions. Our approach shows that phoretic…

We investigate theoretically the bifurcation scenario for colloidal suspensions subject to a vertical temperature gradient taking into account the effect of sedimentation. In contrast to molecular binary mixtures, here the thermal…

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…

Buoyancy-thermocapillary convection in a layer of volatile liquid driven by a horizontal temperature gradient arises in a variety of situations. Recent studies have shown that the composition of the gas phase, which is typically a mixture…

In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…

We propose an extension to the original result derived by Simoncelli et al. (https://doi.org/10.1038/s41567-019-0520-x) to encompass the effects of a space and time dependent heat source. Via a Fourier Transfrom, we obtain closed form…