Jialing Yu | Searcharxiv

arXiv2024

Non-selective Evaporation of Ethanol-Water Binary Mixture within Heated Capillary

In the study, the evaporation of ethanol-water binary mixture within heated capillary is experimentally and numerically investigated. It was found that the ratio of the evaporation rates of ethanol and water equals the ratio of their initial concentrations in the mixture. This observation contradicts the commonly accepted view of selective evaporation, where the ratio of ethanol-to-water evaporation rates is expected to be considerably higher than the concentration ratio owing to the higher volatility of ethanol. We term this novel phenomenon as non-selective evaporation. Subsequently, through numerical study, it was discovered that the changes in component concentration induced by the ethanol preferential evaporation appear solely in the limited area, referred to as the diffusion layer, near the meniscus. When the diffusion layer is fully developed, the evaporation process will transition from selective evaporation stage to non-selective evaporation stage. Due to the short duration of the selective evaporation stage in current study, the evaporation process exhibits distinct characteristics of non-selective. Moreover, by considering the coupled effects of convection and diffusion, an analytical model was proposed, and the criteria related with Pe number were established to determine whether the evaporation process of binary mixture exhibits selective or non-selective characteristics.

physics.flu-dyn↗

arXiv2022

Sharp Lower Bound for the Blow-up Rate of Solutions to the Magnetic Zakharov System without the Skin Effect

In this paper, we consider the Cauchy problem of the magnetic Zakharov system in two-dimensional space: \[ \begin{cases} & i E_{1t}+\Delta E_1-n E_1+\eta E_2 (E_1\overline{E_2}-\overline{E_1} E_2)=0, \\ & i E_{2t}+\Delta E_2-n E_2+\eta E_1(\overline{E_1} E_2-E_1\overline{E_2})=0, \\ & n_t+\nabla \cdot \textbf{v}=0, \\ & \textbf{v}_t+\nabla n+\nabla (|E_1|^2+|E_2|^2)=0, \\ \end{cases} \tag{G-Z} \] with initial data $\left(E_{10}(x),E_{20}(x),n_{0}(x),\mathbf{v}_{0}(x)\right)$, which describes the spontaneous generation of a magnetic field without the skin effect in a cold plasma, where $\eta>0$ is a physical constant coefficient. The two nonlinear terms generated by the cold magnetic field bring in a different difficulty from that for the classical Zakharov system. Assuming the initial mass satisfies the following estimates: \begin{gather*} \frac{||Q||_{L^2(\mathbb{R}^2)}^2}{1+\eta} <||E_{10}||_{L^2(\mathbb{R}^2)}^2+||E_{20}||_{L^2(\mathbb{R}^2)}^2 <\frac{||Q||_{L^2(\mathbb{R}^2)}^2}{\eta}, \end{gather*} where $Q$ is the unique radially positive solution of the equation $-\Delta V+V=V^3 $, we prove that there is a constant $c>0$ depending only on the initial data such that for $t$ near $T$ (the blow-up time), \begin{gather*} \left\|\left(E_1,E_2,n,\textbf{v}\right)\right\|_{H^1(\mathbb{R}^2)\times H^1(\mathbb{R}^2)\times L^2(\mathbb{R}^2)\times L^2(\mathbb{R}^2)}\geqslant \frac{c}{ T-t }. \end{gather*} As the magnetic coefficient $\eta$ tends to $0$, the blow-up rate recovers the result for the classical 2-D Zakharov system due to Merle \cite{25Frank}. For any size positive $\eta$, under the current assumption on the initial mass, we give a mathematically rigorous justification for the fact that the presence of magnetic effects without the skin effect in the cold plasma does not change the optimal lower bound for the blow-up rates.

math.AP↗