Quenta Johann, Vasquez Desiderio A
Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel, Lima 32, Perú.
Department of Physics, Purdue University Fort Wayne, Fort Wayne, Indiana 46805, USA.
Phys Rev E. 2024 Mar;109(3-2):035104. doi: 10.1103/PhysRevE.109.035104.
Chemical reaction fronts separate regions of reacted and unreacted substances as they propagate in liquids. These fronts may induce density gradients due to different chemical compositions and temperatures across the front. In this paper, we investigate buoyancy-induced convection driven by both types of gradients. We consider a thin front approximation where the normal front velocity depends only on the front curvature. This model applies for small curvature fronts independent of the specific type of chemical reaction. For density changes due only to heat variations near the front, we find that convection can take place for either upward or downward propagating fronts if density gradients are above a threshold. Convection can set in even if the fluid with lower density is above the higher density fluid. Our model consists of Navier-Stokes equations coupled to the front propagation equation. We carry out a linear stability analysis to determine the parameters for the onset of convection. We study the nonlinear front propagation for liquids confined in narrow two-dimensional domains. Convection leads to fronts of steady shape, propagating with constant velocities.
化学反应前沿在液体中传播时，会将已反应物质区域和未反应物质区域分隔开来。由于前沿两侧化学成分和温度不同，这些前沿可能会引发密度梯度。在本文中，我们研究了由这两种梯度驱动的浮力诱导对流。我们考虑一种薄前沿近似，其中前沿法向速度仅取决于前沿曲率。该模型适用于小曲率前沿，与化学反应的具体类型无关。对于仅由前沿附近热量变化引起的密度变化，我们发现，如果密度梯度高于阈值，向上或向下传播的前沿都可能发生对流。即使低密度流体位于高密度流体上方，对流也可能发生。我们的模型由与前沿传播方程耦合的纳维 - 斯托克斯方程组成。我们进行线性稳定性分析以确定对流开始的参数。我们研究了限制在狭窄二维区域内液体的非线性前沿传播。对流会导致形成稳定形状的前沿，并以恒定速度传播。
