论文标题
流水机的变质对流扩散系统对泡沫浮选进行建模
A degenerating convection-diffusion system modelling froth flotation with drainage
论文作者
论文摘要
泡沫浮选是矿物加工中使用的常见单位操作。它可以将有价值的矿物颗粒与细矿石中的毫无价值的螺栓颗粒分开。有价值的矿物颗粒是疏水的，并附着在注入纸浆中的空气气泡上。这创建了浮动圆柱顶部的气泡粒子聚集体，它们会积聚到泡沫或泡沫层，该泡沫或泡沫层通过洗衣去除去以进行进一步加工。同时，亲水性脉动颗粒沉降并连续去除。由于毛细血管引起的液体引流对于形成稳定的泡沫层至关重要。这种效应被包括在偏微分方程的先前配制的双曲线系统中，该系统模拟了浮子骨料的体积分数和沉降亲水固体[R. Bürger，S。Diehl和M.C. Martí，{\ it Ima J. Appl。 Math。} {\ BF 84}（2019）930--973]。具有泡沫层的所需稳态溶液的构造是详细的，在进料体积分数上的可行性条件，在所谓的操作图表中可视化饲料，下流和洗涤水的体积流量。得出并采用单调数值方案来模拟浮选柱的动态行为。还证明，在适当的courant-friedrichs-lewy（CFL）条件下，当初始数据为时，大约的体积分数在零和一个之间。
Froth flotation is a common unit operation used in mineral processing. It serves to separate valuable mineral particles from worthless gangue particles in finely ground ores. The valuable mineral particles are hydrophobic and attach to bubbles of air injected into the pulp. This creates bubble-particle aggregates that rise to the top of the flotation column where they accumulate to a froth or foam layer that is removed through a launder for further processing. At the same time, the hydrophilic gangue particles settle and are removed continuously. The drainage of liquid due to capillarity is essential for the formation of a stable froth layer. This effect is included into a previously formulated hyperbolic system of partial differential equations that models the volume fractions of floating aggregates and settling hydrophilic solids [R. Bürger, S. Diehl and M.C. Martí, {\it IMA J. Appl. Math.} {\bf 84} (2019) 930--973]. The construction of desired steady-state solutions with a froth layer is detailed and feasibility conditions on the feed volume fractions and the volumetric flows of feed, underflow and wash water are visualized in so-called operating charts. A monotone numerical scheme is derived and employed to simulate the dynamic behaviour of a flotation column. It is also proven that, under a suitable Courant-Friedrichs-Lewy (CFL) condition, the approximate volume fractions are bounded between zero and one when the initial data are.
