We investigate and classify possible analytical solutions for a simplified version of the foam bubble population model, by varying injection conditions and kinetic foam generation parameter. We prove that the behavior of the analytical solutions changes at the transition between two regions, similar to rarefaction-shock solutions for the Buckley-Leverett equation. In one region (region I), the solutions are in the form of traveling waves, in rather good agreement with CT scanned foam experiments and numerical simulations reported in Simjoo and Zitha (2015). In region II, however, corresponds to solutions as a sequence of waves: one spreading wave and one traveling wave. These corresponding flow profiles are different from those found so far in the experiments.

我们通过更改注入条件和动态泡沫生成参数，对简化的泡沫气泡总体模型进行了调查和分类，并对其进行了分类。我们证明了解析解的行为在两个区域之间的过渡处发生了变化，类似于Buckley-Leverett方程的稀疏冲击解。在一个地区（地区I），解决方案采用行波形式，与Simjoo和Zitha（2015）中报道的CT扫描泡沫实验和数值模拟相当吻合。然而，在区域II中，对应于一系列波的解：一个扩展波和一个行进波。这些相应的流量曲线与实验中迄今发现的不同。