Kuchma Anatoly E, Kuni Fedor M, Shchekin Alexander K
Department of Statistical Physics, Faculty of Physics, St Petersburg State University, Ulyanovskaya 1, Petrodvoretz, St Petersburg 198504, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 1):061125. doi: 10.1103/PhysRevE.80.061125. Epub 2009 Dec 18.
An approach to the kinetics of barrier formation of supercritical gas bubbles in a strongly supersaturated liquid solution is presented. A common assumption of uniform reduction of a dissolved gas supersaturation in a liquid solution via stationary diffusion to nucleating gas bubbles is shown to be not applicable to the case of high gas supersaturations. The approach recognizes that the diffusion growth of supercritical bubbles at high gas supersaturation is essentially nonstationary. Nonstationary growth of an individual gas bubble is described by a self-similar solution of the diffusion equation which predicts a renormalized growth rate and thin highly nonuniform diffusion layer around the bubble. The depletion of a dissolved gas due to intake of gas molecules by the bubble occurs only within this thin layer. An integral equation for the total volume of an ensemble of supercritical gas bubbles within a liquid solution is derived. This equation describes the effect of excluding a total volume of the depleted diffusion layers around the growing bubbles nucleated at all previous moments of time until nucleation of new bubbles ceases due to elimination of the nondepleted volume of the solution. An analytical solution of this equation is found. The swelling of the liquid solution, the number of gas bubbles nucleated, the distribution function of bubbles in their sizes, and the mean radius of the bubbles are determined in their dependence on time.
提出了一种研究强过饱和液体溶液中超临界气泡形成屏障动力学的方法。通过向成核气泡的稳态扩散来均匀降低液体溶液中溶解气体过饱和度这一常见假设，被证明不适用于高气体过饱和度的情况。该方法认识到，在高气体过饱和度下超临界气泡的扩散生长本质上是非稳态的。单个气泡的非稳态生长由扩散方程的自相似解描述，该解预测了重整化的生长速率以及气泡周围极薄且高度不均匀的扩散层。由于气泡吸收气体分子导致的溶解气体消耗仅发生在这个薄层内。推导了液体溶液中超临界气泡集合总体积的积分方程。该方程描述了由于排除在所有先前时刻形成的生长气泡周围耗尽扩散层的总体积，直至由于溶液未耗尽体积的消除导致新气泡成核停止的影响。找到了该方程的解析解。确定了液体溶液的膨胀、成核气泡的数量、气泡尺寸分布函数以及气泡平均半径随时间的变化关系。
