Mechanical Engineering Department, University of Delaware, Newark, Delaware 19716, USA.
J Colloid Interface Sci. 2010 Mar 1;343(1):42-7. doi: 10.1016/j.jcis.2009.11.030. Epub 2009 Nov 20.
Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although bubbles, containing gases other than air, are considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support a net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided.
对微泡中气体扩散的数学模型进行线性稳定性分析。该模型是对埃普斯坦-普莱瑟模型的修正，以考虑封装弹性和有限气体渗透性。尽管考虑了包含空气以外气体的气泡，但最终稳定的气泡（如果存在）仅包含空气，并且仅在周围介质与空气达到饱和或过饱和时才能实现稳定性。在没有封装弹性的情况下，对于零表面张力，仅能实现中性稳定性，另一种解决方案是不稳定的。对于弹性封装，根据饱和度水平以及表面张力是否小于或大于弹性，会得到不同的平衡解。对于弹性封装，弹性可以使气泡稳定。但是，对有效表面张力（由参考表面张力和弹性应力组成）施加非负条件会导致平衡半径仅为中性稳定。如果封装能够承受净压缩应力，则可实现实际稳定性。线性稳定性结果与我们最近的数值发现一致。为各种平衡的稳定性或不稳定性提供了物理机制。
