We present an analysis of an extended Rayleigh–Plesset (RP) equation for a three dimensional cell of microorganisms such as bacteria or viruses in some liquid, where the cell membrane in bacteria or the envelope (capsid) in viruses possess elastic properties. To account for rapid changes in the shape configuration of such microorganisms, the bubble membrane/envelope must be rigid to resist large pressures while being flexible to adapt to growth or decay. Such properties are embedded in the RP equation by including a pressure bending term that is proportional to the square of the curvature of the elastic wall. Analytical solutions to this extended equation are obtained in terms of elliptic functions.

我们对某些液体中的微生物（例如细菌或病毒）的三维细胞的扩展 Rayleigh-Plesset (RP) 方程进行了分析，其中细菌中的细胞膜或病毒中的包膜（衣壳）具有弹性。为了解决此类微生物形状配置的快速变化，气泡膜/信封必须是刚性的以抵抗大压力，同时灵活以适应生长或衰变。通过包括与弹性壁曲率的平方成正比的压力弯曲项，这些特性被嵌入到 RP 方程中。这个扩展方程的解析解是根据椭圆函数获得的。