The fluid mechanics problem of an initially spherical compound drop suspended in another fluid undergoing a nonlinear extensional creeping flow, is the subject of this theoretical report. The compound drop is originally composed from an inner spherical drop positioned at the center of a spherical fluid shell. The problem is governed by six dimensionless parameters: the external capillary number (Ca), two viscosity ratios: shell over external (${\lambda }_{21}$) and internal over shell (${\lambda }_{32}$), the radii ratio: inner over outer ($\kappa$), the surface tensions ratio: inner-shell over outer-shell ($\Omega$), and the nonlinear intensity of the flow (E). When the extensional flow is linear ($E=0$), a case already treated in the literature, a uniaxial flow (Ca > 0) deforms the outer surface into a prolate spheroid and the inner drop into an oblate spheroid, while the reverse occurs for the biaxial flow (Ca < 0). If the extensional flow is nonlinear (E $\ne$ 0), the external fluid behaves different than the linear case suggesting sometimes closed circulations (E > 0) and always separating surfaces (E < 0). As a result, each surface of the compound drop may experience both uniaxial and biaxial flow simultaneously, and the number of shell and internal drop circulations may be doubled. This weird situation, suggests new and exciting deformation and breakup patterns, and it is the result of the inclusions of nonlinear terms to the flow field.

该理论报告的主题是，最初呈球形的复合液滴悬浮在另一种经历非线性扩展蠕变流的流体中的流体力学问题。复合液滴最初由位于球形流体壳中心的内部球形液滴组成。该问题由六个无量纲参数控制：外部毛细管数（Ca），两个粘度比：壳层对外部（${\lambda }_{21}$）和内部over shell（${\lambda }_{32}$），半径比：内比外（$\kappa$），表面张力比：内壳比外壳（$\Omega$）以及流动的非线性强度（E）。当延伸流为线性时（$Ë=0$）（一种在文献中已经处理过的情况），单轴流（Ca > 0）使外表面变形为扁球体，内部液滴变形为扁球体，而双轴流则相反（Ca <0）。如果延伸流是非线性的（E $\ne$0），外部流体的行为与线性情况不同，表明有时是封闭的循环（E > 0），并且始终是分开的表面（E <0）。结果，化合物液滴的每个表面可能同时经历单轴和双轴流动，并且壳和内部液滴循环的数量可能加倍。这种奇怪的情况表明出现了新的令人兴奋的变形和破裂模式，这是流场中包含非线性项的结果。