#7114. Dynamics of a viscous drop under an oscillatory uniaxial extensional Stokes flow

December 2026publication date
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Journal’s subject area:
Fluid Flow and Transfer Processes;
Physics and Astronomy (all);
Mechanical Engineering;
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Abstract:
We quantify the transient deformation and breakup of a neutrally-buoyant drop with viscosity ??? immersed in another Newtonian fluid with viscosity ?? undergoing oscillatory uniaxial extension at zero Reynolds number. The interfacial tension acting between drop phase and medium phase is ??. The drop is initially a sphere of radius a?. Since the external flow oscillates harmonically with a frequency ??, the strength of the imposed flow is characterized by an instantaneous capillary number, Ca=Ca0cos(Det), where Ca0=????a?/?? and De=????a?/?? is the dimensionless frequency, or Deborah number. Here, ?? is the rate of extension in the imposed flow. We utilize boundary-integral computations to calculate the evolution of drop interface as a function of Ca0 and De, focusing primarily on the case where the drop and surrounding fluid have equal viscosities. The computations suggest two families of behavior for the drop deformation. First, below a critical Deborah number (which we determine to be in the interval 0.375Keywords:
Boundary integral method; Drop deformation; Oscillatory uniaxial extensional flow

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