Multiphase flows, such as atomizing jets, are notorious for generating structures that are much smaller than the dominant scales in the flow. Those features often have significant influence on the overall atomization and must therefore be captured in some way, but their smallness makes them very expensive to resolve using standard numerical approaches.

In many cases, however, these small scale features are relatively simple, since surface tension effects are strong and keep the geometry simple and viscous dominate so flow is simple. Simple flows in simple geometries can often be modeled using analytical or semi-analytical methods and we have explored ways to combine analytical or semi-analytical models with numerical solution that resolves the rest of the flow accurately.

Our work includes early work on strained-diffusion combustion [1,2], and more recent studies of the draining of thin films [3] and mass transfer from gas bubbles in high Schmidt number liquids [4,5].

#### References

[1] C. Chang, W. Dahm, and G. Tryggvason. Lagrangian model simulations of molecular mixing, in- cluding finite rate chemical reactions, in a temporally developing shear layer. Physics of Fluids A, 3:1300–1311, 1991.

[2] W. Dahm, G. Tryggvason, and M. Zhuang. Integral method solution of time-dependent strained diffusion-reaction equations with multi-step kinetics. SIAM J. Appl. Math., 56(4):1039–1059, 1996.

[3] S. Thomas, A. Esmaeeli, and G. Tryggvason. Multiscale computations of thin films in multiphase flows. International Journal of Multiphase Flow, 36:71–77, 2010.

[4] B. Aboulhasanzadeh, S. Hosoda, A. Tomiyama, and G. Tryggvason. A validation of an embedded analytical description approach to the computations of mass transfer from bubbles in high schmidt number liquids. Chemical Engineering Science, 101:165–174, 2013.

[5] B. Aboulhasanzadeh, S. Thomas, M. Taeibi-Rahni, and G. Tryggvason. Multiscale computations of mass transfer from buoyant bubbles. Chemical Engineering Science, 75:456–467, 2012.