Applied mathematics seminar: Pattern selection on a periodically excited miscible

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The interfacial tension between immiscible fluids is an equilibrium thermodynamicproperty that results from different cohesion forces between various types of moleculesKorteweg proposed in 1901 that stress caused by a density gradient could act like interfacialtension. Here we consider a tricky miscible interface. Two different binary mixtures ofclosely matching viscosities, which will be brought into contact in a closed cell, arecomposed of the same molecules (water and isopropanol, IPA) but at differentconcentrations. Our recent experiments under normal and reduced gravity conditions haveshown that application of shear stresses along the miscible interface, such as periodicexcitations, leads to an interfacial instability instead of an active diffusion process. The richdiversity of interfacial patterns occurs in miscible liquids under horizontal vibrations.In terrestrial conditions an interfacial instability has a threshold which depends on thefrequency and amplitude. The observed regular structures above the threshold look staticand are often referred to as “frozen waves” [1]. However, the most intriguing is the noveltype of pattern generated by lateral walls which can be called a fish spine [2].In the reduced gravity experiments [3], after the formation of the waviness on theinterface, the growth of the amplitude does not stop, but continues until the interface reachesthe upper/bottom wall with formation of the long lived pattern consists of a series of verticalcolumns of alternating liquids when the different peaks attain a rectangular shape of variouswidths. In addition, we have discovered Faraday waves as a secondary instability whichdevelops on the primary wavy patterns created by periodic vibrations parallel to the interfacebetween two miscible liquids [4].

[1] Y.A. Gaponenko, M. Torregrosa, V. Yasnou, A. Mialdun, V. Shevtsova, Dynamics of the interfacebetween miscible liquids subjected to horizontal vibration, J. Fluid Mech., 784, 342-372 (2015)

[2] V. Shevtsova, Y. Gaponenko, V.Yasnou, A. Mialdun, A. Nepomnyashchy, Wall-Generated Pattern on aPeriodically Excited Miscible Liquid/Liquid Interface, Langmuir, 31, 5550−5553 (2015)

[3] Y. Gaponenko, M. Torregrosa, V. Yasnou, A. Mialdun, V. Shevtsova, Interfacial pattern selection inmiscible liquids under vibration, Soft Matter., 11, 8221-8224 (2015)

[4] V. Shevtsova, Y. Gaponenko, V.Yasnou, A. Mialdun, A. Nepomnyashchy, Two-scale wave patterns on aperiodically excited miscible liquid/liquid interface, J. Fluid Mech. (2016), 795, pp. 409-422.