Dynamic and stationary shapes of rotating toroidal drops in viscous linear flows

Abstract

Abstract

Controlled stabilization of rotating toroidal drops in viscous linear flow

“…Deshmukh & Thaokar 2013;Ghazian, Adamiak & Castle 2013;Texier et al 2013;Zabarankin 2017a,b). A detailed discussion of these phenomena and of applications of the resulting toroidal drops can be found in, for example, Zabarankin et al (2015), Banerjee et al (2021) and Malik, Lavrenteva & Nir (2021). Pairam & Fernández-Nieves (2009) proposed a method for the controlled generation of toroidal drops inside an immiscible fluid: a liquid is extruded from an injection needle into a rotating continuous phase until the resultant jet closes into a torus.…”

“…More complicated than solid body rotation flow structure occurs if the deformation of the drops is dynamic or when a stationary drop is subjected to other types of outer flow. Numerical simulations on toroidal drop dynamics in viscous fluid based on the boundary integral formulation are reported in Stone & Leal (1989), Zabarankin et al (2015), Ee et al (2018) and Malik et al (2021). Zabarankin & Nir (2011) and Zabarankin (2012Zabarankin ( , 2016 developed an alternative approach to the simulation of axisymmetric drop deformation based on generalized analytic functions.…”

“…Such effects were demonstrated in the recent studies of Zabarankin (2016) for spheroidal drops in compressional flow under an electric field and Holgate & Coppins (2018) for charged rotating drops. Malik et al (2021) studied drop deformation in a linear flow field having rotational and axisymmetric extensional or biextensional components. One of the most interesting results of Malik et al (2021) is the existence of a subdomain of the physical parameters exhibiting stable stationary toroidal shapes of a rotating drop when under an extensional flow regime (stable to axisymmetric disturbances).…”

“…Malik et al (2021) studied drop deformation in a linear flow field having rotational and axisymmetric extensional or biextensional components. One of the most interesting results of Malik et al (2021) is the existence of a subdomain of the physical parameters exhibiting stable stationary toroidal shapes of a rotating drop when under an extensional flow regime (stable to axisymmetric disturbances). Recall that if both phases are Newtonian fluids and in the absence of one of the components of the outer flow, all toroidal stationary shapes are unstable to these disturbances.…”

“…Recall that if both phases are Newtonian fluids and in the absence of one of the components of the outer flow, all toroidal stationary shapes are unstable to these disturbances. Typically, the stable to axisymmetric disturbances solutions constructed by Malik et al (2021) correspond to highly extended tori that are likely to be unstable to asymmetric disturbances (see, e.g. Pairam & Fernández-Nieves 2009;Nurse et al 2015).…”