Fluid Morphologies Governed by the Competition of Viscous Dissipation and Phase Separation in a Radial Hele-Shaw Flow

Abstract

The displacement of a less viscous fluid by a more viscous fluid in a radial Hele-Shaw cell makes a circular pattern because the interface is hydrodynamically stable in this condition. Very recently, it has been experimentally reported that the hydrodynamically stable displacement in a partially miscible system induces fingering patterns while stable circular patterns are made at fully miscible and immiscible systems. The fingering instability in the partially miscible system results from complex and entangled elements involving viscous dissipation, molecular diffusion, and phase separation. The analyzing mechanism requires a quantitative relationship between the hydrodynamic interfacial fingering patterns and underlying physicochemical properties. Here, we experimentally investigated the change in fluid patterns formed by the progression of phase separation in the partially miscible systems and categorized them into three patterns: finger-like pattern, annular-like pattern, and circular pattern. Moreover, we propose the mechanism of the pattern formation by an interfacial tension measurement and evaluate the patterns by modified capillary number and newly defined body force ratio, Bf. Our analysis revealed that the deformation index of the pattern can be expressed as a function of Bf on a single curve regardless of the miscibility.

Experimental demonstration of the suppression of viscous fingering in a partially miscible system

“…6 we show the interfacial tension measured by the spinning method and denoted as , where the subscript m 𝜸 𝒎 indicates "measured". The previous report showed that the temporal increase of interfacial tension was evidence for occurrence of the Korteweg force 12,19,20 . In Fig.…”

“…19 Partially miscible systems have also been reported experimentally to show anomalous patterns because of the phase separation. 20,21 Numerical simulations by Seya et al 22 reproduced such multiple-droplet formation with a partially miscible system.…”

“…The fingering pattern has also been shown to be induced in partially miscible systems in a viscously stable situation where the more viscous solution displaces the less viscous one in Hele-Shaw cells 19 . Partially miscible systems have also been experimentally reported to show anomalous patterns because of the phase separation 20,21 . Numerical simulations by Seya et al 22 reproduced such multiple droplet formation with a partially miscible system.…”

Growing Interface with Phase Separation and Spontaneous Convection during Hydrodynamically Stable Displacement

“…Several studies regarding interfacial hydrodynamics that considered fully miscible and immiscible cases have been reported [3,[9][10][11][12]. Recently, Suzuki et al discovered a novel interfacial dynamics feature using a partially miscible system, which can be treated at room temperature and atmospheric pressures [13][14][15][16]. Their partially miscible system was comprised of polyethylene glycol (PEG), Na 2 SO 4 , and water, for which spinodal decomposition phase separation occurred at the boundary of the displacing and displaced liquids.…”

“…Figure 1. Phase diagram of the polyethylene glycol (PEG)-Na 2 SO 4 -water system[15]. The different color symbols show the three systems having different three thermodynamic states: the red circles for the immiscible system, the blue circles for the fully miscible system, and the green circles for the partially miscible system.…”