On physical mechanisms in chemical reaction-driven tip-streaming

Abstract

In this work we provide a basic physical modeling of the spatiotemporal pattern of emulsification produced by chemical reaction-driven tip-streaming and observed by Fernandez and Homsy [Phys. Fluids 16, 2548 (2004)]. Features of this phenomenon—nonlinear autooscillations, a conical drop shape, tip-streaming, and droplet trajectory splitting—are addressed in this paper. In particular, the experimentally found regimes of self-sustained periodic motion and the transitions between them are explained with the help of a nonlinear relaxation oscillator model. An exact self-similar solution for the steady tip-streaming mode supports the suggested mechanism of a Marangoni-driven phenomenon. Finally, the ionic nature of the surfactant produced at the interface offers a reasonable explanation for the formation of a spray cone, which is due to repulsive electrostatic interactions between droplets. These features distinguish this phenomenon from standard tip-streaming.

Cusps and cuspidal edges at fluid interfaces: Existence and application

“…2(a), self-driven Marangoni singularities have not been thoroughly studied. Marangoni-driven flows exhibiting interfacial singularities, which motivated the present study, were found experimentally only recently [19,[36][37][38][39] and are shown in Figs. 2(b) and 2(c).…”

“…The interrelation between these two kinds of singularities is the first key question addressed in the present study and brings together topological and analytical views of fluid dynamics, which are arguably equally important [11,12], Often, mathematical singularities occur when viscosity and/or surface tension is neglected [13], The present study shows that one can get a singularity even if these physical effects are both present. While singular solutions are known in the dynamics of viscous flows, especially in fixed geometries such as the Jeffrey-Hamel flow in a converging channel [14] and on a polygon [ 15], in problems with free interfaces primarily corner [14,16] and cone [5] type solutions were studied, e.g., in the context of Taylor cones [17,18] and chemical-reaction driven tip streaming [19],…”

“…(7) Let us identify the conditions under which a solution local near a cusp singularity exists in the Stokes approximation. The corresponding stream function (6) satisfies the kinematic boundary condition (3) provided [17,35] -viscous stresses in the surrounding phase deform the drop, which forms pointed ends; (b) chemical reaction-driven tip streaming [19,36,37] -the acid-base chemical reaction at the water-oil interface produces a surfactant, which drives the Marangoni flow along the interface leading to a conical shape of the drop with a singular cone tip', (c) surfactant-driven fingering [38,39]-soapy water displaces air in the narrow space between two glass plates (Hele-Shaw cell) and eventually leads to fingering with cusps between the fingers. 043019-2 CUSPS AND CUSPIDAL EDGES AT FLUID INTERFACES: ... which allows us to rewrite the formula (6) as…”

Microscale tipstreaming in a microfluidic flow focusing device

“…This raises questions as to whether the surface tension is bounded at dynamic interfaces as it is at static interfaces, 46 and under which conditions the viscous stresses can overcome surface tension and draw out a thin thread. 49 In addition, it will be necessary to account for the periodic nature of the process by incorporating the removal of surfactants from the interface via the thin thread and the time scales for the diffusion, adsorption, and desorption processes that enable surfactant to repopulate the interface in a finite time.…”

An investigation into the nature and potential of in-situ surfactants for low energy miniemulsification

“…The majority of literature reports on similar systems that invoke interfacial reactions between surface active acid/base pairs suggest the cause is due to the ultra-low surface tension of these systems coupled with induced Marangoni stresses that can result in a self sustaining stream of droplets from the interfacial region. [34][35][36][37][38] For a typical preformed emulsifier, in the absence of droplet breakup, the newly generated oil-water interface becomes saturated with surfactant by first, diffusion of surfactant molecules from the bulk continuous phase to the interfacial region, and second, by adsorption of the surfactant from this region to the oil-water interface. The equilibrium adsorption is determined by the rate of adsorption of monomeric surfactant units from the interfacial region and the rate of desorption from the interface (see Figure 8).…”