Modeling Experimental Oscillations in Liquid Membranes with Delay Equations

Abstract

The oil/water interface has been of great importance in understanding the dynamics of oscillatory interfacial mass transfer phenomenon and other bio-oscillations in excitable membranes. The oscillatory mass transfer across the oil/water interface generates an oscillating interfacial potential, which is measurable with suitable experimental setup. A detailed and systematic experimental study on the CTAB/picric acid system is done and a diffusion model is studied using delay-differential equations. It is found that a two-variable model with delay in one of the variables is able to explain the observed phenomenon satisfactorily.

Quasi-elastic Laser Scattering for Measuring Inhomogeneous Interfacial Tension in Non-equilibrium Phenomena with Convective Flows

“…A considerable number of studies have examined oscillatory liquid-membrane systems with different chemical compositions and geometries. 7,8,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] In all of the cases studied, the surfactants in the donor phase were considered to be dissolved in the membrane phase and to transfer into the acceptor phase, but the origin of the electric potential oscillations remains controversial. 43,46,47 One issue in previous studies, which has caused controversy, is that interfacial tension measurements at the donor/membrane and the membrane/acceptor interfaces have never been made simultaneously.…”

“…7,45,50 A plastic tube with a V-shaped deformation was inserted in order to separate the aqueous phases, similarly to a previous study. 51,60 Figures 3(b), 3(c) and 3(d) show the simultaneously measured time course of the interfacial tensions at the donor/membrane and at the acceptor/ membrane interfaces and of the electric potential between two aqueous phases, respectively. Oscillations in the electric potential were in phase only with those of the interfacial tension at the acceptor/membrane interface, and a strong positive correlation was found between the amplitude of the oscillations in the electric potential and the drop in the interfacial tension.…”

Propagation and Synchronization of Potential Oscillations in Multiple Liquid Membrane Systems

“…Finally, W2 of pure water was overlaid on the O outside of the tubes. According to the literature, 25,28 a V-shaped notch of 3 mm depth was put at the orifice of the tube to approach three phases closely and to improve the reproducibility of oscillation. The glass tubes had been kept inserted deeply in the O during the filling of solutions inside the tubes, and then the glass vessel placed on the lab jack was moved downward to realize the closest approach of W1 and W1′ toward W2 nearby the V-shaped notch and to start the oscillation.…”

“…[5][6][7][8][9][10][11][12] Further, the oscillations of the membrane potential or the current in three-phase liquid membrane systems have been investigated extensively. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] One of the typical liquid membrane systems is composed of an aqueous solution containing cetyltrimethylammonium chloride (CTACl) and alcohol, W1, a nitrobenzene solution containing picric acid (HPic), O, and a pure water phase, W2, 13,[15][16][17][18][19][20][23][24][25] where such a potential oscillation appeared with an amplitude of 0.3 to 0.4 V and a period of 1 min. The oscillation mechanism of this system was proposed by the present authors, 23 where the amplitude of potential oscillation was explained by the difference in the Gibbs energies for the transfer of Pic -and Cl -from O to W2, and the adsorption and desorption of the H + Pic -ion pair at the O/W2 interface were requisite for the oscillation.…”

Spontaneous Oscillation Mechanism by Simultaneous Time-resolved Measurements of Interfacial Tensions of Both the Donor/Membrane and Membrane/Acceptor Phases

“…Considerable numbers of additional researchers have also reported oscillatory liquid membrane systems of varying compositions. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] In all cases, the surfactant in the donor phase is considered to be dissolved into the membrane phase and transferred to the acceptor phase. Conversely, the mechanism of the oscillatory behavior of liquid membranes has been the subject of controversy, and several mechanisms have been proposed.…”