Marangoni instabilities of drops of different viscosities in stratified liquids

For an immiscible oil drop immersed in a stably stratified ethanol–water mixture, a downwards solutal Marangoni flow is generated on the surface of the drop, owing to the concentration gradient, and the resulting propulsion competes against the downwards gravitational acceleration of the heavy drop. In prior work of Li et al. (Phys. Rev. Lett., vol. 126, issue 12, 2021, 124502), we found that for drops of low viscosity, an oscillatory instability of the Marangoni flow is triggered once the Marangoni advection is too strong for diffusion to restore the stratified concentration field around the drop. Here we experimentally explore the parameter space of the concentration gradient and drop radius for high oil viscosities and find a different and new mechanism for triggering the oscillatory instability in which diffusion is no longer the limiting factor. For such drops of higher viscosities, the instability is triggered when the gravitational effect is too strong so that the viscous stress cannot maintain a stable Marangoni flow. This leads to a critical drop radius above which the equilibrium is always unstable. Subsequently, a unifying scaling theory that includes both the mechanisms for low and for high viscosities of the oil drops is developed. The transition between the two mechanisms is found to be controlled by two length scales: the drop radius $R$ and the boundary layer thickness $\delta$ of the Marangoni flow around the drop. The instability is dominated by diffusion for $\delta < R$ and by viscosity for $R<\delta$ . The experimental results for various drops of different viscosities can well be described with this unifying scaling theory. Our theoretical description thus provides a unifying view of physicochemical hydrodynamic problems in which the Marangoni stress is competing with a stable stratification.

Effect of small heat release and viscosity on thermal-diffusive instability

The linear stability of a thermal reaction front has been investigated based on the thermal-diffusive model proposed by Zel’dovich and Frank-Kamenetskii, which is called ZFK model. In the framework of ZFK model, heat-conduction and mass-diffusion equations are treated without the effect of hydrodynamic flow. Then, two types of instability appear: cellular and oscillatory instabilities. The cellular instability has only positive real part of growth rate, while the oscillatory instability is accompanied with non-zero imaginary part. In this study, the effect of heat release and viscosity on both instabilities is investigated asymptotically and numerically. This is achieved by coupling mass-conservation and Navier–Stokes equations with the ZFK model for small heat release. Then, the stable range of Lewis number, where the real part of growth rate is negative, is widened by non-zero values of heat release for any wavenumber. The increase of Prandtl number also brings the stabilization effect on the oscillatory instability. However, as for the cellular instability, the viscosity leads to the destabilization effect for small wavenumbers, opposed to its stabilization effect for moderate values of wavenumber. Under the limit of small wavenumber, the property of viscosity becomes clear in view of cut-off wavenumber, which makes the real part of growth rate zero.

Effect of Nonreciprocal Forces on the Stability of Dust Clusters

Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.

Theoretical Description for an Efficient Rhenium Electrocatalytical Recuperation by Polypyrrole Overoxidation

An interesting process for rhenium recuperation during the polypyrrole overoxidation has been theoretically described. The correspondent mathematical model has been developed and analyzed using linear stability theory and bifurcation analysis. The model's analysis confirms the possibility for the efficient rhenium ion capture by polypyrrole overoxidation, yielding a long-living electrocatalytic material. On the other hand, oscillatory instability is also possible in both stages.

Theoretical Description for Copper (II) Electrochemical Determination and Retention on a 1(2-pyridilazo)-2-naphthole-Modified Anode

A modern and flexible spectrophotometric method for copper determination in food has been proposed to be posted on the electrochemical tracks. The theoretical analysis of the correspondent model confirms the efficiency of the electrochemical reaction for either electroanalytical or electro-synthetical or eliminative processes for copper. As for the oscillatory instability, it will be caused by either chemical or electrochemical influences on the double electric layer.