Liquid-liquid phase separation and cluster formation at deposition of metals under inhomogeneous magnetic field

The formation and dynamic of expansion and deformation of the liquid-liquid interface of an electrolyte at deposition of metals at the surface of the magnetized steel ball is considered in this paper. The electrochemical processes were investigated in an external magnetic field directed at an arbitrary angle to the force of gravity. These processes are accompanied by the formation of effectively paramagnetic clusters of electrochemical products – magnions. Tyndall effect was used for detection of the presence of magnions near the magnetized steel electrode in a solution. The shape of the interface separating the regions with different concentration of magnions, i.e. different magnetic susceptibilities, was described theoretically based on the equation of hydrostatic equilibrium which takes into account magnetic, hydrostatic and osmotic pressures.


Introduction
The effect of inhomogeneous magnetic fields (MF) on electrochemical processes is the subject of current research in the field of magnetoelectrolysis [1][2][3][4][5][6][7][8]. It was discovered experimentally [1][2][3][4] that the course of these processes depends on the gradient of MF and its distribution on the electrode surface. In particular, the formation of regions with higher concentration of electrochemical reaction products near the magnetic poles of a magnetized steel spherical sample was studied in [5][6][7] at the etching [5] and the deposition of metals on its surface [6,7] under the influence of constant MF. The approach of the impact of gradient magnetic force not on single paramagnetic ions, but on the clusters of electrochemical reaction products (magnions) was proposed in [5][6][7]. Magnions can represent paramagnetic or effectively paramagnetic bubbles of gases, nano-and/or microparticles with their ionic environment [5][6][7][8]. Also the concept of effective magnetic susceptibility of magnions ms     as the difference between magnetic susceptibilities of a magnion m  and a solution s  was introduced in this model [5][6][7].
The aim of this work is to study the process of the formation of a heterogeneous state of an electrolyte which is observed at the metal deposition on the surface of a spherical magnetized ferromagnetic electrode in an external MF (EMF) directed at an arbitrary angle to the direction of the force of gravity (FG) without passing of an external electric current through the solution. The theoretical model of the paper is based on the equation of hydrostatic equilibrium consisting of magnetic, osmotic and gravitational pressures and the pressure of the centrifugal force which causes the electrolyte rotation near the electrode surface with the velocity about 1 cm/s [7]. This equation allows calculating the form of the interface in liquid near the electrode surface that separates the regions with higher concentration of magnions and the bulk solution.

Experimental results
Experimental observation of electrolyte phase separation at the deposition of copper ions on the surface of a steel spherical sample was carried out at angles of 90, 80, 70, 60, 50 and 40 degrees between the directions EMF to FG. The Tyndall effect was used to visualize areas with higher magnions concentrations similarly to [6]. The set of photos of liquid-liquid separation at different stages are shown in Fig. 1. Regions with higher magnion concentration are forming near the magnetic poles of the steel spherical electrode where the strength of MF (as the superposition of an uniform EMF and dipole MF of a magnetized steel spherical electrode) is the largest. In addition, the anisotropic sedimentation of copper ions near the magnetic equator of the steel spherical electrode (where the gradient MF is minimal) is observed. As it was shown in [6] the shape of interface remains almost unchanged for about 1000 seconds after its relatively fast formation. This allows considering such state of the system as the quasi-stationary one.

Theoretical model
The hydrostatic equilibrium in an electrolyte depends on the balance of pressures at the interface between regions with different concentrations of electrochemical reaction products:  (1). The effect of the centrifugal force will be significant for smaller electrode sizes and higher electrolyte rotation velocities. Thus, the equation (1) in the case of a spherical ferromagntic electrode can be written as follows: The comparison of theoretical modeling with experimental data is shown in Fig. 2.

Conclusions
The formation of quasi-stationary heterogeneous state of an electrolyte and liquid-liquid phase separation were experimentally detected at the metal deposition on the surface of a magnetized ferromagnetic spherical electrode in an inhomogeneous constant MF. This state of the system exists around 10 3 sec and is characterized by the appearance of regions in the electrolyte with different magnetic susceptibilities. The change of the interface shape was investigated depending on the relative angle between the directions of EMF and FG. Metal deposition in gradient MF is accompanied by the formation of nano-and/or microclusters containing 10 4 -10 5 paramagnetic ionsmagnions.
This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 644348 (MagIC).