Magnetohydrodynamics- and magnetosolutal-transport-mediated evaporation dynamics in paramagnetic pendant droplets under field stimulus

Evaporation kinetics of pendant droplets is an area of immense importance in several applications, in addition to possessing rich fluid dynamics and thermal transport physics. This article experimentally and analytically sheds insight into the augmented evaporation dynamics of paramagnetic pendant droplets in the presence of a magnetic field stimulus. The literature provides information that solutal advection and the solutal Marangoni effect lead to enhanced evaporation in droplets with solvated ions. The main focus of this article is to modulate the thermosolutal advection with the aid of an external magnetic field and comprehend the dynamics of the evaporation process under such complex multiphysics interactions. Experimental observations reveal that the evaporation rate enhances as a direct function of the magnetic moment of the solvated magnetic element ions, thereby pointing at the magnetophoretic and magnetosolutal advection. Additionally, flow visualization by particle image velocimetry illustrates that the internal advection currents within the droplet increase in magnitude and are distorted in orientation by the magnetic field. A mathematical formalism based on magnetothermal and magnetosolutal advection has been proposed via scaling analysis of the species and energy conservation equations. The formalism takes into account all major governing factors, viz., the magnetothermal and magnetosolutal Marangoni numbers, magneto-Prandtl and magneto-Schmidt numbers, and the Hartmann number. The modeling establishes the magnetosolutal advection to be the dominant factor behind the augmented evaporation dynamics. Accurate validation of the experimental internal circulation velocity is obtained from the proposed model. This study reveals rich insight into the magnetothermosolutal hydrodynamics in paramagnetic droplets.

Figure 1

Schematic of the experimental setup employed: (a) laser controller, (b) laser mounted on stand with light sheet optics assembly (not illustrated), (c) electromagnet power supply and controller, (d) droplet-dispensing mechanism (DDM) with backlight illumination assembly, (e) DDM and illumination controller, (f) computer for data acquisition and camera control, (g) programmable electromagnet unit, (h) CCD camera with microscopic lens assembly and three-axis movement control. Components (b), (d), (g), and (h) are enclosed in an acrylic chamber and housed on a vibration-free mount.

Figure 2

Evaporation characteristics of water and different magnetic salt (${\mathrm{FeCl}}_3$, $\mathrm{CoC}{\mathrm{l}}_2·6{\mathrm{H}}_2\mathrm{O}$, and $\mathrm{NiS}{\mathrm{O}}_4·6{\mathrm{H}}_2\mathrm{O}$) solution droplets (0.1 M concentration) at (a) 0 T and (b) 0.16 T.

Figure 3

Time snaps of (a) different magnetic field strength for ${\mathrm{FeCl}}_3$ solution (0.1 M) and (b) different salt solutions (0.1 M) with 0.16 T field. The scale bar represents 1 mm. The time snaps shown are at 0, 1050, and 2100 sec of the droplet's lifetime.

Figure 4

(a) Evaporation characteristics of ${\mathrm{FeCl}}_3$ solution droplet (0.2 M) under the influence of different magnetic field strengths; (b) evaporation rate constants corresponding to magnetic field variation.

Figure 5

(a) Surface tension variation for $\mathrm{CoC}{\mathrm{l}}_2·6{\mathrm{H}}_2\mathrm{O}$ solution (different concentrations) as a function of magnetic field strength and (b) behavior of the evaporation rate constant for different salts (0.2 M concentration) as a function of magnetic field strength.

Figure 6

(a) Comparison of theoretical and experimental evaporation rate constant for different salts with varying concentration and magnetic field employing the diffusion model; (b) percentage contribution of the different mechanism involved in energy transfer based on our analysis.

Figure 7

Velocity contours and vector fields for (a) 0.1 M ${\mathrm{FeCl}}_3$ at 0 T, (b) 0.1 M ${\mathrm{FeCl}}_3$ at 0.16 T, (c) 0.2 M ${\mathrm{FeCl}}_3$ at 0.08 T, (d) 0.2 M ${\mathrm{FeCl}}_3$ at 0.24 T. (e) Comparison of respective theoretical velocities from the proposed scaling model with experimental velocities (spatially averaged).

Figure 8

Stability plot of the Ra and $\mathrm{M}{\mathrm{a}}_{\mathrm{T}}$ for pure water and different salt solution-based droplets of varying concentration in the absence of a magnetic field. Stability criteria lines proposed by Nield [32] and Davis [40] illustrate the regimes for stable internal advection.

Figure 9

Comparison of magnetothermal Ma and Ra for different magnetic salt solution droplets with varying concentration evaporating under the effect of a magnetic field. Iso-Ha lines have been presented to understand the effect of magnetic field strength on the stability regimes.

Figure 10

The dynamic bulk and interfacial ion concentration of ${\mathrm{FeCl}}_3$ (initially at 0.2 M) droplet during the progress of evaporation. The “bulk” represents dynamic bulk concentration, and “dyn” represents dynamic interfacial concentration.

Figure 11

(a) The contribution by different mechanisms based on the magnetothermal convection model; (b) the contribution by a different mechanism based on the magnetosolutal convection model.

Figure 12

Comparison of the thermal Ma against the solutal Ma in absence and presence of a magnetic field. The stability curves represent different iso-Le [42] and iso-Ha lines.

Figure 13

Comparison of magnetothermal Ma against the magnetosolutal Ma. The stability curves iso-Le [42] and iso-Ha lines.