The deformation of a ferrofluid drop under a uniform magnetic field

From shaping to functionalization of micro-droplets and particles

“…8A). [124][125][126] This phenomenon is equivalent to the aforementioned deformation of the conductive droplet suspended in a low-conductive liquid by the electric eld. Landau and Lifshitz derived an analytical model for the aspect ratio of deformed droplets under a low magnetic eld as a function of magnetic bond number (Bo m ¼ m out H 2 a/g, where H and m are the magnetic eld strength and magnetic permeability, respectively), which indicates the ratio of the magnetic force to the interfacial force between the droplet and the carrier liquid.…”

Numerical study of ferro‐droplet breakup initiation induced by a slowly rotating uniform magnetic field

“…After the usual FEM integration‐by‐parts of the Laplacian in (10a) to introduce the normal derivative of the velocity, ∂ u / ∂ n , the integral of the magnetic stress tensor term at the end of (10a) will create, via the divergence theorem, a purely surface magnetic forcing term 8,10 which will antagonize that due to surface tension (2h) to give the full surface tractions shown in (10c).…”

“…There have been many experimental 6‐8 and numerical 8‐12 studies of the simple axisymmetric prolate spheroid equilibrium shapes ferrodrops achieve inside static uniform applied magnetic fields analogous to those of dielectric drops in an electric field, 13‐16 where the prolate elongation from a sphere aligns with the applied field direction and assumes a stable equilibrium configuration directly proportional to the field strength.…”

“…Additionally, if the particles are also "magnetically soft," with a magnetization relaxation time of the order 10 −7 seconds, then hysteresis effects may also be neglected, as will be done here.Finally, a ferrofluid in droplet form gives a rich and varied phenomenology of physical behavior through the competition between magnetic and surface tension forces on the surface, in an analogous manner to that seen between electric and surface tension forces in electrohydrodynamics. [3][4][5] There have been many experimental 6-8 and numerical [8][9][10][11][12] studies of the simple axisymmetric prolate spheroid equilibrium shapes ferrodrops achieve inside static uniform applied magnetic fields analogous to those of dielectric drops in an electric field, [13][14][15][16] where the prolate elongation from a sphere aligns with the applied field direction and assumes a stable equilibrium configuration directly proportional to the field strength.However, if the external magnetic field rotates, then two distinct classes of behavior emerge, dependent on the rotation speed.…”

Droplet Manipulation under a Magnetic Field: A Review

“…Various operations of droplets have been performed under a magnetic field, such as ferrofluid droplet stretching [13][14][15][16][17], deflecting [18,19], sorting [20,21], merging [14,[22][23][24][25] and splitting [26][27][28][29], as well as the application in mixing chemical reagents [30], capsule synthesis [31], microlens [32], etc. Based on droplet manipulation, functional group-modified magnetic nanoparticles (MNPs) [33] dispersed in the carrier fluid are used for oil contamination separation [34], oil and gas processing [35], chemical extraction [36] and detection and extraction of heavy metal ions [37] under the magnetic field.…”