Non‐conforming finite elements for axisymmetric charged droplet deformation dynamics and Coulomb explosions

Radcliffe, Alastair J.

doi:10.1002/fld.3667

Cited by 9 publications

(9 citation statements)

References 29 publications

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“…where the spheroid mass, m, and volume, 4 3 b c 2 , are unchanged from the initial unit radius sphere, so b c 2 = 1. Clearly, in Figure 3, the angular momentum increases the fastest with the lower Ohnesorges, as might be expected given that the droplets can react much quicker with a lower viscosity to the imposed field trying to elongate the drop and, for a given overall rotation, the more elongated a drop, the more momentum stored in its rotation.…”

Section: Resultsmentioning

confidence: 99%

“…With magnetic susceptibility, , already unitless, the nondimensionalization of (2) follows that done in previous work 4 with tildes on the corresponding (untilded) physical quantities to indicate dimensionless timet ≡ t∕t, densitỹ≡ ∕̂, surface tensioñ≡ ∕̂, and pressurep ≡ p∕p wherê…”

Section: Nondimensionalizationmentioning

confidence: 99%

“…With magnetic susceptibility,

χ

, already unitless, the nondimensionalization of (2) follows that done in previous work 4 with tildes on the corresponding (untilded) physical quantities to indicate dimensionless time

\tilde{t} \equiv t / \hat{t}

, density

\tilde{ρ} \equiv ρ / \hat{ρ}

, surface tension

\tilde{γ} \equiv γ / \hat{γ}

, and pressure

\tilde{p} \equiv p / \hat{p}

where

\hat{t} = \sqrt{\frac{ρ a^{3}}{γ}}; \hat{ρ} = \frac{μ \hat{t}}{a^{2}}; \hat{γ} = \frac{μ a}{\hat{t}}; \hat{p} = \frac{μ}{\hat{t}},

giving an equivalence between the dimensionless density and surface tension

\frac{\tilde{ρ}}{\tilde{γ}} = \frac{ρ}{γ} \frac{\hat{γ}}{\hat{ρ}} = \frac{ρ}{γ} \frac{μ a}{\hat{t}} \frac{a^{2}}{μ \hat{t}} = \frac{ρ a^{3}}{γ} \frac{1}{t}

…”

Section: Nondimensionalizationmentioning

confidence: 99%

“…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 3‐5 …”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

Radcliffe

2020

Engineering Reports

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The fully three-dimensional start-up deformations and accelerations of initially spherical magnetically susceptable linearly magnetizable ferrofluid droplets, driven by a rotating uniform magnetic field, are investigated through the use of coupled finite element/boundary element computer simulations. For given magnetic susceptability, a critical viscosity is suggested, proportional to both magnetic field strength and rotation speed, below which the deformations of the initially spherical droplet inevitably lead to breakup, but above which a simple persistent spheroidal solid body rotation is attained. K E Y W O R D Sdroplet deformations, ferrofluids, finite/boundary elements, rotating magnetic field INTRODUCTIONA ferrofluid is a non-electrically conducting, stable colloidal suspension of magnetic particles in a Newtonian carrier liquid that makes the latter sensitive to the presence of a magnetic field. 1 Such "ferrohydrodynamics" (FHD) are distinguishable from the "magnetohydrodynamics" (MHD) of electrically conducting fluids by the complete absence of electric currents and the Lorentz forces they might otherwise induce. The particles typically have sizes of about 10 nm and are often coated with a stabilizing dispersing agent (surfactant) to avoid particle agglomeration 2 -even in the presence of strong magnetic field gradients. 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.

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Section: Resultsmentioning

confidence: 99%

Section: Nondimensionalizationmentioning

confidence: 99%

“…With magnetic susceptibility,

χ

, already unitless, the nondimensionalization of (2) follows that done in previous work 4 with tildes on the corresponding (untilded) physical quantities to indicate dimensionless time