Spheroidal and conical shapes of ferrofluid-filled capsules in magnetic fields

We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

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“…Similar iterative numerical schemes for coupled problems have been applied successfully in Refs. [ 41 , 42 ].…”

Section: Methodsmentioning

confidence: 99%

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

Ender

Kierfeld

2021

Eur. Phys. J. E

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“…This iterative solution scheme for a ferrofluidfilled capsule has been introduced and is explained in detail in Ref. 18.…”

Section: H Numerical Proceduresmentioning

confidence: 99%

“…The linear response of the capsule deformation in spinning drop experiments is actually equivalent to the deformation of a ferrofluidfilled capsule in a small uniform external magnetic field as it has been analyzed in Ref. 18 if we set the magnetic susceptibility to χ = −1 and the magnetic field strength to µ 0 H 2 = ∆ρR 2 0 ω 2 . Both magnetic forces on the ferrofluid-filled capsule in an external field and the centrifugal pressure exerted by a liquid of different density inside the capsule are normal forces (as they are generated by liquids) acting on the capsule surface.…”

Section: Additional Interface Tension In Spinning Drop Experimentsmentioning

confidence: 99%

“…In Ref. 18 the deformation of a ferrofluid-filled magnetic capsule has already been considered also in the presence of an interfacial tension γ, and we can simply adapt the results for the linear response, which are derived in Appendix A of Ref. 18, to the capsule deformation in the spinning drop apparatus by exploiting the equivalence of both problems.…”

Section: Additional Interface Tension In Spinning Drop Experimentsmentioning

confidence: 99%

“…We use this net force to deform the capsule by pushing the flexible particle against the bottom wall of the cuvette. In principle, deformation and shape transitions are also possible in homogeneous magnetic fields, which tend to stretch the capsule in order to increase the dipole moment [18]. For a quantitative understanding of the deformation behavior we measure the magnetic field distribution, calculate the magnetic properties of the ferrofluid from the nanoparticle size distribution and compare the experimental capsule shapes to theoretical shapes calculated using nonlinear elasticity theory by a coupled finite element method (FEM) for the elastic problem and a boundary element method (BEM) for the magnetic field calculation.…”

Section: Introductionmentioning

confidence: 99%

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Strong Deformation of Ferrofluid-Filled Elastic Alginate Capsules in Inhomogenous Magnetic Fields

et al. 2018

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We present a new system based on alginate gels for the encapsulation of a ferrofluid drop, which allows us to create millimeter-sized elastic capsules that are highly deformable by inhomogeneous magnetic fields. We use a combination of experimental and theoretical work in order to characterize and quantify the deformation behavior of these ferrofluid-filled capsules. We introduce a novel method for the direct encapsulation of unpolar liquids by sodium alginate. By adding 1-hexanol to the unpolar liquid, we can dissolve sufficient amounts of CaCl2 in the resulting mixture for ionotropic gelation of sodium alginate. The addition of polar alcohol molecules allows us to encapsulate a ferrofluid as a single phase rather than an emulsion without impairing ferrofluid stability. This encapsulation method increases the amount of encapsulated magnetic nanoparticles resulting in high deformations of approximately 30% (in height-to-width ratio) in inhomogeneous magnetic field with magnetic field variations of 50 mT over the size of the capsule. This offers possible applications of capsules as actuators, switches, or valves in confined spaces like microfluidic devices. We determine both elastic moduli of the capsule shell, Young's modulus and Poisson's ratio, by employing two independent mechanical methods, spinning capsule measurements and capsule compression between parallel plates. We then show that the observed magnetic deformation can be fully understood from magnetic forces exerted by the ferrofluid on the capsule shell if the magnetic field distribution and magnetization properties of the ferrofluid are known. We perform a detailed analysis of the magnetic deformation by employing a theoretical model based on nonlinear elasticity theory. Using an iterative solution scheme that couples a finite element / boundary element method for the magnetic field calculation to the solution of the elastic shape equations, we achieve quantitative agreement between theory and experiment for deformed capsule shapes using the Young modulus from mechanical characterization and the surface Poisson ratio as a fit parameter. This detailed analysis confirms the results from mechanical characterization that the surface Poisson ratio of the alginate shell is close to unity, that is, deformations of the alginate shell are almost area conserving. arXiv:1902.09389v1 [cond-mat.soft]

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Liquid–Liquid Encapsulation of Ferrofluid Using Magnetic Field

Banerjee

Misra

Mitra

2022

Adv Materials Inter

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Encapsulated magnetic microdroplets are of paramount importance in drug targeting and therapeutic applications. However, conventional techniques for generating encapsulated magnetic microdroplets suffer from several challenges, including lack of monodispersity, inflexibility in core–shell combinations, and complex device architecture to achieve encapsulation. Herein, a facile magnet‐assisted framework to controllably wrap ferrofluid (FF) droplets inside polydimethylsiloxane (PDMS) floating on a water bath is developed. A permanent magnet placed at the bottom of a static glass cuvette pulls the ferrofluid droplet across the PDMS–water interface, which results in the wrapping of the FF droplet by a thin PDMS layer. The deformation of the FF–PDMS interface and the encapsulation of FF inside PDMS thereof is attributed to the interplay of magnetic force and force due to PDMS–water interfacial tension. Based on the experimental observations, three regimes are identified, namely, stable encapsulation, unstable encapsulation, and no encapsulation, which depends on the magnetic Bond number (Bom) and the thickness of the PDMS layer (δ). The versatility of the technique is demonstrated further by showing stable wrapping of multiple ferrofluid droplets inside the same encapsulated cargo and successful underwater manipulation of the encapsulated droplets, which finds relevance in the encapsulation and magnet‐assisted actuation of novel encapsulated materials.

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Spheroidal and conical shapes of ferrofluid-filled capsules in magnetic fields

Cited by 17 publications

References 73 publications

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

Strong Deformation of Ferrofluid-Filled Elastic Alginate Capsules in Inhomogenous Magnetic Fields

Liquid–Liquid Encapsulation of Ferrofluid Using Magnetic Field

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