The magnetic body force in ferrofluids

Abstract

The modeling of electromagnetically-operated fluids represents a technologically relevant domain, yet a scientifically challenging study. In particular, real fluids typically fall between existing consolidated models, such as hydrodynamics, electrohydrodynamics, magnetohydrodynamics and ferrohydrodynamics. A key element for the description of dynamic phenomena is the so called magnetic body force, whose role is that of shaping electromagnetic forces under simplified schemes and capturing the broadest phenomena possible. In this study a simple model equation is proposed and justified in light of existing literature, and the benefits of decoupling the effects of temperature and external magnetic field are discussed making reference to the advantages gained in numerical simulations.

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Reply to Comment on ‘The magnetic body force in ferrofluids’

“…As highlighted in our manuscript [1], two forms of magnetic force (separated magnetic charge model used by authors [2,5] and electric current loop model used in our modeling) can be considered physically equivalent if and only if…”

“…In our treatise [1], we propose an alternative definition of magnetic body force in opposition to the most common definition proposed by Rosenweig [2] and widely used in contemporary scientific literature. We consider any ferrofluid (FF) as an ensemble of infinitesimal magnetic dipoles, the magnetite nanoparticles (NPs), uniformly dispersed in colloidal form through a magnetically neutral carrier solvent (oil-based as kerosene, or water-based).…”

“…According to previous considerations, it is now evident why it is possible to model a single magnetic NP as an infinitesimal magnetic dipole. As discussed in [1], Griffiths proposed * Author to whom any correspondence should be addressed.…”

“…Now, considering equation ( 4), if the volume variation of the magnetic induction field can be considered at most constant in module, the relative gradient must be equal to zero. Therefore, using the definition of magnetization field equation ( 5), we obtain the definition [1] of magnetic body force:…”