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S. Banerjee and R. Ganguly
A characteristic biomagnetic fluid is blood, as blood exhibits magnetic polarization in the presence of erythrocytes (Bashtovoy et al. 1988). The magnetic susceptibility of blood arises out of the complex biochemical interactions of the intercellular
protein, cell membrane, and the hemoglobin (a form of iron oxide), which is present
at high concentrations in mature red blood cells. Experimental observations indicate
that erythrocytes preferably orient their disc plane parallel to the external magnetic
field direction (Higashi et al. 1993). In addition, factors like the state of oxygenation
influence magnetic behavior (Plavins and Lauva 1993), as blood exhibit diamagnetism when oxygenated and paramagnetism when deoxygenated. These attributes
render different flow dynamics for venous and arterial blood under external magnetic
fields.
A stable colloidal suspension of erythrocytes in plasma can be mathematically modeled as a homogeneous continuum that constitutes magnetic dipoles in
a liquid carrier (Rosensweig 1985; Tzirtzilakis 2005). Realistic models based on
blood constitution and rheology, as presented in (Tzirtzilakis 2005), also enable to
model nonisothermal flows, whereby the field response of temperature-dependent
fluid susceptibility can be studied and fine-tuned for practical applications. The
Kelvin force then depends dually on the existence of a nonuniform magnetic and/or
temperature fields.
In addition, blood exhibits appreciably high static electrical conductivity, which
varies with temperature, hematocrit (ratio of the volume of red blood cells to total
blood volume), and the flow rate (Jaspard and Nadi 2002). This warrants flow representations to consider the biofluid to be electrically conducting and incorporate the
principles of MHD. In the presence of external magnetic field gradients, the fluid
is then subjected to the Lorentz force (Davidson 2001; Farahbakhsh and Ghassemi
2010). However, the effect of the Lorentz force is significant only for strong magnetic
fields; in situations of sharp field gradient and/or low magnetic field strength, the
Kelvin force dominates (Rosensweig 1985).
As far as practical engineering applications are concerned, a prevalent technique is
the release of artificially created nanoparticles in bloodstream, either attached to the
erythrocytes or moving independently in accordance with the dynamics of flow. This
enables the magnetization of blood to be augmented by several orders of magnitude
and facilitates targeted transport of drugs using magnetic particles as drug carriers,
reduction of bleeding during surgeries, promoting occlusion of the feeding vessels of
malignant tumors, or development of magnetic tracers (Fuh et al. 2000). Moreover,
biomedical applications based on the application of magnetic field directly on blood
are proposed, like the development of magnetic devices for cell separation (Carlton
et al. 2001), field-assisted treatment of internal wounds, or cancer treatment causing
magnetic hyperthermia (Li et al. 2008; Voltairas et al. 2000; Haik et al. 1999).
Literature review presents numerical studies concerning basic BFD flow configurations for biofluids of diverse rheology. The studies all indicate the formation of
recirculating flow-field vortices at the sites of high field intensities. The numerical
studies introduce a magnetization term in the governing equations, which constitutes
a source term that leads to irrotational flows under nonuniform external fields. A wellknown classical, fundamental problem is that of isothermal flow within a rectangular
S. Banerjee and R. Ganguly
A characteristic biomagnetic fluid is blood, as blood exhibits magnetic polarization in the presence of erythrocytes (Bashtovoy et al. 1988). The magnetic susceptibility of blood arises out of the complex biochemical interactions of the intercellular
protein, cell membrane, and the hemoglobin (a form of iron oxide), which is present
at high concentrations in mature red blood cells. Experimental observations indicate
that erythrocytes preferably orient their disc plane parallel to the external magnetic
field direction (Higashi et al. 1993). In addition, factors like the state of oxygenation
influence magnetic behavior (Plavins and Lauva 1993), as blood exhibit diamagnetism when oxygenated and paramagnetism when deoxygenated. These attributes
render different flow dynamics for venous and arterial blood under external magnetic
fields.
A stable colloidal suspension of erythrocytes in plasma can be mathematically modeled as a homogeneous continuum that constitutes magnetic dipoles in
a liquid carrier (Rosensweig 1985; Tzirtzilakis 2005). Realistic models based on
blood constitution and rheology, as presented in (Tzirtzilakis 2005), also enable to
model nonisothermal flows, whereby the field response of temperature-dependent
fluid susceptibility can be studied and fine-tuned for practical applications. The
Kelvin force then depends dually on the existence of a nonuniform magnetic and/or
temperature fields.
In addition, blood exhibits appreciably high static electrical conductivity, which
varies with temperature, hematocrit (ratio of the volume of red blood cells to total
blood volume), and the flow rate (Jaspard and Nadi 2002). This warrants flow representations to consider the biofluid to be electrically conducting and incorporate the
principles of MHD. In the presence of external magnetic field gradients, the fluid
is then subjected to the Lorentz force (Davidson 2001; Farahbakhsh and Ghassemi
2010). However, the effect of the Lorentz force is significant only for strong magnetic
fields; in situations of sharp field gradient and/or low magnetic field strength, the
Kelvin force dominates (Rosensweig 1985).
As far as practical engineering applications are concerned, a prevalent technique is
the release of artificially created nanoparticles in bloodstream, either attached to the
erythrocytes or moving independently in accordance with the dynamics of flow. This
enables the magnetization of blood to be augmented by several orders of magnitude
and facilitates targeted transport of drugs using magnetic particles as drug carriers,
reduction of bleeding during surgeries, promoting occlusion of the feeding vessels of
malignant tumors, or development of magnetic tracers (Fuh et al. 2000). Moreover,
biomedical applications based on the application of magnetic field directly on blood
are proposed, like the development of magnetic devices for cell separation (Carlton
et al. 2001), field-assisted treatment of internal wounds, or cancer treatment causing
magnetic hyperthermia (Li et al. 2008; Voltairas et al. 2000; Haik et al. 1999).
Literature review presents numerical studies concerning basic BFD flow configurations for biofluids of diverse rheology. The studies all indicate the formation of
recirculating flow-field vortices at the sites of high field intensities. The numerical
studies introduce a magnetization term in the governing equations, which constitutes
a source term that leads to irrotational flows under nonuniform external fields. A wellknown classical, fundamental problem is that of isothermal flow within a rectangular