396
S. Nakamae
where D
0
i (ϕ i ), ˆ
S
0
i (ϕ i ) and ξ
0
i (ϕ i ) refer to the corresponding quantities in the absence
of applied magnetic field. The field-dependent modifications, externally applied
field and dipolar interactions, are contained in the parameters αλ, S 1 , βλ and S 2 .
These terms appear as the magnetic component of the chemical potential gradient
in response to
∇ϕ (α λ ), to
∇T (S 1 ) and β λ and S 2 both arise from the local field
perturbations. δ is a Kronecker-like parameter which is equal to 0 if the temperature
and field gradients are perpendicular to one another and to -1 if the two gradients are
in parallel. While more detailed derivations and the exact forms of these parameters
are be found in [24], here we simply show the qualitative behaviour as a function of
magnetic field, expressed in terms of the Langevin parameter, x (Fig. 16.8).
The field-dependent values of D i , ˆ
S i and ξ i are expected to modify the initial
(internal) Seebeck coefficient of ferrofluids as described in 16.8 and 16.10. The
next step will compare these theoretical models to the experimental measurements.
Preliminary results (cite thesis Salez) indicate, however, that the application of
magnetic field not only influence the internal electric field (as predicted here) but
also induce field-dependent nanoparticle layering, in addition to the temperature
gradient-induced adsorption effect already described in the previous section.
16.3 Future Research Direction and Perspectives
16.3.1 Fundamental Challenge—Understanding
the Phenomena Through Theoretical
and Experimental Explorations
The thermoelectric potential production in ferrofluids and other charged nanofluids
arise from multiple components (electrolytes, nanoparticles, redox couples, etc.),
thermoelectric phenomena (thermogalvanic effect, thermodiffusion, electrostatic
adsoption, magneto-diffusion, etc.) and the interplay between them. The underlying
mechanisms of these newly discovered phenomena are only beginning to be understood. Thus, theoretical/mathematical modelling and simulations of constituents at
multiscale levels, from molecular orbital interactions to collective thermodiffusion
of particles, as well as the formation of adsorption layers at the liquid/electrode
interface will become crucial for building foundational knowledge for the proposed
magnetothermoelectric materials research in liquids. A few other experiments were
performed on the Seebeck effect and TE electricity production using ferrofluids
[39] and other nanofluids [40, 41], which have brought into light rather unexpected
and new phenomena such as a field-dependent layering (may be similar to what is
described (numerical simulation) by Richardi and Weiss [42]) and a percolation of
nano-objects. Withall, it is truly an uncharted and exciting field of research to explore.
S. Nakamae
where D
0
i (ϕ i ), ˆ
S
0
i (ϕ i ) and ξ
0
i (ϕ i ) refer to the corresponding quantities in the absence
of applied magnetic field. The field-dependent modifications, externally applied
field and dipolar interactions, are contained in the parameters αλ, S 1 , βλ and S 2 .
These terms appear as the magnetic component of the chemical potential gradient
in response to
∇ϕ (α λ ), to
∇T (S 1 ) and β λ and S 2 both arise from the local field
perturbations. δ is a Kronecker-like parameter which is equal to 0 if the temperature
and field gradients are perpendicular to one another and to -1 if the two gradients are
in parallel. While more detailed derivations and the exact forms of these parameters
are be found in [24], here we simply show the qualitative behaviour as a function of
magnetic field, expressed in terms of the Langevin parameter, x (Fig. 16.8).
The field-dependent values of D i , ˆ
S i and ξ i are expected to modify the initial
(internal) Seebeck coefficient of ferrofluids as described in 16.8 and 16.10. The
next step will compare these theoretical models to the experimental measurements.
Preliminary results (cite thesis Salez) indicate, however, that the application of
magnetic field not only influence the internal electric field (as predicted here) but
also induce field-dependent nanoparticle layering, in addition to the temperature
gradient-induced adsorption effect already described in the previous section.
16.3 Future Research Direction and Perspectives
16.3.1 Fundamental Challenge—Understanding
the Phenomena Through Theoretical
and Experimental Explorations
The thermoelectric potential production in ferrofluids and other charged nanofluids
arise from multiple components (electrolytes, nanoparticles, redox couples, etc.),
thermoelectric phenomena (thermogalvanic effect, thermodiffusion, electrostatic
adsoption, magneto-diffusion, etc.) and the interplay between them. The underlying
mechanisms of these newly discovered phenomena are only beginning to be understood. Thus, theoretical/mathematical modelling and simulations of constituents at
multiscale levels, from molecular orbital interactions to collective thermodiffusion
of particles, as well as the formation of adsorption layers at the liquid/electrode
interface will become crucial for building foundational knowledge for the proposed
magnetothermoelectric materials research in liquids. A few other experiments were
performed on the Seebeck effect and TE electricity production using ferrofluids
[39] and other nanofluids [40, 41], which have brought into light rather unexpected
and new phenomena such as a field-dependent layering (may be similar to what is
described (numerical simulation) by Richardi and Weiss [42]) and a percolation of
nano-objects. Withall, it is truly an uncharted and exciting field of research to explore.