_{1}

^{*}

The equations for gradient of electric field in seawater induced by gradients of salinity, temperature and pressure were developed by means of non-equilibrium thermodynamics. Extrathermodynamic assumptions and accepted chemical model of seawater permit to carry out numerical calculations of electric field caused by diffusion, thermodiffusion and barodiffusion for realistic hydrophysical structure of the ocean. It is shown that contribution of barodiffusion into electric field of the ocean is almost constant (about -3 × 10
^{-7} V/M). This magnitude can be ignored in many cases because it is too small. However natural salinity and temperature gradients significantly impact into electric field of the ocean.

Natural electromagnetic fields in the ocean have two types of the sources: external (ionospheric and magnetospheric current systems) and internal one [

Three important fluxes occur in a multicomponent electrolyte solutions: those of matter, heat, and electricity. These three fluxes are described by well-known laws of Fick, Fourier, and Ohm as being proportional to appropriate thermodynamic force. The more general case, where interactions between these processes occur, leads to a set of simultaneous equations which are formulated by non-equilibrium thermodynamics [

Let us to consider seawater as n-components fully dissociated electrolyte solutions where each ion is assuming as component. When such electrolyte is subjected by thermodynamic forces then

where

when system is in mechanical equilibrium. In the Equation (1)

Here

Kirkwood et al. [

Existence of temperature, concentration, and gravitational field defines thermodynamic forces and Equation (4) can be rewritten as follows [

Here

where

Here

Due to reciprocal Onsager’s relationships (Equation (5)), the equation for transference number of species

Taking into account that

the equation for gradient of the chemical potential is following:

Here

There are two problems of rigorous calculation of the Equation (13). Main problem is that thermodynamic properties of the individual ions cannot be strictly determined from thermodynamic point of view. Second problem is that there are a few experiments, which may to be used for numerical estimations of the Equation (13). Nevertheless, I try to carry out of numerical calculations of the Equation (13) using extrathermodynamic assumptions. These calculations have been approximated by empirical algorithms which provide a valuable tool for non-spe- cialists in thermodynamics working in the other research of the electromagnetic fields of the ocean.

The main feature of the seawater is that molality of major constituents of seawater exhibit an almost constant ratios to one another throughout the oceans. Therefore it is can be written as follows:

Here,

Let us to introduce following notations:

Here

For calculation diffusion potential, the composition of major constituents of seawater was taken from [

The derivatives of the activity coefficients of ions from salinity in the Equation (18) have been calculated by means of the Pitzer method (for example, [

The parameters appearing in the Equations (19)-(20) are defined as follows:

Here “a”, “c” and “n” are cations, anions and neutral species, respectively. ^{1/2}∙mol^{−1/2}, respectively.

For calculations of Equation (16), needed the partial molal volumes of the major ions of seawater are given as function salinity and temperature elsewhere [

Non-isothermal properties of the electrolyte solutions are weakly studied as experimentally and theoretically as well. On this reason, the thermodiffusion properties of the 0.7 m NaCl have been used for estimation of the thermodiffusion potential in seawater. In this case Equation (17) is significantly simplified

The “absolute” entropies of transfer of sodium and chloride ions for 298 K have been published elsewhere [

The scalar fields of the salinity, temperature and gravity cause diffusion of ions. Due to differences in physicochemical properties for each species of the electrolyte solution (mobility, activity coefficients, entropy of transfer, molar masses, and partial molal volume), the diffusion of ions induces electric field inside in seawater. Main feature of the diffusion processes in the electrolyte solutions is fulfillment of electroneutrality on the macroscopic space scale [^{−8} sec or less [^{−8} sec electric field becomes steady state after sharp formed scalar fields. On these reasons diffusion-induced electric field can be considered as distribution of dipoles.

With the purpose of an estimation of possible impact

Ions | |||
---|---|---|---|

0.48616 | 0.2983 | 22.9898 | |

0.01058 | 0.0102 | 39.0980 | |

0.05475 | 0.0510 | 24.3050 | |

0.01074 | 0.0111 | 40.0780 | |

0.56918 | 0.5942 | 35.4530 | |

0.02927 | 0.0352 | 96.0642 |

with those induced by geostrophic currents. Obviously, time-space variations in temperature-salinity structure of the sea have to generate variations in the structure of the electric field. For estimations of these fluctuations,

From

Geological and geochemical processes may cause thermal and concentration anomalies, which give anomalies in the electric field. For example, magnetic and electric field variations associated with eruption of volcano where observed and summarized elsewhere [

Numerical calculations of Equation (13) in application to seawater have two different sources of uncertainty. One of them is fundamental problem, which may be formulated as impossibility of rigorous determination of thermodynamic properties of the individual ions. It means that thermodynamic properties of electroneutral combination of ions can be determined (measured) only. For example, entropies of transfer, activity coefficients (or derivatives of them), and partial molar volumes for salts (NaCl, Na_{2}SO_{4}, etc.) in multicomponents of electrolyte solution can be determined but not for individual ions. On this reason extrathermodynamic assumptions are necessary for evaluation of the thermodynamic properties of individual ions. Activity coefficients of the individual ions and them derivatives were calculated by means of Equations (19)-(25) neglecting by last bracket in Equations (19), (20). There are many evidences that adequately experimental uncertainty, the Equations (19) and (20) describe non-ideal behavior of salts for any components of electrolyte solutions (activity coefficients, osmotic coefficients and them derivatives from concentrations, temperature, and pressure). Moreover, contributions of the Pitzer parameters, taking into account interactions between like-charged ions and interactions between three species are very small as rule. It is should be noted that Pitzer parameters are electroneutral combination of the corresponding virial coefficients. The last bracket of the Equations (19), (20) contains just the second virial

coefficients taking into account interactions between the same ions (for example,

Another important source of uncertainty of the suggested Equations (26), (27), and (29) is quality of available experimental data. At present time, there is a very good dataset of the Pitzer parameters [

I suggest to measure diffusion, thermodiffusion, and barodiffusion potential by means of measurements of electromotive forces (EMF) following cells:

EMF of the cells (A), (B), (C) may be writing respectively:

where,

following electrode reaction:

Here, subscription “s” means solid. I suggest using of rather synthetic seawater than natural seawater because natural seawater contains ^{−6} V. In this case centrifugal cells should be used [^{−7} V/M) and in many cases of electrical fields study it can be negligible.

Electrochemical processes such as diffusion, thermodiffusion, and barodiffusion induce electric field in the ocean due to existence of natural salinity, temperature, and gravitational fields. Diffusion-induced electric field can be considered as distribution of dipoles.

Natural variations of hydrological properties cause variations of electric field in seawater.

Geological and geochemical processes, which induce thermal and concentration anomalies, may result in anomalies in the electric field.

Using of the chemical model of seawater, the Pitzer method for calculations of non-ideal behavior of electrolyte solutions, and available thermodynamic data for major ions of seawater, the numerical calculation of Equation (13) was carried out. Results of numerical calculations are represented by empirical relationships which are easy to apply to any modeling.

Modern theoretical and experimental knowledge of the thermodynamic properties of multicomponent electrolyte solutions does not permit to quantitatively describe diffusion-induced electric field in the ocean. On this reason it is suggested to carry out special potentiometric experiments with synthetic seawater for accurate estimation diffusion-induced electric field in seawater.