<\/div>\n

Fick\u2019s law in reactor theory states that<\/strong>:<\/p>\n

The current density vector J is proportional to the negative of the gradient of the neutron flux. The proportionality constant is called the diffusion coefficient and is denoted by the symbol D.<\/em><\/p>\n

In one (spatial) dimension, the law is:<\/p>\n

$\"Ficks$ <\/a><\/p>\n<\/div><\/div>\n<\/div><\/div>

The derivation of the diffusion equation depends\u00a0on Fick\u2019s law<\/strong>, which states that solute diffuses (neutron current<\/strong><\/a>) from high concentration (high flux) to low concentration. As can be seen, we have to investigate the relationship between the flux (\u03c6)<\/strong><\/a> and the current (J)<\/strong><\/a>. This relationship between the flux (\u03c6) and the current (J) is identical in form to the law (Fick\u2019s law<\/strong>) used in the study of physical diffusion in liquids and gases.\n
In chemistry, Fick\u2019s law states that<\/strong>:<\/p>\n
Suppose the concentration of a solute in one region is greater than in another of a solution. In that case, the solute diffuses from the region of higher concentration to the region of lower concentration, with a magnitude that is proportional to the concentration gradient.<\/em><\/p>\n
In one (spatial) dimension, the law is:<\/p>\n
$\"Ficks$ <\/a><\/p>\n
where:<\/p>\n
\n
J<\/em> is the diffusion flux,<\/li>\n
D<\/em> is the diffusion coefficient<\/a>,<\/strong><\/li>\n
\u03c6<\/em> (for ideal mixtures) is the concentration.<\/li>\n<\/ul>\n
The use of this law in nuclear reactor theory<\/strong> leads to the diffusion approximation<\/strong>.<\/p>\n
Fick\u2019s law in reactor theory states that<\/strong>:<\/p>\n
The current density vector J is proportional to the negative of the gradient of the neutron flux. The proportionality constant is called the diffusion coefficient and is denoted by the symbol D.<\/em><\/p>\n
In one (spatial) dimension, the law is:<\/p>\n
$\"Ficks$ <\/a><\/p>\n
where:<\/p>\n
\n
J<\/em> is the neutron current density<\/strong> (neutrons.cm^{-2<\/sup>.s^{-1<\/sup>) along the x-direction, the net flow of neutrons that pass per unit of time through a unit area perpendicular to the x-direction.<\/li>\n}}
D<\/em> is the diffusion coefficient, \u00a0<\/strong>it has the unit of cm, and it is given by: $\"diffusion$ <\/a><\/li>\n
\u03c6<\/em> is the neutron flux<\/a>, the number of neutrons crossing through some arbitrary cross-sectional unit area in all directions<\/strong> per unit time.<\/li>\n<\/ul>\nThe generalized Fick\u2019s law (in three dimension) is:
\n $\"Ficks$ <\/a><\/p>\n
where J<\/strong> denotes the diffusion flux vector<\/strong>. Note that the gradient operator turns the neutron flux, which is a scalar quantity<\/strong> into the neutron current, which is a vector quantity<\/strong>.<\/p><\/div><\/div>
<\/div>\n
Physical Interpretation<\/h2>\n