Or, mathematically speaking, the flux has other direction than the concentration gradient.

Thanks Yin and Pawlowski for your answers. (i) Pl. clarify: Is the other direction means opposite direction. Then how we decide the direction of concentration gradient :(higher to lower )or (lower to higher). (ii) the negative sign is used only to show sense direction of diffusing atoms or.......?

Yes, other direction means here opposite direction. (i) the gradient is a vector directed always towards greater concentration. (ii) the negative sense is used because gradient is a vector as mentioned. And when you use vectors you have the value and a direction.

yesterday i luckily chanced upon this book in our library, Fundamentals of Physical Metallurgy by JD.Verhoeven (Page.139). It corroborates the same

" The minus sign is required because the atoms flow towards lower concentrations. The atoms move towards right which is a positive direction. However the concentration gradient that causes them to migrate is negative. hence to make the flux positive, we must use a negative sign to compensate for the negative gradient. "

The signal expressed in this equation indicates that the direction of diffusion occurs against the concentration gradient, ie the concetração highest to lowest concentration - Fick's first law

The (direction) movement of the diffusing particles is against the concentration gradient.

Strictly speaking this is not true, diffusion occurs down a chemical potential gradient and can occur up a concentration if the chemical potential gradient favors that. However for most single phase medium, with one diffusing element the chemical potential gradient reverts to concentration gradient.

Dear Rajni, I think the negative sign in Fick's law may be due to the fact that diffusion happens from higher gradient to lower gradient. J is directly proportion to the negative gradient of concentration and the matter flows in the direction of decreasing solute concentration i.e. gradient is negative.

Hi dear Rajni ,I think the negative sign in Fick's law for reason that diffusion ( for example atoms in the lattice) Occurs when some atoms in High density place is migration to low density place , so the sign of this is Against the sign of flux .

The Answer of M Meragiaw is not correct. The time dependent concentration change due to diffusion is taken care of by the Fick's second law. The negative sign in Fick's first law denotes direction of diffusion (downhill).

1) Let us consider two-component system (A and B), and let [A]+[B]=1, so that we can monitor only one component, say A. We designate its concentration as C. Now can draw the dependence of free energy (F) of the system on C, that is, function F(C).

2) Diffusivity (D) is known to be proportional to the derivative of the chemical potential with respect to the concentration. At the same time, chemical potential is, by definition, the derivative of F with respect to C. Thus, diffusivity is proportional to the second derivative of F with respect to C (that is D ~ d2F/dC2).

3) Depending on the energies of pair interactions (interactions between A and A, B and B, and A and B), dependence F(C) of the homogeneous system can take different shapes. The dependence F(C) of a homogeneous system, which actually wants to be heterogeneous, is known to have shape of a cupola, that is, d^2F/dC^2 < 0 or, that is the same, D < 0! It means that component A prefers to move in the region where its concentration is bigger‼! – it is just the negative diffusion. It is the negative diffusivity that results in the phase separation of a homogeneous system, which actually wants to be heterogeneous.

Flux (J) is a positive value (number of particles passing from a unit surface per unit time)

Diffusion occurs from higher concentration (point 1) to lower one (point2). Then dC=C2-C1C2.

most of the case, on a cartesien coordinate sysytem, it is taken x2>x1, because mostly the first point is taken as a reference at origin. These points correspond to the concentrations 1 and 2. Then x2>x1 and dx=x2-x1>0   

Conclusion dC0. In order to get a positive flux (J), you should put a negative signe. 

I am sorry, I am did not understand question. My first answer relates to the specific case of two-phase systems only. .In one-phase systems it is evident that if you removed sign (-) from Fick's equation, particles would move from regions with low concentration to the regions with high concentration of these particles.     

I took a heavier liquid in atest tube then pour a lighter liquid over it, the two liquids are almost immiscible & remain separated in layer. Then I suddenly made the test tube upside down & the heavier liquid passed through the lighter liquid to settle down at the bottom again. Does this supports the fact that the immiscibility or chemical potential gradient is the main deciding factor for the direction of diffusion as said by I. Chattoraj Sir?

But, as I repeated the act of invrting the test tube vertically the length of the interface increases , although the two liquids are clearly seen on either side of the interface

The negative sign in Fick´s first law is a mathematical convention which is used to remind us the direction of flux JA (a vector) with respect to the origin of the "x" coordinate. This is because Fick´s law is based on the hypothesis (which is strictly true for binary systems only) that diffusion of a given species A in a mixture occurs down its concentration gradient. Therefore, if dCA/dx is positive, CA increases with x and JA is a vector in the direction of the negative side of x. The opposite case is also true (i.e., when dCA/dx is negative, JA is directed to the positive side of x). It is noted that the sign of the numerical value of  JA is entirely dependent upon the origin of the coordinate "x", which we can establish arbitrarily. As an example, JA can be either  -1 mol/(m2 s) or +1 mol/(m2s) depending on the position of the origin of "x". On the other hand, Fick´s first law is not actually a "law", but an empirical expression to calculate the diffusion flux JA. As some of my colleagues have pointed out, there are cases in which some species  in a mixture diffuse "against" their concentration gradient (i.e., JA  and dCA/dx happen to be of the same sign). This phenomenon is called "uphill diffusion" and may occur in multicomponent systems (three or more species in a mxture). In such cases, Fick´s first law is not valid, and other (more complex) models should be used to calculate the actual value of JA. 

Considering a 1D system diffusivity constat is negative because it is multiplied by a negative deravative of change of concentration delta C/ delta x. Please see file attacehd as it should give you a better idea why the diffusivity constant/gradient is negative.For 3D system D((dN/dX)*x+(dN/dY)*y+(dN/dZ)*z) or -D gradient(filped triangle)*N

Hi

Flow(flux) happens down Concentration gradient from higher concentration to lower concentration that's why we have -ve sign in Fick diffusion equation.

thanks & regards,

g.sudhakar

phd(materials engineering)

H.C.U

suggest reading Materials Science by D. Callister

thanks & regards,

g.sudhakar

phd(materials engineering)

hcu

For measuring a change, we always do FINAL-INITIAL. The difference in concentration, with which the net flux will be proportional, has just the opposite trend. There, the final concentration is less than that of the initial. Therefore, to make the net flux positive, a minus sign is added.