Relationship between molar flux and density of current

I am studying the mass transport for a charged species in a stirred solution. So, I have obtained the Nernst-Planck equation:
\begin{equation}
\mathbf{J} = -D\nabla C - \frac{zFDC}{RT}\nabla \phi + C\mathbf{v}
\end{equation}


where $\mathbf{J}$ is the molar flux, $C$ is the molar concentration of the charged species, , $z$ is the ion valence, $R$ is the gas constant, $F$ is the Faraday constant, $D$ is the diffusion coefficient, and $\mathbf{v}$ is the stirring rate of the solution.


Now, I want to relate $\mathbf{J}$ with the current $\mathbf{I}$. By definition the current sign is given by the movement of the positive carriers. I have found this relation in many electrochemistry books:
\begin{equation}
\mathbf{J} = -\frac{\mathbf{i}}{zFA}
\end{equation}
where $A$ is the area. I have nearly understood this relation, but I can't understand the sign minus. Why? If $z>0$, the carriers are cathions, positive charges. Therefore their movements should be in the same direction of the current. Where is my mistake?


