How to derive $V_1 Y_1 = -D_{12} \nabla Y_1$ in Fick's law

Question

From Forman Williams' kinetic theory

Diffusion velocity can be related to Binary diff. coeff. and gradient of mass fraction as below.

$V_1 Y_1 = -D_{12} \nabla Y_1$

How can be this derived?

In order to prove this, 2 equations are given.

1. $V_1 Y_1 + V_2 Y_2 = 0$

2. $\nabla X_1 = \frac{X_2 X_1}{D_{12}} (V_2 - V_1)$ or $\nabla X_2 = \frac{X_1 X_2}{D_{21}} (V_1 - V_2)$

Some hints are given in a textbook,

First, get $\nabla X_1 = \frac {W^2}{W_1 W_2} \nabla Y_1$

And then show $V_1 X_1 = - D_{12} \frac{Y_2}{X_2} \nabla X_1$

Here, $V_1, V_2$ are diffusion velocities, $D_{12} = D_{21}$ is binary diffusion coefficient, $X_1, X_2$ are molar fractions and $X_1 + X_2 = 1$ for this condition. $Y_1, Y_2$ are mass fractions and $Y_1 + Y_2 = 1$, too. $W$ is molar weight.