  We have studied the slip length of confined liquid with small roughness of
solid-liquid interfaces. Dyadic Green function and perturbation expansion have
been applied to get the slip length quantitatively. In the slip length, both
effects of the roughness of the interfaces and the chemical interaction between
the liquid and the solid surface are involved. For the numerical calculation,
Monte Carlo method has been used to simulate the rough interfaces and the
physical quantities are obtained statistically over the interfaces. Results
show that the total slip length of the system is linearly proportional to the
slip length contributed from the chemical interaction. And the roughness of the
interfaces plays its role as the proportionality factor. For the roughness, the
variance of the roughness decreases the total slip length while the correlation
length of the roughness can enhance the slip length dramatically to a
saturation value.
