Stability of liquid ridges on chemical micro- and nanostripes

We analyze the stability of sessile filaments (ridges) of nonvolatile liquids versus pearling in the case of externally driven flow along a chemical stripe within the framework of the thin film approximation. The ridges can be stable with respect to pearling even if the contact line is not completely pinned. A generalized stability criterion for moving contact lines is provided. For large wavelengths and no drive, within perturbation theory, an analytical expression of the growth rate of pearling instabilities is derived. A numerical analysis shows that drive further stabilizes the ridge by reducing the growth rate of unstable perturbations, even though there is no complete stabilization. Hence the stability criteria established without drive ensure overall stability.