Scaling properties of coating flows in rectangular channels.

We present an experimental study of the aspect-ratio dependence of two-phase displacement flows in channels of rectangular cross section. Above a buoyancy-dependent threshold Ca[over ;]_{t}, we find that the bulk features of the flow depend only on a modified capillary number Ca[over ;]=[1+0.12(alpha-1)+0.018(alpha-1);{2}]Ca, where Ca is the unmodified capillary number and alpha is the aspect ratio. This novel scaling has tremendous practical significance because it implies that the bulk features of the flows in any rectangular channel can be inferred from those in a square channel for Ca[over ;]>Ca[over ;]_{t}.