Measurements of rivulet flow between parallel vertical plates

The research presented considers laminar, fully-developed rivulet flow in the channel formed by two parallel vertical plates for flows intermediate between a lower limit of droplet flow and an upper limit where the rivulets meander. Although this regime is likely the most simple rivulet flow regime, it does not appear to have been previously investigated in detail. In an earlier paper, the authors derived relations to predict the terminal Reynolds number and non-dimensional width of the rivulet under the approximation that the width is large relative to the gap width of the plates (the spacing between the plates). The objective of the present study is to examine the limits of this simple treatment as the relative width becomes small, i.e., as the rivulets become narrow. Experiments were performed measuring rivulet widths and flow rates for gap widths ranging from 0.152 mm to 0.914 mm with water, light mineral oil, ethyl alcohol and water with a wetting agent. Predictions were found to agree well with the measurements for width-to-spacing ratios as low as unity and less. A numerical analysis shows that a plausible explanation of unexpected agreement for narrow rivulets is that the error in this one-dimensional assumption is approximately countered by the error in neglecting flow in the edge region. To account for curvature of the liquid–air interface at the edges, an additional geometric relationship was assumed; this approach also was found to be a good representation.