Raindrops impacting a sediment surface can transfer part of their momentum to the sediment grains, whence the grains undergo "rainsplash" that largely consists of grains being launched into arced trajectories away from drop impact sites.  On a horizontal surface grains undergo random displacements during a rain storm; displacement distances are determined by the details of the transfer of momentum between drops and grains.  On an inclined surface grains may collectively experience a net downslope drift in their motions; this downslope drift of grains represents rainsplash transport, a process that has received considerable attention in hillslope geomorphology as well as in studies of erosional processes on agricultural lands.

We are conducting experiments to clarify details of the rainsplash process.  Our aim is to formulate a clear relation between raindrop properties and the dispersion and transport of sediment grains.  These experiments involve novel high-speed imaging of raindrop impacts and grain trajectories, and unique "grain catcher" targets that allow us to determine particle splash distances.  Participants include Miriam Borosund, David Furbish, Katherine Hamner, Simon Mudd and Mark Schmeeckle — with critical help from Chelsea Furbish and Amelia Furbish.

In the image to the right, a small ridge of sand grains develops in front of the laterally spreading drop front.  Grains on, and in front of, the ridge are ejected.  The image is taken at 0.004 seconds following initial drop impact.

Experiments

Our experiments involve releasing individual drops from a height of ~ 5 m onto sand targets.  The drops are released from a syringe with blunted needle; the needle size determines the drop size.  The splash guard shown in the schematic figure, used in our initial experiments, has been replaced with a tall PVC pipe.  Drops fall through the pipe, minimizing their lateral "drift" due to air currents.  We are using three drop sizes (2 mm, 3 mm and 4 mm) and three grain sizes (fine, medium and coarse sand).  The target is about 2 cm in diameter and 2 cm deep; the sand surface is flush with the top of the target hole.

The experiments involve both dry and moist sand conditions, although we are currently focusing on dry conditions.  We are stepping through several target slopes, horizontal to 30 degrees.

We use high-speed imaging (500 frames per second) to view details of the drop impacts and resulting ballistic grain trajectories.  To characterize splash distance and azimuth relative to the drop impact position, we place "sticky" paper around the sand target.  The paper traps the splashed sand when it lands.  The paper is photographed, then grain positions are digitized for further calculations.

Particle Splash Distances

For dry conditions and horizontal target, radial splash distances are approximately exponentially distributed as postulated by van Dijk et al. (2002, Soil Sci. Soc. Am. J. 66, 1466-1474), but with a heavy tail.  The low grain count in the 0-1 cm interval is partly due to censorship by the finite target size of 2 cm (thus grains landing within this interval are not accounted for), but is also partly due to the finite size of the drop-impact footprint (up to 1 cm diameter) over which grains are accelerated.  Of particular interest is that, for a given sand size, splash distances are similar for different drop sizes.  The number of detached grains, however, markedly increases with increasing drop size.

Initial experiments with moist sand conditions indicate that the number of detached gains, and their displacement distances, markedly decrease relative to dry conditions.  This result is attributable to surface tension which, by contributing an apparent cohesion to the sand grains, decreases grain detachment during impact.  This difference in behavior between dry and moist conditions also helps clarify a fundamental point regarding grain detachment — that the "splash" of many grains involves those accelerated by grain-grain contacts in front of the laterally spreading drop.  Under dry conditions, grains that become "caught up" in the spreading fluid front either do not detach from it, or are ejected as wetted clumps of grains.

In these radial plots of grain positions, grain size increases from left to right (phi size = 2.5, 1.5 and 0.25) and drop size increases from top to bottom (diameter = 2 mm, 3 mm and 4 mm).  The green circle in each plot is the centroid of the grains.  No coarse grains (phi = 0.25) moved with 2 mm drops, and only a few moved with 3 mm drops.  For a given grain size, splash distances are similar for the three drop sizes, but the number of displaced grains (per drop) increases rapidly with drop size.

Slope Effects

For horizontal targets, detached grain trajectories are radially (statistically) symmetrical.  With increasing surface slope, this radial symmetry is replaced with increasingly asymmetric grain motions; at slopes approaching 30 degrees, virtually no upslope motions occur.  The asymmetry contributing to downslope transport ("drift") therefore consists of two parts.  The first is the well known geometrical effect of surface slope; for similar upslope and downslope trajectories, downslope trajectories travel farther before landing on the surface.  The second effect is one of quantity; more grains move downslope than upslope with increasing surface slope.

In these radial plots of grain position, slopes vary from 0 degrees to 30 degrees (upper left to lower right).  The green circle in each plot is the centroid of the grains, and downslope is to the right in the figure (at the 0 degree position).  These experiments involved dry medium sand and 3 mm drops.  The (measured) number of displaced grains per drop varied from a low of 19 to a high of 116 across all 29 drops, but no systematic variation with slope exists.  The estimated mean of 72 probably underestimates the actual value due to censorship by the finite target size, as described above.

The magnitude of downslope grain splash distances does not noticeably increase with slope.  Most grains land within 5 cm of the drop impact site.  Nonetheless the proportion of downslope grain trajectories generally increases with slope (more on this below).  This is a key element in describing the downslope drift of grain motions contributing to rainsplash transport.

The plot to the right shows the fit (line) to data (points) for a theoretical distribution of grain trajectory angles involving dry medium sand on slopes of tan beta = 0.176 through 0.577.  The data come from the figure above.  For reference, a radially symmetric distribution (Gamma = 0) plots as a straight line.  The "concentration" parameter Gamma is thus a measure of the downslope asymmetry in trajectories.  The theoretical distribution is based on the distribution of drop momentum during impact and spreading.

These contour plots show the theoretical distribution of grain positions with increasing slope, from upper left (0 degrees) to lower right (30 degrees).  Downslope is to the right.  The analysis suggests that the slope-parallel transport rate increases approximately linearly with slope.  The horizontal transport rate increases nonlinearly with slope, by a factor involving the cosine of the slope angle.