Sedimentary microbial oxygen demand for laminar flow over a sediment bed of finite length

Dead organic material accumulated on the bed of a lake, reservoir or wetland often provides the substrate for substantial microbial activity as well as chemical processes that withdraw dissolved oxygen (DO) from the water column. A model to estimate the actual DO profile and the "sedimentary oxygen demand (SOD)" must specify the rate of microbial or chemical activity in the sediment as well as the diffusive supply of DO from the water column through the diffusive boundary layer into the sediment. Most previous experimental and field studies have considered this problem with the assumptions that the diffusive boundary layer is (a) turbulent and (b) fully developed. These assumptions require that (a) the flow velocity above the sediment bed is fast enough to produce turbulent mixing in the boundary layer, and (b) the sediment bed is long. In this paper a model for laminar flow and SOD over a sediment bed of finite length is presented and the results are compared with those for turbulent flow. Laminar flow near a sediment bed is encountered in quiescent water bodies such as lakes, reservoirs, river backwaters, wetlands and ponds under calm wind conditions. The diffusive oxygen transfer through the laminar diffusive boundary layer above the sediment surface can restrict the microbial or chemical oxygen uptake inside the sediment significantly. The developing laminar diffusive boundary layer above the sediment/water interface is modeled based on the analogy with heat transfer, and DO uptake inside the sediment is modeled by Michaelis-Menten microbial growth kinetics. The model predicts that the rate of SOD at the beginning of the reactive sediment bed is solely dependent on microbial density in the sediment regardless of flow velocity and type. The rate of SOD, and the DO penetration depth into the sediment decrease in stream-wise direction over the length of the sediment bed, as the diffusive boundary layer above the sediment/water interface thickens. With increasing length of the sediment bed both SOD rate and DO penetration depth into the sediment tend towards zero if the flow is laminar, but tend towards a finite value if the flow is turbulent. That value can be determined as a function of both flow velocity and microbial density. The effect of the developing laminar boundary layer on SOD is strongest at the very lowest flow velocity and/or highest microbial density inside the sediment. Under quiescent conditions, the effective SOD exerted by a reactive sediment bed of a lake or wetland approaches zero, i.e. no or very little oxygen demand is exerted on the overlying water column, except at the leading edge.