(g) 



3 12 12 \°-^) 



(S) 



where AV is the effective relative velocity of the sediment particles due 



(g) 

 to the shearing motion linearly proportional to the shearing rate G, AV is 



the absolute difference between the settling velocities of the two particle 



groups, and r is the collision cylinder radius equal to the sum of r and 



r^^. Turbulent shearing dominates for smaller particles, while turbulent 



acceleration dominates for bigger particles. Differential settling becomes 



increasingly important as the difference in particle sizes increases. 



The collision efficiency e is a function of the relative Reynolds number 

 of the colliding sediment particles as well as the radius ratio of the drops. 

 In addition, the effect of clay mineralogy and physico-chemical properties of 

 the fluid in affecting the cohesion among particles can be included in this 

 term. 



Development of a Comprehensive Model 



The first prerequisite in utilizing the above information is to have a 

 dynamic model capable of predicting the turbulence of the flow field, in 

 addition to the mean flow. The three-dimensional hydrodynamic model described 

 earlier in this report can be extended to compute the turbulence of the flow 

 field. This procedure is outlined in Sheng (1982). 



Next, to include the coagulation dynamics in the sediment transport 

 model, sediment particles should be divided into several groups, each with a 

 mean radius and a median settling velocity. Conservation equations for the 

 number density and the mixing ratio of each of these particle groups can be 

 derived. In addition to the convection by currents and the gravitation 

 settling, these equations would incorporate the transition rates among the 

 various particle groups based on the collision rates defined by 

 Equation (6.1). 



Collisions among the very small particles generally lead to coagulation 

 and formation of floes. These floes may further coagulate into even bigger 

 floes. As the floes increase in size, the inter-floe cohesive forces decrease 

 in magnitude. Hence turbulence induced collisions may lead to breaking up of 



132 



