Similitude and Transport Experiments

While the viscous sublayer may be important for momentum transport, it is everything for mass and heat transport through liquids. Virtually the entire concentration boundary layer is within the viscous sublayer This difference is important in our assumptions related to interfacial transport, the topic of Chapter 8, where mass is transported through an interfacial boundary layer. 

There are many transport conditions where experiments are needed to determine coefficients to be used in the solution. Examples are an air-water transfer coefficient, a sediment-water transfer coefficient, and an eddy diffusion coefficient. These coefficients are usually specific to the type of boundary conditions and are determined from empirical characterization relations. These relations, in turn, are based on experimental data. 

how does an experiment run in a laboratory at different velocities and with different length scales relate to the problem that needs to be solved A powerful tool to utilize in this task is similitude. By choosing an appropriate length scale and velocity scale, dimensionless parameters can be developed to characterize the experiments and to apply the results to other similar applications. 

There are three techniques of developing the dimensionless similarity parameters. The use of Buckingham s pi theorem can be found in most fluid mechanics books, where the variables of importance are used to determine the number of dimensionless parameters that should describe an application and help to identify these parameters. One difficulty with Buckingham s pi theorem is the unspecified form of the dimensionless numbers, which can result in unusual combinations of parameters. 

The second technique is physical insight into the problem, where ratios of forces or mass/heat transport determinants are factored to develop dimensionless numbers. This technique can also be found in most fluid mechanics texts. 

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