A dimensionless number analysis of the hybridization process in diffusion- and convection-driven DNA microarray systems

The present theoretical analysis aims at providing a general understanding of the combined effect the many different process variables have on the hybridization rate in diffusion- and convection-driven DNA microarray systems. It is shown that all process variables can be grouped into only four different dimensionless numbers (the Damkohler number Da, the dimensionless association constant κA, the dimensionless initial concentration C′0C′0 and a geometrical ratio α). These four numbers have a straightforward physical meaning and only contain easily measurable parameters. Reducing the solution space from 7D to 4D, the dimensionless number representation greatly facilitates the insight in the conditions leading to the occurrence of diffusion-limited hybridization rates in both diffusion- and convection-driven DNA microarray systems. This in turn simplifies their design and the interpretation of the experimental results that are obtained with these systems.