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Abstract:

 

It is commonly stated in the literature that the “breakthrough” point at the transition from slow high-order to fast firstorder dissolution kinetics in limestone occurs at an exit aperture of about one centimetre, and that this coincides with the transition from a wholly laminar flow to a turbulent flow. These relationships are approximately true for a range of conduit geometries in sub-horizontally bedded strata. However, the exit aperture for the onset of turbulence varies with the hydraulic gradient whereas the exit aperture for the onset of first-order kinetics varies with the hydraulic ratio, which is the hydraulic gradient divided by the path length. These transitions only occur at the same exit aperture for planar fissures and cylindrical tubes of lengths 290 m and 452 m. Breakthrough can occur before or after the onset of turbulence. Aperture sizes for breakthrough and turbulence can be over a metre for long and shallow conduits but sub millimetre for short and steep conduits. This paper analyses these relationships for many conduits in natural and artificial conditions and discusses their relevance to the multitude of possible karst situations, where hydraulic ratios can be considered over 17 orders of magnitude.