Experimental studies of two-solute double-diffusive finger convection in a Hele-Shaw cell

When two solutes with different diffusion coefficients and opposing linear concentration gradients are present in a density stable configuration, the potential energy of the system can be released due to local buoyancy changes caused by the differential diffusion. These local buoyancy influences can develop small-scale instabilities on the order of millimeters that can grow and influence mass transport over much larger scales. This phenomenon, referred to as double-diffusive finger convection, was studied experimentally in a transparent Hele-Shaw cell for a two-solute (sodium chloride-sucrose) system with a lighter sucrose solution layered above a heavier salt solution. Growth of the unstable fluid motion was tracked using transmitted light and a dye tracer mixed in the sodium chloride solution.; It is common in the double-diffusive literature for the convection to be characterized as a function of the dimensionless buoyancy ratio, however, recently, characterization with respect to only the buoyancy ratio has come into question. A series of 14 experiments was conducted along a fixed buoyancy ratio line in Rayleigh space to give more insight into the full possible range in behavior for a given two-solute system. Results reveal trends in both the vertical and horizontal growth with respect to the dimensionless Rayleigh numbers for a fixed buoyancy ratio. A light transmission system, with a charge-coupled device (CCD) camera, was applied to obtain full-field, non-intrusive, point wise measurements of the evolving concentration fields in order to explore the influence of these trends on mass transfer rates.; To develop more fully an understanding of the trends revealed in the earlier experiments, a series of 5 experiments was conducted along a fixed buoyancy ratio line in Rayleigh space, and a relationship for the dimensionless vertical velocity as a function of the dimensionless buoyant driving forces is presented. Scale analysis of the momentum equation over predicts the dimensionless vertical velocity, and reasons for the discrepancy are discussed. The dimensionless mass transfer rate is found to be independent of time, and the dimensional mass transfer rate shows power law dependence on the dimensionless buoyant driving forces.; Finally, 12 more experiments were conducted along three additional buoyancy ratio lines. For the first time, relationships that characterize the vertical finger growth rates and mass transfer rates as a function of the buoyant driving forces spanning Rayleigh space between the neutral buoyancy and stability boundaries are presented.