I think the starting point for this question has almost everything to do with size of the salt or soda ash particles, the concentration of the solutions, and the resulting dissolving rates. A mixer must be large enough to keep the particles suspended, but more mixing intensity will probably not increase the rate of dissolution much. So dissolving rate is all about the particle sizes and solution concentrations.
 
Once the dissolution rate is established for the particles, then the vessel size can be determined for flow rate or batch size necessary for the desired capacity. From the volume required for capacity, a vessel design with a diameter approximately equal to the height and with baffles would be the starting point for a mixer design. The mixer design would depend on vessel volume, the particle size and density and the mixing requirements for off-bottom suspension.