Non-newtonian fluid selection for achieving flow similarity in stirred vessels

Abstract

Many key engineering applications in the chemical sector incorporate the “duty of agitation” through the use of mixing-based unit operations to achieve the desired transport phenomena governing the particular system. These industrial processes often occur in stirred vessels equipped with centrally-mounted impellers, with the material commonly associated with high levels of toxicity, expense, handling difficulty and complex rheological behaviour. The industrial fluids of interest to this project display viscoplastic behaviour, where the fluid deforms with shear-thinning characteristics, once a yield stress has been exceeded. The mixing of viscoplastic fluids in stirred vessels can lead to the formation of caverns, where regions of flow surround the central impeller, outside of which the material is stagnant. The optimisation of industrial processes often involves the implementation of appropriately scaled-down systems and the utilisation of suitable replacement model fluids. After an extensive literature review of typical viscoplastic materials and the agitation of these fluid types in stirred vessels, a vast number of viscoplastic model fluids were formulated, rheologically characterised and fitted with mathematical rheology models. A computational platform (the ‘Model Fluid Selection Tool’) was developed and acted as a rheological database, which was used as part of an operational function of the tool for suggesting suitable model fluids that most closely match the rheological properties of the ‘real’, industrial formulations. Highly transparent Carbopol model fluids were mixed in stirred vessels equipped with small, centrally-mounted impellers (Rushton turbines and pitched-blade turbines) over multiple scales, ranging in volume from 2-20 L, with key geometrical length scale ratios being maintained. A method for achieving cavern size similarity was determined, by scaling the dimensionless cavern diameter, Dc/D, against a combination of dimensionless parameters: Rem-0.3Rey0.6n-0.1ks-1, where Rem, Rey, n and ks are the modified power-law Reynolds number, yield stress Reynolds number, flow behaviour index and impeller geometry constant, respectively. The functional relationship between Dc/D and Rem-0.3Rey0.6n-0.1ks-1¬ was utilised in a second computational platform (the ‘Matching and Predictive Mixing Tool’) for predicting cavern sizes in systems of known scale and rheology, and matching dimensionless cavern sizes in a second system when the scale and/or rheology was changed. Finally, the mixing effectiveness in dual-impeller systems for agitation of viscoplastic fluids was assessed. This research project presents novel methods for matching fluids in terms of rheological properties, whilst presenting a protocol for scaling the mixing of these fluids in stirred vessel systems.