A Model for the Determination of Mixing Time for Viscous Systems in a Stirrer Pot by Statistical Regression of Response Surface Analysis Employing Central Composite Design Methodology

Abstract

Mixing is a significant unit operation in process industry, which has an important role in enhancing the rate of reaction in homogeneous or even in multiphase reactions. Mixing can increase the rate of transport processes that may reduce the processing time by several folds to obtain a product of desirable quality. The principal requirement for such achievements is the homogeneous state of the bulk fluid that is subjected to a pre-designed condition of mixing or agitation. In the present study, model equations for calculating mixing time as a function of relative volume of tracer slug to the volume of liquid bulk, relative viscosity of the liquid bulk and impeller speed of the agitator have been developed based on two fundamental model configurations. They are the following: (1) a quadratic model, based on statistical data processing and (2) a power law model using logarithmic least square method. The first model category offered higher accuracy in predicting the mixing time. Also, an effort has been made to relate mixing time against Reynolds number obtained during mixing. These locuses have shown: (1) a saturation characteristic of mixing time beyond an upper limit within the investigated range of Reynolds number, and (2) a breakage or change in slope in the transition region between laminar and turbulent flow regime.

Keywords:

• Agitated vessel
• Mixing time
• Power number
• Response surface methodology
• Viscous fluid

Acknowledgements

The authors thank Mr Ashani Sarkar for designing the LED–LDR assembly and writing the real-time software for measuring the mixing time.

Nomenclature
µ cp	=	Viscosity of bulk sample
µw cp	=	Viscosity of water
ρ gm.cm−3	=	Density of the bulk
D cm	=	Diameter of the Agitator
P W	=	Power required for mixing to occur
TME sec	=	Experimental Mixing time
TMM sec	=	Calculated Mixing time
X1 (= µ/µw)	=	Relative Viscosity
X2	=	Stirrer speed
X3 (=Vs/Vt)	=	Relative Volume
Vt ml	=	Volume of tracer
Vs ml	=	Volume of bulk sample