Document Type


Date of Award

Spring 5-31-2019

Degree Name

Master of Science in Pharmaceutical Engineering - (M.S.)


Chemical and Materials Engineering

First Advisor

Piero M. Armenante

Second Advisor

Ecevit Atalay Bilgili

Third Advisor

Murat Guvendiren

Fourth Advisor

Andrei Potanin


Njs, the minimum agitation speed needed to just suspend all the solid particles in a solid-liquid mixture stirred in an agitated vessel, is a critical parameter to properly operate industrial tanks in a large number of industrial operations. As a result, a significant literature on Njs is available. The oldest and the most common method to measure Njs experimentally is that of Zwietering’s (Chem. Eng. Sci., 1958, 8, 244-253), where Njs can be visually obtained by determining when the solids stay at the bottom of the tank for no more than 1-2 seconds before being swept away. Although this has been shown to be a reliable method, it still relies on visual observation of the bottom of the vessel and it is therefore potentially susceptible to observer’s bias. To address this issue new experimental approaches to determine Njs using measurements of the fraction of solids on the vessel bottom were previously developed by our research group. However even those methods are unsuitable to be used in opaque fluids or if images of the vessel bottom cannot be taken.

In order to experimentally determine Njs even in systems where the tank content cannot be inspected, in this work a novel method using Electrical Resistance Tomography (ERT) was developed and tested. Accordingly, a sensor array probe consisting of a straight plastic rod mounting 16 electrodes was placed vertically in a tank containing water and non-conductive glass beads approximately 300 ?m in diameter. The electrodes were connected to an external ERT system and data acquisition apparatus (P2+ System, Industrial Tomography Systems, Manchester, UK) dynamically measuring the conductivity distribution and resistivity in the solid-liquid system data between the electrodes. The apparatus consisted of a signal source, voltmeters, electrode multiplexer array, signal demodulators, and a system controller, connected to a computer where image reconstruction algorithms generated 2-D images of the conductivity distribution inside the tank. The system generated Alternating Current (AC) between pairs of neighboring electrodes and the resulting voltage was measured across all other neighboring electrodes. Current injection was applied to all neighboring electrodes. Through this approach it was possible to measure the mean bulk resistance across the electrodes on the sensing array probe and also measure the conductivity distribution on a portion of a vertical place inside the tank.

Here the array probe was placed in the tank, and after proper calibration, the mean bulk resistance of the solid-liquid mixture was obtained as the mixture was stirred by an impeller in the mixing tank at different values of the impeller agitation speed, N. As N increased, increasing larger fractions of the non-conducting solids became suspended, thus increasing the resistivity of the suspension measured by the ERT apparatus. A plot of the percent resistance variation vs. the agitation speed resulted in an S-shaped curve, which eventually reached an asymptotic limit value as all solids became suspended and dispersed in the liquid. In order to extract Njs from the data, a mathematical approach previously developed by our groups for a different system was used (Huang and Armenante, Chem. Eng. Sci., 1992, 47, 2865-2870). Accordingly, the experimental data were interpolated with cubic spline curves and the agitation speed at which the function Φ(N), equal to the ratio of the second derivative to the first derivative of the combined spline curve function, showed a minimum point was takes as the Njs value (Njs-ERT). The rationale for this approach is as follows: Φ(N) represents how the change in slope of the spline curve (second derivative) with respect to the spline curve slope (first derivative) varies with N. Φ(N) can be expected to reach a minimum value when the spline function is just about to bend to approach the asymptote.

Experiments were conducted where Njs was obtained under different operating conditions, i.e., where the impeller type, impeller ratio-to-tank diameter ratio, and impeller clearance were varied. Njs was not only experimentally obtained using the proposed ERT approach but also using the Zwietering method as well as the method recently developed by Shastry and Armenante (Shastry, 2016). Then, parity plots were constructed in which Njs-ERT was plotted against the Njs values obtained with the other two methods. Excellent agreement was observed in all plots, indicating that the novel method proposed here can be effectively used for the experimental determination of Njs.

The results of this work show that ERT combined with the analysis of the data proposed here can be used to effectively measure Njs in solid-liquid dispersion in mechanically stirred vessels. The proposed approach is observer-independent method and can be used even in systems that cannot be directly observed, such as industrial tanks. Therefore, it is expected that this approach could find extensive practical applications in the chemical, pharmaceutical and biopharmaceutical industries.