A Systematic Method For Scaling Of Industrial Mixers

Mixing is a common unit operation in the cosmetic industry and other industry’s governed by Good Manufacturing Practices (GMPs). Most mixing operations in this industry occur in tanks with baffled, anchor agitators to provide bulk movement of high viscosity, Non-Newtonian emulsions. They also have a homogenizer to reduce the droplet size of the emulsion, which allows for changes in the fluid’s rheology. It is important for companies to know how to transfer products from one tank to another during scale-up. Without a systematic scale-up method, companies lose time and money as more trial batches are needed. The scaling method in this paper relies on knowledge of the “working” viscosity of a fluid, which is the viscosity at a temperature and a shear rate, with an optimized process for a smaller tank. To scale to another tank, homogenizer shear rate and the number of turnovers are kept constant. The shear rate can be used to find the rotor speed of the homogenizer, which can then be used to calculate its flow rate at the working viscosity. The batch volume is divided into the flow rate to find the time for one turnover, then multiplied by the required turnovers for the optimized process to find the time. The agitator is scaled by keeping its power input to batch volume (P/V) ratio constant. Power can be calculated using a dimensionless power number, which depends on Reynolds number and the agitator geometry. The working viscosity is used to calculate the power number and power, then the power is divided by the batch volume. The agitator speed for the new tank is changed until the P/V ratio is equal to the smaller tank’s ratio. Mixing time data was collected for fluids for which pH or hydrogen peroxide concentration could be easily tracked. The mixing times were converted to a dimensionless number by multiplying by the agitator speed. The power number was calculated for each sample on the largest tank from its working viscosity. A power equation was fitted to have dimensionless mixing time as a function of power number. The data from the additional tanks were used to support the equations developed to calculate power number. A right tailed t-test was run for each tank with a null hypothesis that the variation in the power number calculation was greater than the variation in the mixing time measurements. To support the equations, there needs to be 95% confidence that the variation comes from the mixing time measurements. The test rejected the null hypothesis for each tank, thus supporting the equations for power number. The mixing time collection also revealed that two of the systems studied are being mixed on average ten times more than required. Reducing these values to around the required time would save over $30k annually. Overall, this scaling method will save time and money as new products are introduced