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Time and Length Scales of Mixing: The Macro Scale

By Richard K. Grenville, Jason J. Giacomelli, Benjamin A. Boyer and Sarah Jean Johnson, Philadelphia Mixing Solutions, an SPX FLOW Brand |

Successfully scaling up a mixing process involves understanding several important timescale parameters that can impact chemical reactions and equipment performance Many industrial processes are defined by rates. For example, rates of mass and heat transfer, rates of reaction and rates of addition to a reactor. Even a batch process can be described in terms of a rate — the number of batches to be completed in a day. If mixing is required to achieve the process result, then the rate of mixing must often be related to the process rate. In reaction engineering, the ratio of mixing rate to reaction rate is the Damkohler number [1]. It is also useful to consider the inverse of the rate, which is a timescale. Comparison of rates or timescales enables an engineer to determine which is likely to dominate the process and identify when interactions are likely to occur. Understanding the role of mixing and quantification of these rates often plays an important role in successful process design and scaleup. There is a spectrum of scales to consider depending on the nature of the process in question. There are five timescales, with associated length scales, of interest in mixing processes, which are defined in Table 1. Note that in this article,…
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