Mass Conservation Principles: Macro Vs Micro. A Powerful Learning Road Map In the Scaling of Transport Phenomena

Wednesday, October 19, 2011: 4:55 PM
Marquette V (Hilton Minneapolis)
Parvin Golbayani, Jennifer Pascal and Pedro E. Arce, Chemical Engineering, Tennessee Technological University, Cookeville, TN

The concept of mass is introduced to students from a very young age, and is therefore a familiar topic once students reach the college level. In chemical engineering, the concept of mass is key for the development of a rigorous and useful understanding of professional applications with or without chemical reactions. Separations, drug delivery, environmental remediation and intracellular transport are some relevant examples where concepts based on “mass transfer” play a significant role in analyzing and “sizing” or scaling a device. Didactically, mass conservation offers a powerful road map to introduce students to the framework of conservation quantities and conservation principles, i.e. mass, energy, and momentum.

In this contribution, the authors will present a method to introduce engineering students to the conservation of total mass through a fundamental approach that builds upon the previous knowledge of the students.  This approach begins with fully understanding what mass is (i.e. total mass vs. component mass), defining total mass from the continuum scale  followed by systematically deriving the conservation of total mass from a continuum point of view for closed and open systems, and finally incorporating the idea of scaling into the analysis by converting the macroscopic equations into microscopic equations. The authors, here, apply concepts learned by students in calculus, i.e. the Green’s or divergence theorem, Leibniz’s rule of integration, and so on and offer the students an effective illustrative application by introducing the idea of “time-scale switcher” and a “space-scale switcher”. Furthermore, students are connected with the idea that, in transport phenomena, global or macroscopic variables are associated with “integration” and microscopic or point variables are related to “differentials” . In short, the contribution describes an effective road map in educating students on conservation principles in continua. Several details of this road map will be introduced and illustrated.

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