(147b) Mass Conservation Principles: Macro. Vs. Micro. A Powerful Learning Road Map in the Scaling of Transport Phenomena

The concept of mass is introduced to students during the early stages of their school activities. For example, high school physics (i.e. mechanics) is a typical place where mass is analyzed for its role in inertial forces. Concepts of mass are also discussed when talking about properties of matter such impenetrability, density, etc. At the college level, and in engineering in particular, mass plays an important role in introducing the concept of continua (Arce et al., 2010) among other related aspects. In the field of chemical engineering, it is imperative that students are knowledgeable of the various conservation laws (e.g. total mass, momentum, energy). Since mass is a concept students are generally familiar with, it didactically makes sense to begin the process of learning the aforementioned conservation laws, with mass. Furthermore, in chemical engineering, "mass" concepts need to be carefully characterized before attempting to write and understand a conservation principle. Since we deal with chemical reacting systems, the distinction between "total" mass and "species" mass is quite useful. Unfortunately, the usual textbooks deal with these types of masses in a "casual" way largely contributing to the misunderstanding of the role that "mass" plays in continuum conservations laws. Once students are confident in their knowledge of the "mass" conservation law, they can move to the more complex, or less familiar cases, such as the conservation laws of linear momentum and energy, for example.

In this contribution, after carefully analyzing the different kinds of "mass" and introducing the different types of "control domains," an integral, or macroscopic level formulation is used to capture all aspects of mass conservation. The authors will present a method to introduce chemical engineering students to the conservation of total mass (first) 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 a continuum point of view, 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. One novel aspect is the introduction of the learning concept based on "switches" both in time and space so that "tools" (such as the divergence theorem and the Reynolds Transport Theorem) are needed to conduct the scaling. The authors have found that the approach is highly beneficial for the student learning and sets a "template" or POK (Arce, 1994) for other conservation laws.

Arce, P. Jr. of Sci. Educ. and Technology, 3, 145, (1994a). Arce, P.E., J.A. Pascal, C.M. Torres. Chemical Engineering Education. In press.