Connecting Mass and Energy Balances to the Continuum Scale with COMSOL DEMos

In transport phenomena courses, students often struggle with the visualization of mass, momentum, and heat transfer. In this paper, we use COMSOL Multiphysics® to develop modules to help students connect high-level mass, momentum, and energy balances with the underlying physical phenomenon at the continuum scale. These modules are part of a larger project of Desktop Experiment Modules (DEMos) that enable students to experiment to deduce cause / effect in a demonstration tool. We focus on microfluidics and fuel cells because few examples exist in the chemical engineering literature in this area. These modules were implemented in chemical engineering in a special microdevice course for undergraduate upper-classmen and beginning graduate students, a senior level elective course on Computational Methods, and a junior-level transport / unit operations course. Introduction and Motivation: The Typical Transport Course Transport phenomena is a subject of the chemical engineering undergraduate curriculum that is taught in widely differing ways, depending upon the institution and its focus. In general, courses in fluid mechanics, heat transfer, and mass transfer can be categorized as: 1. Transport phenomena approach – in this approach, instructors focus on theoretical derivation of microscopic conservation equations and methods for obtaining analytical (and sometimes numerical) solutions. A typical book is that Bird, Stewart, and Lightfoot. 2. Unit operations approach – in this approach, instructors focus on the practical use of macroscopic balance equations and using them for the design of pumps, heat exchangers, and membranes. A typical book is that of McCabe, Smith, and Harriott. 3. A balance between the transport phenomena and unit operations approaches, such as that contained in the text of Geankoplis. At Michigan Technological University, students must complete a two-semester sequence of lecture courses (CM 3110 Transport / Unit Operations 1; CM 3120 Transport / Unit Operations 2). Based upon the title of the course we typically follow the third classification; however, content can vary depending on the instructor. Nevertheless, we have found that our hands-on students typically do well with the practical unit operations problems but struggle with the mathematics and conceptualization of transport theory. The literature supports our observations. For example, Krantz noted that transport texts analyze simple problems with analytical or basic numerical solutions. He then discusses the utility of computationally-based software to allow instructors of transport phenomena to focus on model development by introducing more complex problems. An additional P ge 22371.2 advantage of the software is that it allows the students to visualize the transport processes taking place. Other studies have also used computers to help students learn concepts in chemical engineering education, most notably in transport phenomena. At Michigan Technological University, Zheng and Keith have developed JAVA applets for unsteady and steady state transport problems. Keith, Morrison, and King have developed COMSOL Multiphysics® problems for introducing fuel cell concepts in fluid mechanics, heat transfer, or mass transfer courses. In this paper, we build upon this concept but utilize the Multiphysics® mode with two applications in mind: microfluidics and fuel cells. A special topics course in chemical engineering entitled Analytical Microdevice Technology was developed for undergraduate upper-classmen and beginning graduate students. One challenge when discussing microfluidics in microdevices is facilitating student visualization of the mathematical expressions and physical behaviors observed in the micron length scales. A microscale module is described that involves fluid transport, diffusion, and reaction. The module begins with pressure-driven flow in a microchannel and then adds electro-osmotic forces, which are linked to ion-association kinetics at the microchannel wall surface. The module presents step-by-step instructions to develop this in an open system and to measure the integrated velocity profile at various axial locations in the channel. It can be seen that the total mass flow rate is constant for any axial length. Subsequent student-oriented additions include protein transport via isoelectric focusing to the isoelectric point as well as electrolysis reactions in the fluid reservoirs at the ends of the channels. A senior level elective course titled Computational Methods in Chemical Engineering was developed for upper level undergraduate students. About one-third of the course focuses on solving partial differential equations. The students are taught finite difference methods and practice them in MATLAB. They are also taught COMSOL Multiphysics. We describe a module building upon the pressure driven flow of the microdevice module and add transverse mass transfer of hydrogen gas through a gas diffusion layer to a catalyst surface (mimicked in the example problem by a surface with zero concentration) for fuel cell applications. Student-oriented additions include extension to flow in a complex bipolar plate channel geometry. We begin with overviews of the two technologies addressed, microfluidics and fuel cells. The module instructions are included at the end of the paper. Microfluidics Overview The use of electric fields to transport fluid, cells, biomolecules and other analytes is pervasive at the microscale. The reason for this is that micropumps are bulky and the pressure drops that develop across microchannels can be substantial due to the large wall surface area to volume ratio. Transport of fluid is typically accomplished via electroosmotic flow, which occurs when any fluid is in contact with a charged surface in the presence of an externally applied electric field. Figure 1 provides an example of the P ge 22371.3 wall’s ion dissociation behavior in the presence of an electrolyte. A Debye layer forms near the wall that is dominated by counterions of opposite charge to the fixed wall charges. When an electric field is applied, these counterions and the water molecules associated with them are pulled uniformly toward the oppositely charged electrode. This drags the fluid along in a flat velocity profile. Note that the length scale of the Debye layer is on the order of hundreds of nanometers and the channel diameters are on the order of tens of microns or less. Figure 1: Schematic of the surface chemical groups of a fused silica capillary in contact with a) air, b) an electrolyte, and c) an electrolyte and a remotely applied DC electric field. Figure 1 assumes an ideal, uniformly charged channel wall. However, the Debye layer is a function of electrolyte concentration via the Smoluchowski slip velocity at the wall: where ε is the electric permittivity of the fluid, ζ is the zeta potential, and η is the viscosity of the fluid. Zeta potential is the potential difference between the wall surface and the bulk fluid. Research has shown that the wall surface charge is dependent on the local ionic conditions, namely pH and that the pH can vary along the length of a microchannel when a DC field is applied via electrodes at either end of the channel. Thus, the zeta potential can vary with position in the capillary. This fascinating phenomenon is the basis for the COMSOL module presented in this paper.