Erik Birgersson

Analysis of a Two-Phase Non-Isothermal Model for a PEFC

A non-isothermal, two-phase model for a polymer electrolyte fuel cell (PEFC) is presented, analyzed, and solved numerically under three different thermal, and two hydrodynamic, modeling assumptions ...

Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC

An isothermal two-dimensional liquid phase model for the conservation of mass, momentum, and species in the anode of a direct methanol fuel cell (DMFC) is presented and analyzed. The inherent electrochemistry in the DMFC anode active layer is reduced to boundary conditions via parameter adaption. The model is developed for the case when the geometry aspect ratio is small, and it is shown that, under realistic operating conditions, a reduced model, which nonetheless describes all the essential physics of the full model, can be derived. The significant benefits of this approach are that physical trends become much more apparent than in the full model and that there is considerable reduction in the time required to compute numerical solutions, a fact especially useful for wide-ranging parameter studies. Such a study is then performed in terms of the three nondimensional parameters that emerge from the analysis, and we subsequently interpret our results in terms of the dimensional design and operating parameters. In particular, we highlight their effect on methanol mass transfer in the flow channel and on the current density. The results indicate the relative importance of mass-transfer resistance in both the flow channel and the adjacent porous backing.

Reduced Two-Phase Model for Analysis of the Anode of a DMFC

An isothermal two-phase ternary mixture model that takes into account conservation of momentum, mass, and species in the anode of a direct methanol fuel cell (DMFC) is presented and analyzed. The slenderness of the anode allows a considerable reduction of the mathematical formulation, without sacrificing the essential physics. The reduced model is then verified and validated against data obtained from an experimental DMFC outfitted with a transparent end plate. Good agreement is achieved. The effect of mass-transfer resistances in the flow field and porous backing are highlighted. The presence of a gas phase is shown to improve the mass transfer of methanol at higher temperatures (>30 degreesC). It is also found that at a temperature of around 30 degreesC, a one-phase model predicts the same current density distribution as a more sophisticated two-phase model. Analysis of the results from the two-phase model, in combination with the experiments, results in a suggestion for an optimal flow field for the liquid-fed DMFC.

Modeling of multiphase smart hydrogels responding to pH and electric voltage coupled stimuli

A model, entitled the multi-effect-coupling pH-electric-stimuli (MECpHe) model, is presented and analyzed for the response of smart hydrogels to changes in the coupled stimuli of an external electric field and the solution pH. It considers finite deformations, the electric potential and distribution of fixed charge density in the hydrogel and surrounding solvent. The MECpHe model is validated with previously published experimental measurements and good agreement is shown. A steady-state study is carried out for various pH values and applied electric voltages to ascertain the impact of these on the deformation of the hydrogel and distribution of ionic species, electric potential, and fixed charge density, both inside the hydrogel as well as in the surrounding solvent.

Non-invasive bioimpedance of intact skin: mathematical modeling and experiments

The functional integrity and pathology of the skin is reflected in its electrical impedance spectra. Non-invasive electrical impedance measurements of intact skin are dominated by the high impedic stratum corneum in low frequencies and with increasing frequency gradually comes to be dominated by viable skin. Models of this multi-layered organ can increase our understanding of the actual physical properties/dimensions and facilitate better diagnostics in certain applications. Therefore, a mathematical model considering conservation of charge in the various layers of the skin and adjacent electrodes is derived and validated with experimental findings; the latter was carried out on 60 young female subjects. The impact of the stratum corneum thickness, inundation, solvent and cohort size on the electrical properties is studied. Both model parameters and experimental conditions were adjusted for calibration and subsequent validation of the model with measurements. It is found that both the models thickness of the stratum corneum as well as experimental soaking conditions (both time and saline concentration) affect the fit between the model and measurements. It is concluded that it is essential that the electrical properties of the skin are presented in the context of the ion concentration (if a moisturizer is employed) as well as the soaking time. Further refinements should be made to determine even more accurate dielectrical properties of the stratum corneum and viable skin layers by accounting for the true skin thickness and the heterogeneity of the skin layers-this would be useful in applications where subtle alterations in the skin are of interest.

Numerical Investigation of Liquid Water Cooling for a Proton Exchange Membrane Fuel Cell Stack

The operation of proton exchange membrane fuel cell (PEMFC) stacks requires careful thermal and water management for optimal performance. Appropriate placement of cooling plates and appropriate cooling conditions are therefore essential. To study the impact of these design parameters, a two-phase model accounting for the conservation of mass, momentum, species, energy, and charge, a phenomenological model for the membrane, and an agglomerate model for the catalyst layer, is developed and solved. The model is validated for a single cell, in terms of both the local and the global current density, and good agreement is found. Four repetitive computational units are then identified for the number of single cells placed between the coolant plates: (i) one cell; (ii) two cells; (iii) three cells; and (iv) four cells. The flow fields in the single cells and the cooling plates are of a net type. The results show that there is a strong correlation between stack performance and the operating conditions/placement of the coolant plates. For the limiting case of one coolant plate between each unit cell, similar operating conditions can be achieved in every individual cell throughout the stack. As more cells are placed in between coolant plates, the stack performance drops due to an increase in temperature and decrease in water content in the membranes, unless the cooling temperature is lowered. The coolant temperature and inlet velocity need to be monitored carefully and adjusted to the operating conditions of the stack. This model can be employed for design and optimization of liquid water cooling of a PEMFC stack.

A thin-walled polydimethylsiloxane bioreactor for high-density hepatocyte sandwich culture

In vitro drug testing requires long‐term maintenance of hepatocyte liver specific functions. Hepatocytes cultured at a higher seeding density in a sandwich configuration exhibit an increased level of liver specific functions when compared to low density cultures due to the better cell to cell contacts that promote long term maintenance of polarity and liver specific functions. However, culturing hepatocytes at high seeding densities in a standard 24‐well plate poses problems in terms of the mass transport of nutrients and oxygen to the cells. In view of this drawback, we have developed a polydimethylsiloxane (PDMS) bioreactor that was able to maintain the long‐term liver specific functions of a hepatocyte sandwich culture at a high seeding density. The bioreactor was fabricated with PDMS, an oxygen permeable material, which allowed direct oxygenation and perfusion to take place simultaneously. The mass transport of oxygen and the level of shear stress acting on the cells were analyzed by computational fluid dynamics (CFD). The combination of both direct oxygenation and perfusion has a synergistic effect on the liver specific function of a high density hepatocyte sandwich culture over a period of 9 days. Biotechnol. Bioeng. 2013; 110: 1663–1673.

Analysis of a Model for Multicomponent Mass Transfer in the Cathode of a Polymer Electrolyte Fuel Cell

A chief factor that is thought to limit the performance of polymer electrolyte fuel cells (PEFCs) is the hydrodynamics associated with the cathode. In this paper, a two-dimensional model for three-component (oxygen, nitrogen, water) gaseous flow in a PEFC cathode is derived, nondimensionalized, and analyzed. The fact that the geometry is slender allows the use of a narrow-gap approximation leading to a simplified formulation. In spite of the highly nonlinear coupling between the velocity variables and the mole fractions, an asymptotic treatment of the problem indicates that oxygen consumption and water production can be described rather simply in the classical lubrication theory limit with the reduced Reynolds number as a small parameter. In general, however, the reduced Reynolds number is O(1), requiring a numerical treatment; this is done using the Keller--Box discretization scheme. The analytical and numerical results are compared in the limit mentioned above, and further results are generated for vary...

Validated Reduction and Accelerated Numerical Computation of a Model for the Proton Exchange Membrane Fuel Cell

Amongst the severest drawbacks of many models for the proton exchange membrane fuel cell (PEMFC) are excessive memory requirements and computing time; consequently, using these for stack modeling is impractical. While reduced models alleviate these difficulties to some extent, most of the available reduced models do not preserve geometrical resolution. In this paper, we present a reduced model for a PEMFC that both reduces computational requirements and preserves geometrical resolution. The model is for a PEMFC equipped with porous flow fields and takes into account conservation of mass, momentum, species, energy, and charge. The results of the reduced model are then verified against those of the full model and validated against global polarization curves and local current-density distributions for three different experimental fuel cells; good agreement is obtained. In computational terms, the solution of the reduced model is found to require between 2 and 3 orders of magnitude less random access memory and execution time than that of the full model; furthermore, it scales well when run on up to four processors. Finally, we discuss the suitability of our reduced model for extension to a PEMFC stack model comprising tens or hundreds of single cells.

Estimating electrical properties and the thickness of skin with electrical impedance spectroscopy: Mathematical analysis and measurements

Abstract Electrical impedance spectroscopy (EIS) allows for the study and characterization of tissue alterations and properties associated with the skin. Here, the potential application of EIS to estimate the thickness of the stratum corneum is explored in the form of a mathematical model for EIS, which is analyzed in the limit of 1 kHz and closed-form analytical solutions derived. These analytical expressions are verified with the numerical solution of the full set of equations and validated with an EIS study comprising 120 subjects: overall, good agreement is found in the frequency range 1-100 kHz, where the impedance is governed by the stratum corneum. Combining the closed-form expression for the thickness of the stratum corneum predicted by the model with the experimental EIS measurements, a distribution for the stratum corneum thickness of the subjects is found with a mean and standard deviation that agree well with reported stratum corneum thicknesses from other experimental techniques. This, in turn, suggests that EIS could be employed to measure the thickness of the stratum corneum with reasonable accuracy. In addition, the electrical properties relevant to EIS – conductivity and relative permittivity – of the stratum corneum can be estimated with the closed form expressions if the stratum corneum thickness is known.