Numerical Simulation of Paper-Based Flow Cells during Dynamic Infiltration Phase

Microfluidic electrochemical cells are increasingly being used as power sources for energizing portable electronic devices [1]. Of particular interest is the capillary-driven flow cells because they do not need any type of micropump to establish the flow. In a recent work [2], we developed a general, robust mathematical/numerical model for designing capillary-driven, paper-based, microfluidic flow cells. The model was validated against experimental data available for a novel single-use microfluidic flow cell of this nature called PowerPAD [3]. This flow cell is activated by a drop of water when poured on its sample pad. After dissolving the solid electrolytes stored below the sample pad, the liquid electrolytes produced this way infiltrate the porous electrodes before entering the cellulosic absorbent pad situated below the porous electrodes. Soon after entering the pad, they start flowing in the lateral direction until they are brought into direct contact with each other (at some point in time) so that the electrochemical reactions can take place at the electrodes. The two liquids then continue flowing co-laminarly until the pad becomes fully-saturated and the flow rate drops to zero. The experimental data reported by the inventors of the PowerPAD actually correspond to the fully-saturated case [3]. (Under these conditions the cell works like an ordinary battery when connected to an external load.) They demonstrated that, dependent on the thickness of the absorbent pad, the cell can generate electricity for roughly an hour. In [2], we showed that, for a given electrode, by modifying the microstructure of its absorbent pad (e.g., its porosity or pore-size) and/or its flow structure the runtime of the cell can be extended to roughly three hours so that it can be used for energizing certain portable electronic devices. However, there are other prospective applications in which the power might be needed for merely a few seconds [4]. Remote sensors used for measuring/reporting the pH of acid rains belong to this category. PowerPAD can be used for such short-lived applications, but the mathematical model presented in [2] has to be refined to simulate power generation during the dynamic infiltration process, which is the objective of the present work. As the first step, Darcy’s equation is solved numerically to find the bulk velocity from which the Reynolds number is obtained and used to calculate the mass-transfer coefficient. More importantly, the Richards equations is solved numerically to find the time-dependent saturation field, S(t), which is needed for calculating the mass-transfer coefficient during the infiltration process. Here, the empirical correlation proposed by Barton and Brushett [5] for the Sherwood number (Sh) is modified to incorporate a diffusion-limited term which varies linearly with the saturation field, S(x,y,t); that is: where Re is the Reynolds number and Sc is the Schmidt number. Figure 1a shows the two-dimensional model of PowerPAD used for the simulations, which were performed using the finite-element software package COMSOL; see [2] for the details. According to the imbibition results obtained for the 4h-PAD system [3], the cell is predicted to start generating electricity after t = 0.33 s; see Fig. 1b. The system, however, needs roughly t = 20 s to become fully-saturated. Figure 1c shows the polarization curves for the 4h-PAD system at discrete times, whereas Fig. 1d shows variation of the maximum power as a function of time, up to the fully-saturated time. In these figures the discrete times (5.2, 8, 12, and 20 s) correspond, respectively, to the flow rates 11, 4.5, 0.4, and 0.01 mm3/s. According to Fig. 1d, during the transient phase the maximum power is roughly 50% larger than that for the fully-saturated case. The higher power generation during this initial infiltration process is attributed to the bulk fluid flow through the porous electrodes implying that the mass-transfer coefficients are improved through Re and Sc. References: [1] O.A. Ibrahim, M. Navarro-Segarra, P. Sadeghi, N. Sabaté, J.P. Esquivel, and E. Kjeang, Chem. Rev., 122 (7) (2022) 7236–7266. [2] P. Sadeghi, and E. Kjeang, Computational modelling of paper-based capillary-driven microfluidic flow cells, J. of Power Sources, 548 (2022)232084. [3] J.P. Esquivel, P. Alday, O.A. Ibrahim, B. Fernández, E. Kjeang, and N. Sabaté, A metal-free and biotically degradable battery for portable single-use applications, Adv. Energy Mater., 7 (2017) 1700275-86. [4] C. Dincer, R. Bruch, E. Costa-Rama, M.T. Fernández-Abedul, A. Merkoçi, A. Manz, G.A. Urban, and F. Güder, Disposable sensors in diagnostics, food, and environmental, monitoring, Adv. Mater., 31 (2019)1-28. [5] J.L. Barton, and F.R. Brushett, A one-dimensional stack model for redox flow battery analysis and operation, Batteries, 5 (2019) 1-25. Figure 1

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