A Non-Steady-State Electric Circuit in Electrophoresis on Paper: Thermal Consideration of Electrophoretic Lateral-Flow Assays

Non-steady-state behaviors are not expected in electric circuits that lack significant capacitance, inductivity, and/or active feedback. Here, we report that electrophoresis on paper (used to conduct/enhance paper-based assays) can create a non-steady-state electric circuit. We studied electrophoresis on 4-mm wide nitrocellulose-membrane strips utilized in lateral-flow immunoassays; the voltage was applied to strip termini immersed in reservoirs with a running buffer. If the total supplied power exceeded approximately 0.5 W, neither the electric current nor the temperature map reached their steady states on a multi-minute time scale. The current grew slowly to its maximum and then slowly decreased, and the temperature map evolved slowly, with one or more hot spots appearing and disappearing gradually in different positions on the strip. The slow evolution of a temperature map led to the occurrence of a terminal hot spot in which the strip burned. No chaotic behavior was observed, i.e., time dependences of both the current and temperature map were reproducible. We analyzed major processes involved in paper-based electrophoresis and explained the non-steady-state behavior. Unlike ordinary electric circuits with metal conductors, paper-based electrophoresis involves two slow processes: (i) intense buffer evaporation from hot spots and (ii) buffer supply from the reservoirs by an interplay of the capillary penetration and the electroosmotic flow. These processes affect heat generation and/or dissipation on the strip and, accordingly, the resistivity profile along the strip. The slow evolution of the resistivity profile is responsible for the non-steady-state behavior. Our work is the first detailed and conclusive study of heat maps in electrophoretically-enhanced LFA. We demonstrate spatiotemporal temperature distribution, which emphasizes the need for the empirical study of thermal behaviors due to the inability to create predictive quantitative models of the complex interplay of multiple processes, including evaporation.