Nonlinear phenomena and qualitative evaluation of risk of clogging in a capillary microreactor under imposed electric field

Abstract Electric field imposed on a microchip, when electrokinetic pumping is used, can cause precipitation of electrolyte components and consequential clogging of the microchannels. We have found that the precipitation will occur in much broader range of electrolyte concentrations than in the case without the imposed electric field. For example, concentrations of the ions in the physiological fluids analyzed in the diagnostic microchips can also reach the solubility product when the gradient of the electric potential is used. This follows from the study of the mathematical model of the electrolyte transport and ionic interactions in microcapillaries. The studied microsystem consists of two reservoirs containing aqueous electrolytes, a solution of potassium carbonate and a solution of calcium chloride, separated by a microcapillary containing a hydrogel. As the calcium and the carbonate ions diffuse and/or migrate in electric field in the microcapillary, calcium carbonate is formed and the risk of clogging increases at the locations where the concentration product of the calcium and carbonate ions exceeds the CaCO3 solubility product. Two qualitatively different spatio-temporal concentration patterns in the microcapillary of finite length in dependence on the applied difference of the electric potential have been found by means of the dynamical analysis. We have observed patterns with one and two maxima on the spatial profile of reaction rate of the calcium–carbonate interaction. Bifurcation diagram, in which the peak splitting has been clearly detected, was computed in dependence on the imposed gradient of electric potential. The peak splitting and thus the possibility of more complex precipitation patterns in the microcapillary follow from the existence of the sigmoidal profile of the electric potential arising in the presence of electric field. We have also found that the existence of sigmoidal profile strongly modifies the transport times of the chemical ionic components ( t p ≈ Δ Φ − 1 / 3 in a broad range of applied gradient of electric potential Δ Φ / l ∈ 0.02 , 20  kV m−1). As the mathematical description of the model system is spatially one-dimensional, the obtained results are applicable especially in capillary microsystems with a large length/diameter ratio (e.g., separation microchannels or microchannels for isoelectrical focusing).

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