Interfacial pH-gradient induced micro-capillary filling with the aid of transverse electrodes arrays in presence of electrical double layer effects

In the present work, we outline the design and analysis of a micro-capillary filling mechanism through the aid of interfacial pH gradients (and hence interfacial tension gradients) generated by employing arrays of transverse electrodes inducing step changes in voltages, in a natural buffer system that requires low power and no synthetic ampholytes. The capillary transport is modulated by a dynamic and non-trivial coupling between the interfacial tension and viscous resistances, as a consequence of the underlying intermolecular interactions. The competing effects of the driving and the retarding forces effectively determine the displacement, velocity and acceleration characteristics of the capillary front, in a dynamically evolving manner. A comprehensive theoretical model of capillary dynamics is developed here to address these issues in details, thereby revealing the combined influence of the interfacial electrochemistry and the applied transverse voltages, as guided by the pertinent fundamental thermodynamic principles governed by free energy considerations and the physico-chemical phenomena over interfacial scales. Non-trivial implications of the pH-gradient driven micro-capillary transport are aptly emphasized, so as to offer significant physical insights on the adopted strategy as a guiding principle for facilitating capillary filling processes by inducing a modulation in the effective interfacial energy. Particular implications on the capillary filling time are also pinpointed, revealing the effectiveness of the adopted design strategy. Finally, a universal scaling relationship of the capillary filling time as a function of the pertinent operating parameters is derived, so as to provide a generalized guideline for implementing the design scheme. A non-dimensional parameter, depending simultaneously on the inter-electrode pitch and the transverse voltage, is identified, which may be kept to a minimal limit within the other operating constraints of the chosen system, towards minimizing the capillary filling time.