Design of capillary flows with functionally graded porous titanium oxide films fabricated by anodization instability.

We have developed an electrochemical fabrication method utilizing breakdown anodization (BDA) to yield capillary flows that can be expressed as functions of capillary height. This method uses anodization instability with high electric potentials and mildly acidic electrolytes that are maintained at low temperature. BDA produces highly porous micro- and nano-structured surfaces composed of amorphous titanium oxide on titanium substrates, resulting in high capillary pressure and capillary diffusivity. With this fabrication technique the capillary flow properties can be controlled by varying the applied electric field and electrolyte temperature. Furthermore, they can be expressed as functions of capillary height when customized electric fields are used in BDA. To predict capillary flows on BDA surfaces, we developed a conceptual model of highly wettable porous films, which are modeled as multiple layers of capillary tubes oriented in the flow direction. From the model, we derived a general capillary flow equation of motion in terms of capillary pressure and capillary diffusivity, both of which can be expressed as functions of capillary height. The theoretical model was verified by comparisons with experimental capillary flows, showing good agreement. From investigation of the surface morphology we found that the surface structures were also functionally graded with respect to the capillary height (i.e. applied electric field). The suggested fabrication method and the theoretical model offer novel design methodologies for microscale liquid transport devices requiring control over propagation speed.