Techniques for Hierarchical Bio-Inspired Vascular Networks: Electrohydrodynamic Viscous Fingering and Electrical Treeing

Vascular networks provide a method to distribute fluid throughout a system. Artificial vascular materials with enhanced properties are being developed that could ultimately be integrated into systems reliant upon fluid transport while retaining their structural properties. An uninterrupted and controllable supply of liquid is optimal for many applications such as continual self-healing materials, in-situ delivery of optically index matched fluids, thermal management (sweating) and drug delivery systems could benefit from a bio-inspired vascular approach that combines complex network geometries with minimal processing parameters. Two such approaches to induce vascular networks whilst mimicking nature's design are electrohydrodynamic viscous fingering (EHVF) and electrical treeing (ET).

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Figure 1. Optical images of EHVF (a) in a 1,000 cSt silicone oil system containing ~ 60 v/v% glass beads, (b) interfacial polymerization of of hexamethylene diamine and sodium chloride in water and sebocyl chloride in 10,000 cSt silicon oil, and in three dimensions (3DEHVF) using fumed silica in an index matched fluid.

Viscous fingering (VF) is a phenomenon that occurs when a low viscosity liquid is forced through a high viscosity fluid or matrix. The flowing liquid will branch, or form fingers due to capillary and viscous forces in the high viscosity material. EHVF is a modification on viscous fingering in which a DC voltage is applied to the low viscosity conductive fluid (Fig. 1a) and forced through a dielectric matrix material. The application of a large electrical potential, 10-60 kV, induces fingers with a reduction in size and an increased branching behavior. The ensuing patterns mimic those found in biology and geology (lung tissue and plants as well as river beds). Observation of VF and EHVF requires Hele-Shaw conditions in which a 2D system must possess a thin gap (0.8 mm used in these experiments) or in a porous system. In the 2D instance a silicone oil system is used as the matrix material, the surfactant concentration was optimized, through a reduction in the interfacial tension, thereby producing a branched pattern of small diameter fingers while still maintaining continuity when dyed water is pushed through the system. Various loadings of glass beads where subsequently used to represent a more 3D system. Typically, in a two fluid system, the fingers relax as soon as the applied voltage is removed. Addition of glass beads, up to 60 v/v%, aids in a retardation of finger relaxation while producing fine channels throughout the porous system. Delayed relaxation allows for greater control of the curing process in UV-curable systems, such as polydimethylsiloxane (PDMS). Fabrics, woven and random glass fiber mats were also investigated as a matrix to provide a different porosity to the system. Matrix filling was used as a method to reduce finger relaxation and allow for curing to occur after the voltage was turned off. Interfacial polymerization EHVF (IPEHVF), a technique in which the polymerization occurs at the interface of two materials, was also studied in producing fingers in the silicone oil phase. For EHVF to be studied in a similar system, hexamethylene diamine (C6H16N2) and sodium chloride were dissolved in the water phase, while sebacoyl chloride (C10H16Cl2O2) was disperse in the silicone oil phase. Robust, polymerized, fingers were formed (Fig. 1b) and remained after the voltage was turned off. These fingers were subsequently filled with water to show fluid transport. In moving toward a true 3D system, materials such as fumed silica (Fig 1c) and crushed glass were investigated under 3D (porous) Hele-Shaw conditions.

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Figure 2. Optical image of ET (a) in a EPON 828/PACM system, (b) under AC driven electrical current showing “bush-like” features, (c) under DC driven electrical current showing “tree-like” features and (d) filling of an ET grown vascular network with a UV visualization dye.

Electrical treeing (ET) is the result of partial discharges in a dielectric material. In the vicinity of a small diameter electrode, the local electric field is greater than the global dielectric strength, causing a localized, step-wise, breakdown to occur forming a highly branched interconnected structure (Fig. 2a). The growth of these structures is influenced by the configuration of the electrodes, with geometries of a point lead electrode to a point or plane ground electrode being of most interest. ET is a viable method to produce networks in 2D systems and in more robust 3D systems on a smaller, micron, scale than the products of the EHVF method. AC driven electrical current (Fig. 2b), harnessing a sine wave at 100 Hz, grows a “bush-like” structure with many branches and therefore a larger volume within the epoxy samples. DC driven electrical current (Fig. 2c) produces a more “tree-like” structure with fewer branches and bifurcations. The surface of the electrodes were modified with dispersed multi-walled carbon nanotubes (MWCNTs) to aid in increasing the local electric field, and thus enable a higher rate of tree initiation and growth. Inclusion of particles was investigated to determine if the growth direction can be manipulated. The use of self-clearing electrodes (as a grounding material) was investigated with the infiltration of a UV dye through the hollow channels produced by ET resulting in a vascularized network capable of repeated fillings and evacuations. Fluid delivery (Fig. 2d) can be tailored through the applications of different electrode and ground manufacturing techniques for optimized flow rates for a given application.