Bio-Inspired Hierarchical Vascular Networks: Electrohydrodynamic Viscous Fingering

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. One such approach to induce vascular networks whilst mimicking nature's design is electrohydrodynamic viscous fingering (EHVF).

(a)                                                        (b)                                         (c)

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.