Can nature design and build for us?
The above image shows the fluid tunnelling process that occurs when a less viscous fluid (in the above case air) displaces a more viscous fluid (in the above case soap) in porous media.The instability produces a branched fractal pattern similar to the structure of mammalian tissue vascularity (Zamir, 2001), and its design (fractal bifurcation) follows that of an optimal flow pathway for microfluidic networks (Bejan, 2001; Chen et al., 2010; Wu et al., 2010).
Nature self-designs and self-forms. Embedded in its processes is both the information necessary for conception and the physical capacity for construction. Architects and engineers have long taken advantage of nature’s capability to self-design. However, they have rarely taken advantage of nature’s capacity to self-form. Most often natural inspirations are modelled using data-intensive algorithms, and fabricated using cost- and energy-intensive machinery. In an architectural context, nature is rarely utilized to self-fabricate for free. Accordingly, we propose an adaptive architectural skin that is not only self-designed, but self-formed: a millifluidic vasculature constructed using a pressure instability between fluids.
The fractal bifurcation pattern produced from the above fluid tunnelling process represents the optimal flow pathway with the maximum flow efficiency for fluidic transport. This network accordingly follows Murray’s Law, stating that when a network branch splits (with radius r), the thickness of the resulting new branches (with radius r1 and r2) is optimized for flow efficiency (Wu et al. 2010). In its simplest form, Murray’s Law states:
r^3 = r1^3 + r2^3
Murray’s Law is obeyed in both the vascular and respiratory systems of animals and in the xylem in plants. It is also obeyed in river branching, as displayed above (Roger Beaty). Accordingly, the resulting fluidic network produced using the Saffman-Taylor instability is also optimal for delivering or removing heat within a fluidic network (Bejan, 2001; Chen et al., 2010).
The above sequence of images illustrates the introduction of a less viscous fluid evenly on both sides of a more viscous fluid, resulting in an even fluid displacement, and an even fractal bifurcation structure.
Can we control fluid pocket patterns with physics?
Sequences 1-4 show the pressure-induced expansion of fluid pockets within a different fluid. The instability (patterning) results from a difference in viscosities between the two fluids. 1 shows the displacement of oil with water. Sequences 2-4 show the displacement of the same oil with gradually more viscous versions of the same water. The effect of viscosity difference between fluids on pattern geometry can be observed. This will inform work on sea-creature-inspired fluid pockets within the skin of buildings.
The effect of the ratio between viscosities of the inner and outer fluid on the ratio between the inner and outer finger radii is shown. From this, a relationship between the light transmission potential and the fluidic characteristics within the window can be determined. This will inform work on sea-creature-inspired fluid pockets within the skin of buildings.
It also turns out this patterning takes a similar form to that of the Paenibacillus Dendritiformis bacteria colony. Left: bacteria colony (Ben-Jacob); Right: imitation chromatophore cell within the skin of building in response to EM radiation (Kay et al., unpublished, 2020)