Journal Club for August 2022: The route towards engineered multifunctional hair and fur

Sameh Tawfick, University of Illinois at Urbana-Champaign (tawfick@illinois.edu)

Birds have feathers, animals have fur, humans and plants have hair, and mimicking these multifunctional morphologies will undoubtedly improve future robots, buildings, and drones 

Introduction:

Hair, fins, and other slender structures are ubiquitous in nature. They are observed with various morphologies, at different scales and packing densities, yet are typically highly deformable and exhibit complex, collective, and responsive motion. Plants, insects, and animals use hair, fur, or fins for a variety of critical purposes including defense, temperature regulation, optical appearance, mechanical protection, visual, acoustic, and chemical signaling. It is interesting that for laypeople, softness is almost synonymous with long deformable hair, as in the case of animal fur. Also, according to laypeople, the primary function of hair and fur is this amazing combination of thermal regulation and mechanical compliance. Beyond the obvious examples of fur found in most animals, nature displays examples of some really unusual thermal regulation functions that exploit the slenderness of hair. The hairy leaves of the silver tree (Leucadendron argenteum) enable this tree to survive throughout extreme hot dry and humid weathers (Figure 1e,f). The silky silver hair on silver tree leaves lies down parallel to the leaves to protect them from drying during hot dry weather by reflecting radiation and impeding water evaporation, while in damp weather, the hairs bundle and stay vertical to allow better air circulation, which also make the leaves appear less dazzling and hence less attractive to predators. Another fascinating example was recently discovered in the unusual thermal regulation exploiting the fur deformability and complex collective response in sea otters. The bundling morphology of the fur covering the body of sea otters plays a crucial role in thermal regulation allowing them to swim in the cold ocean by trapping air between their long hairs (Figure 1g,h), forming the intricate tepee structures with air entrapment. Last but not least, the most complex and unusual hair response is seen in the tarsa-hair on beetles feet which control their bundling and aggregation morphology to promote self-defense against predators by increased feet adhesion. This is achieved by secreting oil from pores going through their skin to assemble these hairs and stiffen the adhesion interface (Figure 1b-d). We note here the emergence of integrated hair material systems where not only hair can change its morphology for adaptive functions, but also does so in response to internal stimulation with another medium such as oil secretion. Finally, fluid-structure interaction in hair arrays is thought to reduce fluid drag.

Figure 1. Bioinspiration for multifunctional hair. (a) Natural hairs are truly multifunctional materials, exhibiting tailored properties for [i] transport barrier against uncontrolled water loss from leaf interior, [ii] surface wetting, [iii] self-cleaning properties for protection against pathogen attack and insects, [iv] optical signaling: cues for host/insect recognition and epidermal cell development, [v] protection against harmful radiation, [vi] mechanical properties: resistance against mechanical stress and maintenance of physiological integrity, and [vii] temperature regulation by increasing turbulent air flow over the boundary layer. (b) Beetles can fix themselves and survive large pulling weights by changing their tarsa hair aggregation. (c) Side view of the beetle showing their small apparent feet. (d) Aggregated feet hair (top) and dispersed hair (bottom) controlled via secreting special liquid from glands for feet adhesion defense. (e) The dense horizontally aligned hair on the silver tree leaves which protects its from heat and change its orientation to allow circulation in more humid environments. (f) High magnification scanning electron microscope (SEM) of the tree hair. (g) Sea otters have an amazing temperature regulation enabled by the ability of their long dense hair to trap air before each dive.  (h) Aggregation and coalescence morphology of the hair enables them to trap hair during swimming and diving.

An extraordinary engineering material:

Hair and fur hence can be an extraordinary future engineering material. Inspired by the use in nature, one can imagine buildings and structures coated with multifunctional hair: it would act as an active and adaptive thermal regulation material which changes their properties by the time of the day, weather and/or season. The hair array can also be self-cleaning, water repellant, and be used as an active façade display which can change its pattern and organization, creating an unusual but attractive architecture feature. Small drones and mobile robots can also benefit from hair and fur for thermal regulation, self-cleaning, shock absorption and camouflage. While hair and fur are so prominent in nature, they are almost entirely absent in engineering application. Here, we will try to discuss the engineering challenges that impede the use of hair as an engineering material. 

 Engineering definition of hair and hair arrays:

Here, it is suitable to first start by articulating a more precisely defining hair: “A single hair is a slender high aspect ratio structure, fixed at its base and freely bending by more than +/- 90° without failure, yielding, or fracture.” Further, we define hair array or fur: “Hair array is a large dense assembly of hair giving rise to interesting interactions and collective mechanics. The collective behavior within this array is observed when the length of each hair is at least 5-folds the spacing between the hairs. This allows it to interact with at least four other hairs when it bends in any direction.” A mechanics-rooted definition is used here, which catalyzes the forthcoming mechanics discussions. For instance, consider a cylindrical hair made from a material having ~0.001 yield strain limit, such as most metals. Subject to large deflections, the surface strain needs to be ~ r/R< 0.001, where r is the hair radius, and R is the radius of curvature achieving the +/- 90° in the definition. It follows then that the aspect ratio, (length/radius) must be on the order of 1000. Examining human hair, it typically has 0.02 mmm radius and hence it bends and flows like hair when its length is ~ O(10) mm or higher. Many organic materials have a higher strain limit of ~0.01 and hence behave like hair when the length is O(1) mm. Hair should also be reversibly sticking, i.e. always able to recover its original shape and reconfigure its assembly. The exact length and radius are defined by the function: for instance, long dense hair is needed for thermal regulation of large animals while short hair can be sufficient for signal transmission in insects. Hair length in nature is most commonly > 5 mm. We expect that a 5 mm length will be the mean length for hair as an engineering material in a wide variety of applications.

What are the challenges that impede this rich plethora of functions provided by hair and fur? In my opinion the three main challenges are: manufacturing, mechanics, and reliability.

 Manufacturing:

There is currently no scalable process to produce three-dimensional parts with integrated hair on their surface. With this definition, the vast majority of fabricated micro- and nano-pillars are not mimicking the natural hair and fur relevant to this discussion. For example, the Bosch deep reaction ion etching (DRIE) produces pillars of aspect ratio of >20, too short to be considered hair and of course not deformable by the +/- 90° in the hair definition.  DRIE can be used to fabricate negative molds from a silicon wafer by cutting holes of 0.02 mm radius and up to 0.4 mm height, reaching an aspect ratio of >10.  In turn, these molds are used to fabricate elastomeric pillars, which are indeed highly deformable, but too short to mimic biological hair and its functions for instance in thermal regulation or signaling. Recently, there was one study from the MIT Media Lab (Tangible Media Group) that modified a 3D printer to draw the filament, and hence thin it and elongate it. The project, called cilia, also includes a vision for a variety of application such as human-computer interfaces based on long hair. I was personally inspired by the ideas in this project which align with my own. The manufacturing technique is interesting and can potentially be scalable if arrays of nozzles are used. To produce hair on 3D surfacers, two other rotation axes are needed beyond XYZ linear motion to provide the degrees of freedom for instance to produce hair on a spherical shape. 

Figure 2. Additive Manufacturing (AM) of hair by continuous Digital Light Manufacturing (cDLM) (Unpublished results). (a) Traditional digital light projection is intrinsically slow and cannot precisely print long hair due to the limitation placed by polymer curing, requiring the pull-out of the print object between steps to allow for the spreading of a new polymer layer and its oxygen assisted cross linking. (b) cDLM allows for the rapid printing of high aspect ratio textures due to the use of a patented oxygen permeable window which allows the continuous printing of parts without interruption, and the seamless alignment of voxels. (c) Our team is developing a Functional Rapid Texture Creation (FUR-TEC) technology which will enable the integration of designed hair diameter, length, density, gradient cross section and patch design on any parts topography. (d-f) Examples of hair printed by this process. Smallest hair diameter of 100 μm can be successfully printed. Part width is 5 mm in (d) and (e), and 15 mm in (f). The hard thermoset hairs in (d) and (e) are before and after capillary self-assembly demonstrating their self-assembly.

My lab explored high precision light-based 3D printing, such as the Digital Light Synthesis (DLS) process  from Carbon 3D or the similar continuous Digital Light Manufacturing (cDLM) from Etec (previously EnvisionTEC). The main feature of these technologies that enable high aspect ratio hair printing is the continuous addition of cured material layers away from the air-liquid resin interface and without any “slider”. This is advantageous compared to the common stereolithography used in the Formlabs printers that use a slider after each layer. We fabricated high aspect ratio and dense hairs from DLS and cDLM technologies and the results are very promising. We have exceeded aspect ratios of 100, the materials are sufficiently elastic and hence the +/- 90° can be achieved. In addition to direct printing, it is possible to use 3D printed molds to produce ~10 aspect ratio hairs from elastomeric materials which hence can bend by large angles without failure. Finally, one can imagine using special chemistries to extrude hair directly from surface pores mimicking the growth of natural hair.

Mechanics:

The mechanics of hair is an equally major challenge impeding the use of hair as an engineering material. Engineers work with deterministic, well-controlled structures. Traditionally, engineering materials and structures had to be precisely modeled and their behavior fully predictable with high fidelity.  This necessitates homogeneous behavior on extended scales and enables the use coarse grained models. Hair and fur are the antonyms of this deterministic behavior: they are highly heterogeneous, mechanically responsive to environmental stimulations and with no spatially monotonic behavior on extended areas. However, nature uses such complex material very effectively owing to its great advantages, and so this could be the next engineering challenge for the current generation of scientist and engineers. 

With the definition of hairs and hair arrays in the previous section, several mechanics complications arise when mathematically modeling hair. Firstly, we classify the behavior of individual hair as large deformation, strongly non-linear structure when it is produced from a simple linear elastic material. In this case, the theory of elastica (as posed by Bernouilli and later investigated by Euler) can be used to describe non-extensional bending behavior. The treatise by Love which builds on Kirchhoff’s kinetic analogy is very insightful, and should be taught in graduate course on the topic. Of course, the mechanics of hair behavior gets more complex if the material is elastomeric and extension/compression and twisting is considered. In this case, numerical approaches using for instance the Cosserat rod can be very effective. The "elastica" software tool by my colleague Prof. Mattia Gazzola is enabling many numerically efficient developments in this area. Moreover, hair arrays present yet another level of complexity owing to their granular-like interaction which involve simultaneous friction, sliding, entanglement, and large deformation in addition to granular-like crowding and densification effects. Force chains methods typically used in (spherical) granular materials are not yet sufficiently developed for fur and hair arrays.  

Figure 3. Library of polymorphic hair self-assembly by dynamic elastocapillarity. Each column represents a class of recently discovered transformation, which are found in our articles (third column is still unpublished). 

Interaction with fluids is an essential environmental effect for hair and presents both a challenge and an opportunity. Owing to their thin, slender structure, hair significantly deforms due to the capillary forces of a liquid. The balance between the negative pressure created underneath a meniscus and the restoring forces due to deforming hair defines the final shape. In their seminal one-page letter in Nature, Jose Bico et al. studied the coalescence of wet hair due to capillary forces and defined the elastocapillary length. When the hair length reaches the elastocapillary length, its compliance allows it to deform and wrap around a droplet to minimize the total energy (bending strain energy and surface energy). When hair is much longer than the elastocapillary length, it readily deforms under capillary forces, making various types of hierarchical bundles. 

We have discovered extremely interesting structure-liquid interactions arising in dense hair arrays especially in the dynamic liquid flow regime (non-negligeable liquid velocity). First, our work has shown that bundles re-organize and morph their cross-section shape due to granular-like effects as the fibers coalesce and densify. We have derived simple nonlinear stiffness relation (F ~ d^2) governing the sequential fiber contacts and densification. We used this law to predict the unusual bundle shape morphing observed experimentally: polygonal hair arrays densify into pointy star-like shapes due to capillary forces. Hollow circular bundles remain hollow (no cross-section change) but with much thinner, tapered, and dense walls. Moreover, our experiments demonstrated that the drain rate (flow dynamics) results in polymorphic patterns due to the interplay between liquid viscosity and fiber densification. Some of these new effects are shown in the figure, and were highlighted in Physics by APS. Our articles (polygons 1 and polygons 2, twisting, hollow bundles) derive simple models that capture the main elements of these transformation including the elastocapillarity with nonlinear stiffness due to densification, and the diffusion-limited liquid flow creating various shapes of liquid columns. This work is reminiscent of the hair tepee structures formed on the otter’s fur during swimming which regulate their body temperature and possibly reduce drag. 

Hair simulation software is an extremely active area of development for computer simulation and animation. Some interesting videos and articles can be found here Youtube (Pixar),  YouTube (Columbia), Review, Eitan Grinspun Google Scholar. 

Reliability, shedding, and hair growth:

The final consideration for hair and fur as a multifunctional engineering material is reliability. Due to its extremely long aspect ratio, hair mechanics lead to frequent failure by cutting and shedding. Humans and animals constantly shed their hair, but new hair is also constantly growing to replace the lost ones. Hence, nature uses hair as a dynamic constantly growing and evolving material. This is a critical consideration: it is likely that if hair is used on engineered structures and robots, it will be constantly broken and a biomimicking growth mechanism is perhaps the most effective. To grow hair on engineering structures, it must be part of an active material system which is capable of outward extruding slender material. This can be accomplished by epidermal pores, and likely a sub-surface microfluidic network for resin pumping. Further, this growth process must be activated via a sensing process which indicates the need to growth more hair. Such a system is in effect in biology and works extremely high energy, power and mass efficiency. Hence, the use of multifunctional hair in engineering structure must be supported by the ability to sense and regrow hair in situ.

Summary:

In summary, hair and fur are marvelous biological materials and can undoubtedly offer extraordinary multifunctionality for engineering systems. This blog has identified three major areas of investigation in the route towards realizing this vision: Advancement in manufacturing, mechanics, and reliability. Each area pushes the limit of the current state of the art in knowledge, but surely the fruits of such an implementation will be worth it.