Corrsin lecture on hairy hydrodynamics

Flexible slender structures in flow are everywhere. While a great deal is known about individual flexible fibers interacting with fluids, considerably less work has been done on fiber ensembles, such as fur or hair, in flow. These hairy surfaces are abundant in nature and perform multiple functions from thermal regulation to water harvesting to sensing. Motivated by these systems, I consider two examples of hairy surfaces interacting with flow which were presented in the Corrsin lecture at the 2018 APS-DFD meeting (71st Annual Meeting of the APS Division of Fluid Dynamics, Atlanta, 2018). In the first example I consider a toy problem of angled hairs in Couette flow. Using this simple model, I explore asymmetry in the flow and anomalous drag scaling by exploiting various limits in the parameter space. In the second example I consider viscous dipping, a feeding method utilized by many nectar drinking animals. Previous studies have analyzed these drinking strategies through the Landau-Levich-Derjaguin framework; however, many viscous dippers have hairy structures on their tongues that enhance fluid uptake. Here I investigate the impact of mesoscale hairy structures on feeding efficiency and conclude with general comments on drainage through beds of hairs.

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Figure 1

Schematic of a toy problem to illustrate asymmetry induced by deformable hairs in channel flow. In the absence of flow, $\theta ={\theta }_S$.

Figure 2

(a) Flow ratio $R$ for a fixed ratio of channel height to hair length $\alpha =0.7$. (b) Flow ratio $R$ at fixed ${\theta }_S=\pi /2$. Color indicates $R$ with black indicating no asymmetry in the flow.

Figure 3

Dimensionless drag as a function of $\beta \sim 1/V$. The dashed line indicates a slope of 1/3. Solid lines indicate different values of ${\theta }_S$ with the topmost (highlighted by circles) ${\theta }_S=0$. In all calculations $\alpha =0.999$.

Figure 4

Schematic of hair geometry in draining films. Circles represent hair cross sections. Gravity points in the $x$ direction.

Figure 5

Fluid uptake as a function of dimensionless hair diameter $e^{*}$ and dimensionless hair spacing $r^{*}$. Color corresponds to dimensionless volume of fluid captured. The dashed line indicates the optimal spacing for a given hair radius $e^{*}$; dotted lines indicate the region in which the fluid uptake is within 99% of the maximum value. White points indicate measured values of hair diameter and spacing for different species taken from the literature.

Figure 6

Functional dependence on ${\varphi }_s/{\varphi }_m$ for $\mathrm{\Delta }V/V$ and $F_{\mathrm{fluid}}/F_{\mathrm{hair}}$. The solid line depicts $\psi ({\varphi }_s/{\varphi }_m)$ as defined in the text. The dashed line depicts the dependence of $F_{\mathrm{fluid}}/F_{\mathrm{hair}}$ where ${\psi }_2({\varphi }_s/{\varphi }_m)\equiv {[1-{({\varphi }_s/{\varphi }_m)}^{1/2}]}^{5/2}/({\varphi }_s/{\varphi }_m)$.