Exploring the interplay of viscous flow and structural deformations in self-intersecting soft channels

Controlling fluid flow is an essential challenge for both natural and artificial systems, and efficient and steady distribution of nutrients in animals and plants requires advanced regulation mechanisms. In the mammalian cardiovascular system, blood flow autoregulation is attributed to active mechanisms that adjust the blood vessels’ fluidic resistances according to dynamic changes in blood pressure by the contraction or dilation of smooth vascular muscles. However, the proximal arrangement of soft arteries and veins suggests that a purely passive mechanism based on elastohydrodynamic interactions could account for some of the observed autoregulation.
When a viscous fluid flows within a soft channel, the fluid pressure can cause deformations of the channel boundary, which can reciprocally influence the fluid flow rate. This can result in a flow-versus-pressure relationship that deviates from Hagen-Poiseuille’s proportionality law and potentially enables flow control strategies in natural and artificial systems. This thesis explores fluid-structure interactions in bio-inspired fluidic systems comprising self-intersecting flexible channels through experiments and predictive mathematical models. These systems, we show, can be used to address flow control challenges within technological applications.
First, we study pressure-driven flow in a single self-intersecting flexible channel inspired by the proximal arrangement of arteries and veins that feed into and out of organs and limbs to evaluate the possibility of a purely passive elastohydrodynamic autoregulation mechanism. Our experiment is conducted on a microfluidic device comprising two channels (representing an artery and vein) separated by a thin elastomeric sheet. The two channels are connected via a rigid resistor, representing the vascular resistance of a capillary bed within an organ or limb. Our experiments and model reveal that flow limitation, i.e., a region in the flow-pressure relationship where the flow rate is independent of applied pressure, can occur when the capillary bed resistance is not significantly larger than the overlap resistance. This suggests that passive elastohydrodynamic interactions can play a role in autoregulation in cases where an artery-vein overlap is close to the organ it feeds into and out of.
Inspired by the dense entanglement of capillaries in some organs, such as the kidney glomerulus, we extend the scope of our study on self-intersecting channels to include multiple self-intersections. We introduce the concept of a ”hydraulic knot,” a fluidic device where multiple individual intersections are connected in a circuit. Nesting intersections within other intersections, a ”nested knot,” permits shifting the flow limitation, and connecting multiple individual intersections serially allows shifting the pressure at which flow limitation is initiated. The controllable flow-limiting properties of hydraulic knots present opportunities for designing tuneable autoregulatory fluidic systems for technological applications.
We use the passive flow-limiting behavior of self-intersecting flexible channels to study a particular engineering challenge related to controlling the fluid flow output from a peristaltic pump. It is not uncommon for peristaltic pumps to produce a pulsatile flow with an amplitude equal to the mean flow rate, which is a significant pain in, e.g., cell-counting instruments. By connecting the peristaltic pump to a compliant vessel and a flow-limiting resistor, we find that the pulsatile component of peristaltic flow can be reduced to < 1% of the mean flow rate output.
In the thesis’ final part, we explore passive flow regulation in conifer trees. Experiments conducted by our collaborators at UC Davis provide evidence that xylem tissue segments, i.e., the water pipeline in trees, exhibit flow-limiting behavior arising from fluid-structure interactions in elastomeric pit-pore valves that interconnect individual xylem cells. To elucidate the observations, we characterize and model synthetic pit pore valves. The individual synthetic valves show negative differential conductivity behavior at relatively high pressure, which interestingly permits the creation of almost arbitrary flow-rate-versus-pressure controllers by combining several carefully tuned valves in small serial and parallel networks. A constant mass flow rate controller (i.e., flow-limiting) is constructed from three synthetic valves connected in parallel.
In conclusion, the exploration of passive fluid regulation mechanisms in both biological and engineered systems offers promising avenues for innovative flow control strategies. By leveraging principles of fluid-structure interactions, such as those observed in self-intersecting channels and elastomeric pit-pore valves, we unveil opportunities to design tunable autoregulatory systems with implications for diverse technological applications and biological understanding.