Unidirectional flow from continuous broken symmetries

Abstract

Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal transport, a rectification mechanism that operates continuously across scales and frequencies. Here, we show that this concept applies beyond condensed matter, to fluid transport in living organisms and artificial systems. We take the example of the lymphatic vascular system, which transports interstitial fluid in mammals, and demonstrate that distributed leaflets act as continuous broken symmetries. We build an artificial model of a collecting lymphatic and investigate the naturally richer dynamics of unidirectional transport that arises from spatiotemporal excitations. We observe robust and scalable transport for any waveshape and external pressure gradients. We show experimentally and theoretically that the contraction wavelength, directionality, and pulsatility control the flow rate. In particular, we counterintuitively find waveshapes that maximize transport when propagating against the direction of the flow. Overall, our findings advance the understanding of unidirectional fluid transport in living systems and beyond, and reveal how coupling nonlinearities with spatiotemporal excitations can tune such transport across fields.

Figures (5)

• Figure 1: Robust and scalable unidirectional flow in a contracting vessel with continuous valves.(a) Schematic representation of the contracting vessel containing continuously distributed valves. (b, c, d) For sinusoidal contractions (a), valves in the vessel always impose positive flow rates (continuous lines) in opposition to vessels without valves (dashed lines). Robust flow rectification is observed independently of the vessel length, the contraction wavelength (c), or the pressure gradient (d). $\Delta P$ is defined as the pressure at the inlet (left end) minus the pressure at the outlet (right end), meaning that a negative value of $\Delta P$ corresponds to an adverse pressure gradient. The directionality of the wave propagation has no influence on the flow rate until large favorable pressure gradients. (e, f, g) For pulsatile contractions (e), the vessel retains the previous properties, but optimal transport is surprisingly observed for backward propagating waves until large favorable pressure gradients.
• Figure 1: Flow rectification for synchronous contractions The black dots correspond to measurements and the continuous lines to the model obtained with a sinusoidal contraction. In both cases, the flow rate is expressed in dimensionless form using the characteristic flow rate $Q_0$, defined at the contraction frequency introduced in the main text.
• Figure 2: Contracting vessel with distributed valves(a) Artificial lymphatic vessel design inspired by imaging of rat lymphatics bohlen2009phasicleak1980lymphatic. (b,c) Sketch of the vessel cross-section. The vessel consists of repeating segments called lymphangions, separated by valves. An actuator locally contracts each lymphangion with an amplitude $R_i(t)$, where $i$ indicates the actuator index. (d) Flow-pressure response of a single valve. For large adverse pressure gradients, the valve is closed and no flow is measured. For favorable pressure gradients, the valve is open and the flow linearly increases with $\Delta P$. Contrary to perfect valves described in Fig. \ref{['Fig1']}, a negative flow rate is measured for small adverse pressure gradients.
• Figure 2: Scalable and robust flow rectification for pulsating waves. (a,b,c) For pulsatile contractions with an asymmetry towards relaxation (a), optimal transport is observed for forward propagating waves (b,c). This observation is confirmed experimentally and theoretically for soft vessels (d,e,f).
• Figure 3: Unidirectional Flow from distributed broken symmetries in a soft vessel: experiment and theory.(a, b, c) For sinusoidal contractions (a), valves in the vessel always impose positive flow rates (continuous lines) in opposition to vessels without valves (dashed lines). Robust flow rectification is observed independently of the imposed pressure gradient (c), the vessel length or the contraction wavelength (b). The directionality of the wave propagation has no influence on the flow rate until large favorable pressure gradients. (d, e, f) For pulsatile contractions (d), the vessel retains the previous properties, but optimal transport is surprisingly observed for backward propagating waves until large favorable pressure gradients. The continuous lines correspond to the theoretical model considering soft vessels.