Gas flow in plant microfluidic networks controlled by capillary valves

The xylem vessels of trees constitute a model natural microfluidic system. In this work, we have studied the mechanism of air flow in the Populus xylem. The vessel microstructure was characterized by optical microscopy, transmission electronic microscopy (TEM), and atomic force microscopy (AFM) at different length scales. The xylem vessels have length $\approx 15$ cm and diameter $\approx 20\mu \mathrm{m}$. Flow from one vessel to the next occurs through $\sim {10}^2$ pits, which are grouped together at the ends of the vessels. The pits contain a thin, porous pit membrane with a thickness of 310 nm. We have measured the Young's moduli of the vessel wall and of the pits (both water-saturated and after drying) by specific nanoindentation and nanoflexion experiments with AFM. We found that both the dried and water-saturated pit membranes have Young's modulus around 0.4 MPa, in agreement with values obtained by micromolding of pits deformed by an applied pressure difference. Air injection experiments reveal that air flows through the xylem vessels when the differential pressure across a sample is larger than a critical value $\Delta P_c=1.8$ MPa. In order to model the air flow rate for $\Delta P⩾\Delta P_c$, we assumed the pit membrane to be a porous medium that is strained by the applied pressure difference. Water menisci in the pit pores play the role of capillary valves, which open at $\Delta P=\Delta P_c$. From the point of view of the plant physiology, this work presents a basic understanding of the physics of bordered pits.

Figure 1

Schema of microfluidics plant networks. The pit field is at the end of the xylem vessel.

Figure 2

(a) Force-displacement curves for PMMA ($•$) and for silicon wafer (+). The continuous lines (−) display the linear fit, the calibration factor is $1/\chi =2.89\pm 0.14{10}^8\mathrm{V}/\mathrm{m}$. (b) Nanoindentation curve of PMMA ($\blacksquare$) with its linear fit (−).

Figure 3

Diagram of air seeding experiments.

Figure 4

Silicone micromolding of Populus pits at $\Delta P=2.2\mathrm{MPa}$ observed by SEM.

Figure 5

(a) Optical observation of a primary pit field ($\times$100). (b) Topography image of a dried Populus pit measured by AFM in tapping mode.

Figure 6

TEM observation of a dried intervascular Populus pit. The pit membrane (PM) thickness is around 311 nm. The pit border (PB) partially covers the pit membrane.

Figure 7

(a) Force-displacement curves on a xylem vessel wall ($•$) and on a silicon wafer (+). (b) Nanoindentation curve on a xylem vessel wall ($\blacksquare$) with its linear fit (−).

Figure 8

(a) Force-displacement curve on a pit membrane (PM) ($•$). (b) Log-log representation of the force-distance curve of the pit membrane ($\blacksquare$) with its linear fit (−).

Figure 9

(a) Force-displacement curves for water-swollen pit membranes (PM) ($•$), pit border extremity (PB1) ($\blacksquare$), and pit border near the intravascular pit junctions (PB2) ($*$) fitted by a Zener model (−). (b) The Zener model.

Figure 10

Experimental air seeding flow rate vs. difference pressure ($⧫$). Modeling of the flow rate at constant number of pit membrane pores: (−) pressure effects, (- - -) pressure effects combined with the pit membrane deformation ($E=0.41\mathrm{GPa}$), and ($···$) pressure effects combined with the pit membrane deformation ($E=0.65\mathrm{GPa}$).

Figure 11

Deflection of the pit membrane as a function of the normalized radial position $r/R_{\mathrm{pit}}$, measured from micromolding experiments by SEM image analysis at $\Delta P=0.2\mathrm{MPa}$ (a), $\Delta P=\Delta P_c$ (b) and $\Delta P=2.2\mathrm{MPa}$ (c). The profiles were fitted by Eq. (6) (−) with $E=0.41\pm 0.15\mathrm{GPa}$ (a), $E=0.41\pm 0.13\mathrm{GPa}$ (b), and $E=0.66\pm 0.097\mathrm{GPa}$ (c).