Active Osmotic Exchanger for Efficient Nanofiltration Inspired by the Kidney

In this paper, we investigate the physical mechanisms underlying one of the most efficient filtration devices: the kidney. Building on a minimal model of the Henle loop—the central part of the kidney filtration—we investigate theoretically the detailed out-of-equilibrium fluxes in this separation process in order to obtain absolute theoretical bounds for its efficiency in terms of separation ability and energy consumption. We demonstrate that this separation process operates at a remarkably small energy cost as compared to traditional sieving processes while working at much smaller pressures. This unique energetic efficiency originates in the double-loop geometry of the nephron, which operates as an active osmotic exchanger. The principles for an artificial-kidney-inspired filtration device could be readily mimicked based on existing soft technologies to build compact and low-energy artificial dialytic devices. Such a “kidney on a chip” also points to new avenues for advanced water recycling, targeting, in particular, sea-water pretreatment for decontamination and hardness reduction.

Popular Summary

Access to fresh, safe drinking water is a problem in many parts of the world. However, recycling water is an extremely costly process, both energetically and commercially, and it involves subtle sieving processes on the subnanoscale. This domain accordingly requires out-of-the-box ideas beyond traditional sieving principles. Here, we explore new routes for water recycling and access to fresh water by drawing on inspiration from the human kidney.

We show that new avenues can be proposed based on the separation principles underlying one of the most efficient filtration devices: the human kidney, which is able to recycle roughly 200 L of water and 1.5 kg of salt per day. Based on a theoretical modeling of the physics at play in this device, we investigate the detailed out-of-equilibrium fluxes taking place in an “osmotic exchanger” inspired by the nephron (i.e., the central part of the kidney’s filtration system, of which there are millions in a human kidney). Our analysis reveals that the counterintuitive double-loop design of the kidney separation operates at a remarkably small energy cost—typically 1 order of magnitude smaller than traditional sieving processes such as nanofiltration—while working at much smaller pressures. We also derive the theoretical limits for the efficiency of a kidney. We are accordingly able to propose a bio-inspired counterpart of the kidney recycling process incorporating electric fields as the only driving force in simple designs that can be readily mimicked using microfluidic technology.

Our findings accordingly point to new avenues for efficient separation processes and advanced water recycling and, at the same time, suggest new routes for future compact and low-energy artificial dialysis systems.

Figure 1

The osmotic exchanger filtration system. Model for a concentrating device based on the geometry of Henle’s loop in the kidney. Water, waste, and salt are carried through the loop of Henle, consisting of the descending limb (D) and ascending limb (A) and continued by the collecting duct (CD). Each limb wall allows exchanges with the interstitium (I), enabling water and salt to evacuate the loop. The remaining waste is concentrated and evacuated by the CD.

Figure 2

Spatial distributions of the fluxes and molar fraction in the $U$-loop and full double loop (HL and $\mathrm{HL}+\mathrm{CD}$ models). (a) Fluxes of water (divided by a scaling factor of 100), osmotic activator (salt), and waste along the D and A limbs, left panel; and along the CD for the $\mathrm{HL}+\mathrm{CD}$ case; in this graph, the water loss ratio $\eta =q_{\text{Water}}^{\mathrm{out}}/q_{\text{Water}}^{\mathrm{in}}$ is the final normalized flux. (b) Spatial distribution of the molar fractions of water (divided by a scaling factor of 100), osmotic activator, and waste along the D and A limbs and in the interstitium. Note that in the ($\mathrm{HL}+\mathrm{CD}$) double-loop geometry, the interstitium exchanges with all three branches (D, A, CD); although two were plotted for convenience, they have the same composition. Numerical data are calculated with parameters $L=4.3\mathrm{mm}$, $P_f=2500\mu \mathrm{m}/\mathrm{s}$, $n=1$.

Figure 3

Separation ability and minimal bounds. (a) Water loss ratio $\eta =q_{\text{Water}}^{\mathrm{out}}/q_{\text{Water}}^{\mathrm{in}}$ as a function of the initial concentration of osmotic activator $[\mathrm{Osm}{]}^{\mathrm{in}}$ (salt). Both the numerical results (crosses and dotted lines) and the predicted lower bounds (solid lines) are reported, for the single loop (HL), double-loop ($\mathrm{HL}+\mathrm{CD}$) and two double-loop cycles (2 $\mathrm{HL}+\mathrm{CD}$). The latter quantities are given by Eqs. (4) and (6) for the HL and $\mathrm{HL}+\mathrm{CD}$ geometries, respectively. Numerical data are calculated with parameters $L=4\mathrm{mm}$, $P_f=2500\mu \mathrm{m}/\mathrm{s}$, $n=3$. (b) Schematics of the nephron-inspired systems studied in (a).

Figure 4

Comparison of filtration efficiencies of various systems. We show power required versus water loss ratio for the different systems. The data points are from the analytical expressions of the text. Here, $2(\mathrm{HL}+\mathrm{CD})$ corresponds to two successive $\mathrm{HL}+\mathrm{CD}$ cycles, with the addition of osmotic activator in between the two cycles. Thermo corresponds to the minimal energy required to achieve a separation defined by a given water loss ratio. The nephron working conditions correspond to $\eta \approx 0.01$. Inset: Sketch of corresponding systems. Here, HL is for a single $U$-loop, $\mathrm{HL}+\mathrm{CD}$ is a double loop, SL is a single limb, and PDF is for pressure-driven filtration. See text for detail.