Valveless Microfluidic Pumps Get Their Flow From Nonlinearity, Simulations Reveal

A valveless pump small enough to sit on a laboratory chip does not push fluid with any internal moving part. Instead, it relies on repeatedly squeezing a flexible membrane at an off-center spot, letting waves ripple along the elastic wall and somehow conspire to drive fluid steadily in one direction. For more than two decades, researchers have disagreed about exactly how that happens, with some attributing the net flow to wave dynamics and resonance and others insisting that nonlinearity is indispensable. A new computational study published in Annals of Biomedical Engineering by Dikla Kesner, Moshe Rosenfeld, and Sara Naftali now untangles these explanations. Using a large set of three-dimensional fluid-structure interaction simulations of a membrane-actuated rectangular channel, the authors report three linked findings: nonlinear steady streaming directly generates the net flow rate, resonance and wave dynamics amplify velocity oscillations but do not by themselves create net flow, and optimal actuator placement must align with standing-wave antinodes, a criterion they identify as not previously recognized.

The device simulated is a compact rectangular channel, 50 millimeters long, 10 millimeters wide, and 1.5 millimeters high, with a 40-millimeter latex membrane, 0.25 millimeters thick, covering the top. Repeated pinching was modeled as a time-dependent pressure applied over a 2-millimeter patch of the membrane, with a sinusoidal-like waveform of roughly 50 percent duty cycle. The simulations solved the time-dependent, laminar, incompressible Navier-Stokes equations coupled two-way with nonlinear large-deformation membrane equations, in contrast to most earlier computational studies that used one-dimensional approximations with a simplified relation between cross-sectional area and pressure. The small scale of the model placed the flow in a low-Reynolds-number, high-Womersley-number regime, a combination the authors describe as previously under-explored and directly relevant to lab-on-chip and organ-on-chip platforms, where planar membrane-actuated channels are commonly fabricated.

Two representative cases illustrate the mechanism at work. Pinching at 3.7 hertz produced a propagating wave on the membrane and a net flow rate of only 0.5 milliliters per minute, while pinching at 53 hertz produced an approximately standing-wave pattern and a net flow of 2.45 milliliters per minute, roughly five times larger. In both cases the mean velocity was an order of magnitude smaller than the root-mean-square oscillatory velocity, indicating a highly pulsating flow field in which most of the invested energy ends up as oscillation rather than net transport. Maximum instantaneous flow rates reached 20 to 30 milliliters per minute, more than one order of magnitude above the net values. In the standing-wave case, the inlet and outlet flow rates oscillated approximately in phase, whereas the propagating-wave case showed them roughly in antiphase.

The dependence of net flow on pinching frequency was strongly non-monotonic. Peaks appeared near harmonics of the system’s natural frequency of about 4.1 hertz, at pinching frequencies of approximately 12, 19, 25, 32, 37, 54, and 69 hertz, and small shifts could matter enormously: raising the frequency from 54.5 to 55 hertz dropped the net flow from 2.77 to 0.80 milliliters per minute. Large net flow generally coincided with a standing-wave pattern, consistent with resonant operation. One case, however, broke the rule. At 19 hertz, far from resonance, a propagating wave nonetheless delivered a large net flow because the imposed pressure waveform happened to synchronize constructively with the local membrane motion, allowing efficient energy transfer. Resonance, the authors conclude, is advantageous but not essential.

Direct evidence for the role of nonlinearity came from varying the Reynolds number by changing the fluid viscosity. At the standard case, corresponding to a mean Reynolds number near 5, the net flow was modest. When the Reynolds number was increased tenfold, the net flow rose substantially at most frequencies and even reversed sign in some cases. Sweeping the Reynolds number at 53 hertz produced a monotonic increase: at one-hundredth of the standard value, in a viscous-dominated, nearly linear flow, the net flow essentially vanished, while at one hundred times the standard value it was almost three times larger. These results support the interpretation that the nonlinear convective terms of the Navier-Stokes equations rectify the oscillatory motion into a steady mean flow, a mechanism known as steady streaming.

An energy analysis reinforced this conclusion quantitatively. Because the inlet and outlet were held at zero gauge pressure, all actuator work was converted into fluid kinetic energy, membrane elastic energy, and dissipation. The simulations showed that positive power delivery requires the applied pressure to act in phase with the membrane moving toward the opposite wall at the actuator patch. Plotting the net flow rate against the work delivered per second across many cases differing in frequency, strength, actuator location, and two-pincher phase angle revealed an approximately monotonic relationship, which the authors present as direct quantitative support for the nonlinear rectification mechanism. The relatively long duty cycle of about 0.5 made tight synchronization difficult, which helps explain why even the best cases here yielded comparatively small net flows; earlier studies using duty cycles below 0.2 achieved easier synchronization.

The antinode placement rule is the study’s most actionable contribution. For the 53-hertz case, three full wavelengths spanned the membrane, placing antinodes in the actuated half at positions of roughly 0.08, 0.25, and 0.42 of the membrane length. Sweeping a single actuator along the channel showed peaks in net flow where an antinode developed near the actuated region and substantially smaller values where a nodal region sat beneath it. The logic is that an antinode offers large membrane displacement and velocity, maximizing the work transferred from the applied pressure into the coupled system. This criterion reconciles earlier observations: in most prior studies, pinching near the second natural frequency produced a single antinode at 0.25 of the membrane length, exactly where maximum net flow was reported.

Multi-actuator results add nuance to the assumption that more actuators mean more pumping. With two actuators, each driven at half the original pressure amplitude and phased at roughly 180 degrees plus or minus 30 degrees, the standing-wave pattern was preserved and the net flow rose slightly to 2.65 milliliters per minute, a fourfold gain in net flow per actuator compared with a single actuator at the reduced amplitude. At most other phase angles, however, the standing pattern was destroyed and net flow was low. Configurations with three or four equally spaced actuators, driven with a constant phase delay, failed to maintain a standing-wave pattern in any case tested, so the two-actuator arrangement was the most effective improvement within the studied set. The benefit depends on reinforcing the global membrane-wave response, not on the actuator count alone.

The authors frame their conclusions with clear scope limits. The pressure-actuated membrane patch differs from the rigid, contact-based pinchers used in many experiments, though the authors note it reproduces essential phenomena seen in studies with physical pinchers. Zero-pressure-drop boundaries mean the analysis addresses free-delivery operation rather than pumping against a load, and the framework cannot predict the direction of the resulting net flow. The rectangular geometry may introduce corner-related wave reflections absent in circular tubes, although qualitative agreement with prior tubular studies suggests these effects are secondary. Within those limits, the study reconciles the wave-based and nonlinearity-based camps: significant net flow can occur even off resonance because nonlinearity alone generates it, while resonance typically maximizes flow by amplifying the oscillations that undergo nonlinear rectification. The antinode criterion, the synchronization requirement, and the emphasis on delivered work together offer microfluidic engineers a coherent qualitative foundation for designing valveless, membrane-driven pumps for lab-on-chip and organ-on-chip devices.

Subject of Research: Mechanisms of valveless net flow generation in membrane-actuated microfluidic impedance pumps

Article Title: Nonlinear Flow Generation in Microfluidic Impedance Pumps

Article References: Kesner, D., Rosenfeld, M., & Naftali, S. (2026). Nonlinear Flow Generation in Microfluidic Impedance Pumps. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04402-4

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04402-4

Keywords: impedance pump, microfluidics, steady streaming, resonance, fluid-structure interaction, valveless pumping, lab-on-chip, organ-on-chip, standing waves, Liebau pump, net flow rate, membrane actuation