Can a sub-millimetre robot copy the jet propulsion of squids and octopuses without copying their soft anatomy? The authors 3D-print, by direct laser writing, CeFlowBot: a ~420 × 500 µm two-lobed body with six tilted cylindrical cavities (L = 100 µm) that trap air bubbles and flank an open inner channel. Under sound the bubbles vibrate and drive acoustic streaming that pumps fluid from the wide inlet to the tapered outlet; a 2D simulation and tracer-particle experiments agree on this flow. Measured speeds peak near 1.9 mm/s at about 40.5 kHz (80 Vpp drive) and rise steeply with drive voltage. A

Small · 2022 · University of Twente

Could a robot half a millimetre long swim through liquid, drop off a cargo where it is needed, and be followed where no camera can see? Meet CeFlowBot . It has no motor and no moving parts, only six trapped air bubbles.

Play the right note and it comes alive. Drag the frequency dial and watch the tracer particles.

Then scroll to find out why it works, and what the team built next

Speeds are the authors' measurements at an 80 V drive (Fig. 2d, read from the published plot). The swirling flow is a simplified teaching model of the pattern they simulated and filmed.

01 · The inspiration

Nature's jet engine

Squid, octopus and cuttlefish swim by jet propulsion. They draw water into a cavity inside the body, then squeeze it out through a narrow funnel, the siphon. The jet shoots backwards, and the animal shoots forwards.

Their bodies are springy. After each squeeze the elastic mantle bounces back by itself, like a mass on a spring with its own natural rhythm. The researchers cite this spring-like behaviour as their starting point. Pump in step with the spring, and each squeeze is large for little effort.

Change the squeeze rhythm. When does the squid travel fastest?

The problem with copying a squid

Engineers have built squid-like robots at the centimetre scale from cast silicone, 3D prints, shape-memory alloys and stretchy membranes. Shrinking that anatomy to a fraction of a millimetre is another matter. Tiny moving parts need complicated, multi-step and expensive fabrication.

So the team asked a different question: can a robot copy what the squid does, pumping water through itself, without copying how its body is built? Copy the pump, not the anatomy.

How small is half a millimetre?

Shapes drawn to the same scale: 1 px ≈ 10 µm.

02 · The spring

A bubble is a spring

CeFlowBot is 3D-printed with a laser, coated with metal, then treated so that its surfaces repel water. When it is dipped in liquid, each of its six pockets (100 µm long and 40 µm wide) traps a small air bubble straight away.

Air is squishy, so a trapped bubble acts like a spring. The short plug of water in the pocket's open end is the mass that the spring pushes back and forth. Like any mass on a spring, the pair has a natural note. Sound at that pitch makes it wobble hard. At other pitches it barely moves.

Predict first, then slide the bubble length and drive frequency.

Predict If the bubble fills more of its pocket (50 → 90 µm), will its natural note go up or down?

Challenge: the real robot swam fastest at 40.5 kHz. Find the bubble length whose natural note matches it. How full are the pockets?

03 · The pump

Six bubbles make a pump

A wobbling bubble pushes water back and forth tens of thousands of times a second. You might expect that to average out to nothing, but it doesn't. Near the wobbling surface, the to-and-fro motion leaves behind a slow, steady swirl: a pair of counter-rotating eddies that push water away from the bubble. Physicists call this acoustic streaming .

CeFlowBot's trick is the arrangement. Its six pockets face each other across an open channel, each tilted 45° toward the tail. Their streaming all pushes the same way, so together they draw water in through the wide front and squirt it out of the tapered tail. It is the squid's pump, made of bubbles.

Tap bubbles to dissolve them. How many can the robot lose? Then try a single-bubble robot.

In this model, flow scales with the number of working bubbles. The paper reports, qualitatively, that CeFlowBot keeps working when a few bubbles dissolve during experiments.

Real device A printed CeFlowBot under the microscope. Scale bar 100 µm. Fig. 1c.

All six bubbles are ringing. Watch the tracers get drawn in at the front and shot out of the tail.

04 · Steering and delivery

Point it with a magnet

Sound gives CeFlowBot thrust but no sense of direction. For steering, the team coated the robot with a 240 nm film of nickel, topped with 50 nm of gold to stop it corroding. Nickel turns magnetic in a field, so a weak, uniform field from two electromagnets turns the robot like a compass needle while the sound pushes it along.

Fields of 1–2 millitesla nudged the robot but did not reliably line it up. From about 4 mT it aligned readily. At 4 mT the authors steered it through the letters S, R and L, for Surgical Robotics Laboratory.

The volume dial matters too. Raising the drive voltage (louder sound) took the speed from about 90 µm/s at 20 V to about 1,500 µm/s at 160 V. The same dial lets the robot grab things. At low power, the bubbles' pull and the inflow draw a nearby object into the channel mouth. At 100 V the object is pushed toward the exit, and at 160 V it is let go as the robot speeds off.

Mission: deliver the star to the ring.

Turn the sound on and point the magnet at the star

Approach gently (≤ 80 V) to grab it

Steer to the dashed ring

Crank to 160 V to push it out and let go

Turn the sound up and point the magnet toward the star.

Speeds follow the measured power sweep (Fig. 3a, 41 kHz, real time). Weak fields (1–2 mT) do not align the robot reliably, as reported. Grab at low power, push at 100 V and release at 160 V follow the demonstration in Fig. 4. Carrying the star over a distance is a game simplification.

05 · Seeing it

Seeing it where cameras can't

Inside a body there is no window for a microscope. Doctors look inside with ultrasound: a probe sends out pulses of very high-pitched sound and listens for the echoes. An ultrasound image can't show details much smaller than the wavelength of the sound it uses.

Earlier bubble robots relied on a single bubble, roughly 10–100 µm across, which is hard to make out with common scanners working at 1–10 MHz. CeFlowBot's bubbles are just as small, but together they make a body about half a millimetre across. With a 600 µm, eight-pocket version and a 14 MHz probe (wavelength ≈ 105 µm), the authors followed it on the ultrasound screen as it travelled 4–5 body lengths, matching the optical camera.

Raise the imaging frequency, swap robots, and hide the robot behind tissue.

06 · The evidence

What the experiments showed

CeFlowBots were 3D-printed by direct laser writing, coated with nickel and gold, and treated to repel water, so that bubbles are trapped the moment the robot is immersed. They were then tested in salt solution on a glass plate above a ring-shaped piezoelectric transducer, between two electromagnets.

The simulation and tracer experiment agree. Water enters the wide inlet, runs down the inner channel and leaves the tapered outlet as a double-lobed jet. Fig. 2a,b.

Top speed at an 80 V drive, nearly four body lengths per second. Half a kilohertz away, speeds fall to a few hundred µm/s or less. Fig. 2d.

At 41 kHz, speed climbs steeply as the drive rises from 20 to 160 V. Fig. 3a.

Steered along letter-shaped paths with a 4 mT field, showing the fine direction control that winding channels or blood-vessel-like paths would demand. Fig. 3b.

A 450 µm star is drawn in at low power, pushed to the exit at 100 V and let go at 160 V. Fig. 4.

Tracked with a submerged ultrasound probe over 4–5 body lengths, in agreement with the optical camera. Fig. 5.

07 · What came next

Eighteen bubbles, all the way round

CeFlowBot's paper ended with a wish list. Arrange the bubble pockets in a ring around the channel. Use the tapered channel as a sieve. Build bigger, easier-to-handle robots out of many small bubbles. In 2023, members of the same team and new collaborators published a follow-up in Advanced Intelligent Systems that took up these ideas.

The recipe is easy to say. Take CeFlowBot's row of three tilted pockets and repeat it all the way round the central channel. Six rows of three make 18 bubbles , every pocket still tilted 45° toward the narrow end, with three rings holding the rows together. The robot measures about half a millimetre in every direction, nearly big enough to see with the naked eye.

The team calls the design metamaterial-inspired . Acoustic metamaterials are built from many identical tiny units, and in large arrays of bubbles the swirls of neighbouring bubbles add up into a stronger flow. Does that work inside a robot?

Predict, then wrap four more rows of pockets round the channel. Drag the robot to turn it.

Predict Both robots get the same sound (65 kHz, 20 V). With three times as many bubbles, how much faster does water rush in at the robot's mouth?

Curves traced from the published plot (Fig. 5c) and scaled so the 6-bubble peak is 1. The ≈ 4.4× total comes from the integrated inflow the paper reports for each robot (6.98 × 10−3 and 3.06 × 10−2). Both robots were filmed under the same drive; the speeds were measured from tracer particles with particle image velocimetry.

A lip that holds the bubble in

CeFlowBot kept its bubbles by being treated to repel water. The sequel's authors point out a catch: the whole robot becomes water-repellent, so it is harder to submerge, and air can cling in unwanted places. Their fix needs no coating at all. Each pocket mouth gets a small inward lip, a re-entrant edge , that pins the bubble's surface in place.

How big should the lip be? A narrower doorway holds the bubble longer. But the bubble can only wobble through the opening, and the wobble is what drives the streaming.

Choose the doorway, then run the sound for longer. Which opening would you build?

Wobble per kPa of sound pressure read from Fig. 3b (61 kHz, approximate). Dissolving start times from the authors' time-lapse (Fig. 3c, 67 kHz, about 20 kPa). How quickly the bubble shrinks after that is illustrative.

A new note, and a new trick

Different bubbles ring at a different note. The sequel's pockets are 100 µm long, 40 µm across and full of air. Filmed with a high-speed camera at 500,000 frames per second, a single bubble's surface swung furthest, about 5 µm, near 62 kHz. The sound came from a transducer dipped into a water tank about 4.5 cm from the robot, never touching the dish.

On the whole robot, streaming was strongest at 67 and 77 kHz. Then came something new. Near 67 kHz, the robot's own inflow sucked it upright: it stood on its wide end and began to hover around the dish, at a sound pressure of only about 50 kPa. Standing up, it pulled nearby debris in from every direction and shot it out of its narrow end, up and away from the floor.

Find the note that stands the robot up, then pick what it should clean up.

Dotted marks: 67 and 77 kHz, where the whole robot streamed hardest.

Frequencies and behaviours follow the paper: streaming across 60–90 kHz, standing up at 65–70 kHz (most consistently at 67), hovering, higher wobble modes above about 80 kHz and bubble surfaces coming loose above 90 kHz. The hovering path, catch distance and debris counts are a teaching model. The team also showed that a thin nickel coating lets a magnet steer the robot and fetch it back.

Go back to the bubble lab in chapter 02 and push the bubble length toward 100 µm. The note shoots up, because the water plug, the mass on the spring, shrinks toward nothing. Equation 1 cannot describe a pocket that is completely full of air, which is exactly what the sequel's pockets hold.

So the team used a fuller model of a gas-filled cavity that also includes the pocket's radius (20 µm) and the surface tension of water. For a fully air-filled 100 µm pocket it predicts 73 kHz . The high-speed camera measured the strongest wobble near 62 kHz , about 15% lower. The authors put the gap down to the real pocket's shape, neighbouring bubbles and the curve of the bubble surface. They also divided each wobble by the sound pressure actually delivered at that frequency, so the transducer's own preferences would not masquerade as the bubble's note.

08 · Back to the question

What one note brings closer

We began by asking whether a half-millimetre robot could swim, deliver a cargo to a chosen spot, and be seen where cameras can't. In a laboratory dish, CeFlowBot did all three. It swam on sound, steered by magnet, grabbed and released a star-shaped object, and showed up on ultrasound.

The central idea is to use many small bubbles instead of one . The robot is big enough to see and handle, yet driven by bubbles small enough to ring fast and stir strong local flows. It also keeps going if a few bubbles dissolve.

The sequel pushed that idea further. Tripling the bubbles to 18 pulled in about four times as much water under the same drive. A small lip at each pocket mouth helped hold the bubbles in without any coating, and the robot showed a new trick: standing up, hovering and clearing debris such as dead cells.

CeFlowBot's wish list, a year on

Into 3-D Built in 2023 Arrays arranged in a ring around the channel. The 18-bubble robot stands up and hovers; the authors suggest adding CeFlowBot's magnetic steering to direct it.

A micro-sieve Demonstrated The tapered channel used to collect nearby particles. The sequel pulled in particle debris, dead HeLa cells and 200 µm cell spheroids. Sorting particles is still to come.

Bigger, modular Part-way Larger robots carrying many bubble arrays, each with its own job. The sequel's robot is about half a millimetre in every direction and easy to handle; arrays with separate jobs remain an idea.

Toward the clinic Steps taken Handling living cells once viability is confirmed, and navigating tissue under ultrasound guidance, toward uses like targeted drug delivery. The sequel drove its robot from a transducer dipped into a tank, never touching the dish, and worked with dead cells.

And the sequel's own next steps

More than 18 bubbles, to see whether the flow keeps growing. Pockets of different lengths and openings in one robot, so bubbles ringing at different notes could give it several modes of operation. Add-on units to collect, filter or sort particles.

Source

Sumit Mohanty, Aniruddha Paul, Pedro M. Matos, Jiena Zhang, Jakub Sikorski & Sarthak Misra. “CeFlowBot: A Biomimetic Flow-Driven Microrobot that Navigates under Magneto-Acoustic Fields.” Small 18(9), 2105829 (2022). doi:10.1002/smll.202105829 · article page

Figures are reproduced from the article, © 2021 The Authors, published by Wiley-VCH GmbH under a Creative Commons Attribution 4.0 licence. They have been cropped and colour-converted for this page.

Speed values in the interactive panels were read from the published plots (Fig. 2d and Fig. 3a) and are approximate. The flow patterns, squid, bubble-wobble, game and ultrasound panels are simplified teaching models, not the authors' simulations.

Follow-up work (chapter 07)

Sumit Mohanty, Yu-Hsiang Lin, Aniruddha Paul, Martin R. P. van den Broek, Tim Segers & Sarthak Misra. “Acoustically Actuated Flow in Microrobots Powered by Axisymmetric Resonant Bubbles.” Advanced Intelligent Systems 6(1), 2300465 (2024; published online 2023). doi:10.1002/aisy.202300465

Follow-up figures are reproduced from that article, © 2023 The Authors, published by Wiley-VCH GmbH under a Creative Commons Attribution 4.0 licence, and cropped for this page. Inflow profiles (Fig. 5c), bubble wobble (Fig. 2e) and pocket wobble (Fig. 3b) were read from the published plots and are approximate. The 3-D robot, tracers, doorway animation and clean-up panel are simplified teaching models.