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Small—but finite—fluid inertia can be leveraged to generate steady flows out of liquid vibrations around an immersed interface. In engineering, external high-frequency drivers $\left({10}^2\text{–}{10}^5\mathrm{Hz}\right)$allow this inertial rectification phenomenon, known as viscous streaming, to be employed in micron-scale devices for precise flow control, particle manipulation, and spatially controlled chemistry. However, beyond artificial settings, streaming has been hypothesized to be accessible by larger-scale biological systems pertaining to lower frequencies. Then millimeter-size organisms that oscillate or pulsate cilia and appendages in the 1 to $10\mathrm{Hz}$range may be able to rectify surrounding flows, for feeding or locomotion, removing the need for external actuators, tethers, or tubing. Motivated by this potential for bio-hybrid robotic applications and biophysical exploration, here we demonstrate an living system able to produce streaming flows endogenously, autonomously, and unassisted. Computationally informed, our biological device generates oscillatory flows through the cyclic contractions of an engineered muscle tissue, shaped in the form of a torus and suspended in fluid within a microparticle image velocimetry setup. Flow patterns consistent with streaming simulations are observed for low-frequency muscle contractions $(2–4\mathrm{Hz})$, either spontaneous or light-induced, illustrating system autonomy and controllability, respectively. Thus, by connecting tissue engineering with hydrodynamics, this work provides experimental evidence of biologically powered streaming in untethered, millimeter-scale living systems, endowing bio-hybrid technology with inertial microfluidic capabilities. It also illustrates the potential of combining bio-hybrid platforms and simulations to advance both biophysical understanding and fluid mechanics. Published by the American Physical Society2025 

Viscous streaming is an efficient rectification mechanism to exploit flow inertia at small scales for fluid and particle manipulation. It typically entails a fluid vibrating around an immersed solid feature that, by concentrating stresses, modulates the emergence of steady flows of useful topology. Motivated by its relevance in biological and artificial settings characterized by soft materials, recent studies have theoretically elucidated, in two dimensions, the impact of body elasticity on streaming flows. Here, we generalize those findings to three dimensions, via the minimal case of an immersed soft sphere. We first improve existing solutions for the rigid-sphere limit, by considering previously unaccounted terms. We then enable body compliance, exposing a three-dimensional, elastic streaming process available even in Stokes flows. Such effect, consistent with two-dimensional analyses but analytically distinct, is validated against direct numerical simulations and shown to translate to bodies of complex geometry and topology, paving the way for advanced forms of flow control.