All-aqueous printing of viscoelastic droplets in yield-stress fluids

Abstract

All-aqueous printing of viscoelastic droplets (aaPVD) in yield-stress fluids is the core of an emerging voxelated bioprinting technology that enables the digital assembly of spherical bio-ink particles (DASP) to create functional tissue mimics. However, the mechanism of aaPVD is largely unknown. Here, by quantifying the dynamics of the whole printing process in real-time, we identify two parameters critical to aaPVD: (1) acceleration of print nozzle, and (2) droplet/nozzle diameter ratio. Moreover, we distinguish three stages associated with aaPVD: droplet generation, detachment, and relaxation. To generate a droplet of good roundness, the ink should be a highly viscous shear-thinning fluid. Using particle image velocimetry and scaling theory, we establish a universal description for the droplet displacements at various printing conditions. Along the direction of nozzle movement, the droplet displacement is determined by the detachment number, a dimensionless parameter defined as the ratio between the dragging force from the nozzle and the confinement force from the supporting matrix. Perpendicular to the direction of nozzle movement, the droplet displacement is determined by the Oldroyd number, a dimensionless parameter that describes the yielded area of the supporting matrix near the print nozzle. For a relaxed droplet, the droplet tail length is independent of droplet/nozzle diameter ratio but determined by the nozzle acceleration. We conclude that printing droplets of good fidelity requires a relatively large droplet/nozzle diameter ratio and intermediate nozzle accelerations. These ensure that the droplet is more solid-like to not flow with the nozzle to form a tadpole-like morphology and that the confinement force from the yield-stress fluid is large enough to prevent large droplet displacement. Our results provide the knowledge and tools for in situ generating and depositing highly viscoelastic droplets of good roundness at prescribed locations in 3D space, which help establish the foundational science for voxelated bioprinting. Statement of significance: Analogues of pixels to two-dimensional (2D) pictures, voxels – in the form of small cubes or spheres – are the basic units of three-dimensional (3D) objects. All-aqueous printing of viscoelastic droplets (aaPVD) is the core of voxelated bioprinting, an emerging technology that uses spherical bio-ink voxels as building blocks to create 3D tissue mimics. Unlike existing technologies relying on the classic Rayleigh-Plateau instability to generate droplets, aaPVD exploits previously unexplored nonlinear fluid dynamics of complex fluids to precisely manipulate viscoelastic droplets in 3D space. The developed knowledge and tools not only help advance biomanufacturing but also stimulate new research directions in soft matter and complex fluids.