We considered pattern formation, i.e. viscous fingering, in the ink splitting process between an elastic flexographic printing plate and the substrate. We observed an unexpected scaling behavior of the emerging pattern length scale (i.e., finger width) as a function of printing velocity, fluid viscosity, surface tension, and plate elasticity coefficients. Scaling exponents depended on the ratio of the capillary number of the fluid flow, and the elastocapillary number defined by plate elasticity and surface tension. The exponents significantly differed from rigid printing plates, which depend on the capillary number only. A dynamic model is proposed to predict the scaling exponents. The results indicate that flexo printing corresponded to a self-regulating dynamical equilibrium of viscous, capillary, and elastic forces. We argue that these forces stabilize the process conditions in a flexo printing unit over a wide range of printing velocities, ink viscosities, and mechanical process settings.
Mammalian tissue comprises a plethora of hierarchically organized channel networks that serve as routes for the exchange of liquids, nutrients, bio-chemical cues or electrical signals, such as blood vessels, nerve fibers, or lymphatic conduits. Despite differences in function and size, the networks exhibit a similar, highly branched morphology with dendritic extensions. Mimicking such hierarchical networks represents a milestone in the biofabrication of tissues and organs. Work to date has focused primarily on the replication of the vasculature. Despite initial progress, reproducing such structures across scales and increasing biofabrication efficiency remain a challenge. In this work, we present a new biofabrication method that takes advantage of the viscous fingering phenomenon. Using flexographic printing, highly branched, inter-connective channel structures with stochastic, biomimetic distribution and dendritic extensions can be fabricated with unprecedented efficiency. Using gelatin (5%–35%) as resolvable sacrificial material, the feasability of the proposed method is demonstrated on the example of a vascular network. By selectively adjusting the printing velocity (0.2–1.5 m s−1), the anilox roller dip volume (4.5–24 ml m−2) as well as the shear viscosity of the printing material used (10–900 mPas), the width of the structures produced (30–400 µm) as well as their distance (200–600 µm) can be specifically determined. In addition to the flexible morphology, the high scalability (2500–25 000 mm2) and speed (1.5 m s−1) of the biofabrication process represents an important unique selling point. Printing parameters and hydrogel formulations are investigated and tuned towards a process window for controlled fabrication of channels that mimic the morphology of small blood vessels and capillaries. Subsequently, the resolvable structures were casted in a hydrogel matrix enabling bulk environments with integrated channels. The perfusability of the branched, inter-connective structures was successfully demonstrated. The fabricated networks hold great potential to enable nutrient supply in thick vascularized tissues or perfused organ-on-a-chip systems. In the future, the concept can be further optimized and expanded towards large-scale and cost-efficient biofabrication of vascular, lymphatic or neural networks for tissue engineering and regenerative medicine.
We use deep learning (DL) algorithms for the phenomenological classification of Saffman-Taylor-instability-driven spontaneous pattern formation at the liquid meniscus in the fluid splitting in a gravure printing press. The DL algorithms are applied to high-speed video recordings of the fluid splitting process between the rotating gravure cylinder and the co-moving planar target substrate. Depending on rotation velocity or printing velocity and gravure raster of the engraved printing cylinder, a variety of transient liquid wetting patterns, e.g., a raster of separate drops, viscous fingers, or more complex, branched liquid bridges appear in the printing nip. We discuss how these patterns are classified with DL methods, and how this could serve the identification of different hydrodynamic flow regimes in the nip, e.g., point or lamella splitting.
Numerical simulation of the fluid flow in the gravure printing nip, based on a discontinuous Galerkin (DG) algorithm, is used to study the fluid-splitting process, the transition between point and lamella splitting. We study the pressure and shear singularities at the contact point of printing cylinder and substrate as a function of the variable microscopic residual gap and variations of the printing fluid quantities introduced to the nip. As the hydrodynamic boundary value problem is ill-defined by the nip singularity, we enhance the simulation using renormalization group and algebraic scaling techniques in order to obtain a numerically stable and physically meaningful prediction. Our simulations are compared to analytical results from lubrication theory, and to experimental observations on a gravure press.
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