Effect of 3D-bioprinted droplet impact dynamics on a pre-printed soft hydrogel matrix

3D droplet-based bioprinting technology is an innovative and time-saving method to precisely generate cell laden 3D structures for multiple clinical and research applications. It is important that the printed droplet must impact so as to leave a single isolated drop, for high printing resolution and accuracy. Therefore, understanding the criteria that control spreading behaviour and prevent droplet splashing is of great importance in optimizing the printing performance. In this experimental work, the physics of the impact of bioink droplets on a pre-printed soft hydrogel matrix was investigated. The droplet size, velocity, and input cell density were varied to generate a range of droplet impact behaviours. It has been shown that the soft substrate inhibited the droplet spreading after impact. The deposition/splashing boundary on the dry/wet flat surface (Nunclon TM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\text{TM}}$$\end{document} Delta surface-treated plastic) was defined by K=We0.5Re0.25=86.19\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K = {\text{We}}^{0.5} {\text{Re}} ^{0.25} = 86.19$$\end{document}. The splashing threshold on the soft hydrogel matrix was defined by K=44.78\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K = 44.78$$\end{document} and L=WeRe-0.4=13.85\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = {\text{We}} {\text{Re}}^{-0.4} = 13.85$$\end{document} for both blank and cell-laden inks on dry/wet soft substrates. Beyond this threshold, the printed droplet volume will be much lower than the expected volume due to splashing, leading to poor printing performance. The absolute splashing threshold on the dry/wet soft hydrogel matrix was defined by K=73.41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K = 73.41$$\end{document} and L=27.36\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = 27.36$$\end{document}. The printed 3D cell-laden structures were also presented to illustrate how the impact behaviours influence the possible printing fidelity and structure integrity.


Introduction
Three-dimensional (3D) bioprinting is an innovative technology for the fabrication of artificial tissues and organs. Functional biological 3D structures are formed by depositing biological materials, biochemicals and living cells, layer-by-layer, from the bottom up (Murphy , Atala 2014;Derakhshanfar et al. 2018;Chameettachal et al. 2019;Mobaraki et al. 2020;Vanaei et al. 2021).
The essential idea for droplet-based 3D bioprinting is to print bioink droplets with precise control to create 3D structures on the substrate (Murphy , Atala 2014;Liu and Derby 2019;Mobaraki et al. 2020;Vanaei et al. 2021). The first step in the process is to manufacture bioink with defined fluid properties for successful droplet printability. The biomaterials must be printed onto a substrate or a previously printed solidified layer and undergo a phase transition: becoming a solid deposit and forming the desired structural features. To produce 3D structures, the deposition and solidification processes must be repeated (Derby 2010;Gong et al. 2020).
Ultimately, droplet-based bioprinting requires the precise control of the printed pattern and shape. Thus, understanding the impingement of a droplet onto a solid surface, or previously deposited material, is crucial as it provide insights regrading printing resolution and structural integrity (Gudapati et al. 2016;Gong et al. 2020). The two major impingement characteristics are the spreading and splashing of the droplet. For the former, the droplet spreads over the impact surface due to its kinetic energy and surface energy interactions between the droplet and the substrate. This consequently affects the bioprinting resolution. For high initial droplet kinetic energy, the droplet is not fully captured by the impact substrate; the droplet breaks into secondary droplets after collision, which is caused splashing (Yarin 2006;Derby 2010;Gudapati et al. 2016;. Splashing of the droplet results in displacement of the deposited biomaterial from the ideal position and may also cause structural failure or cross-contamination in 3D bioprinting (Derby 2010;Gudapati et al. 2016).
The dynamics of liquid droplet impingement onto a surface, is mainly influenced by the bioink and substrate properties, and impact velocity (Mao et al. 1997;Yarin 2006;Gudapati et al. 2016;. The maximum droplet spread and critical conditions for splashing are characterized by two non-dimensional parameters. The Reynolds number, Re, and the Weber number, We, defined as: where , v, , and are the fluid density, impact velocity, dynamic viscosity, and surface tension, respectively; D is the characteristic length, here taken as the initial droplet diameter D o . Mao et al. found that the maximum spread of a droplet upon impact depends strongly on the liquid viscosity and the impact velocity on solid substrates. The maximum spread increases with an increase in the Reynolds number and the Weber number (Mao et al. 1997). Derby (Derby 2010) has summarized that the threshold for the onset of splashing on flat, smooth surfaces is K = We 0.5 Re 0.25 > 50 . On wet, flat surfaces, Weiss and Yarin (Weiss and Yarin 1999) have found that the threshold of splashing with a crown shape is We ≫ 40 . Most of the previous works consider a relatively small Weber number to reduce or eliminate the splashing on dry/wet flat surfaces (Weiss and Yarin 1999;Yarin 2006;Howland et al. 2016;Gudapati et al. 2016;Li et al. 2020). Ng et al. (Ng et al. 2022) printed cell-laden droplets directly onto a pre-printed thin liquid film using an inkjet-based 3D bioprinter and found a splashing threshold of We 0.5 Re 0.17 = 63 . Moreover, the increase in input cell density helps to mitigate droplet splashing and improve the printing fidelity (Ng et al. 2022).
In 3D bioprinting, the previously printed layer can be viewed as a soft elastic substrate. The dynamics of droplets impinging on soft substrates is different from the case of flat surfaces. Howland et al. (Howland et al. 2016) found that the additional energy dissipation due to surface deformation during droplet impact on soft surfaces can reduce or even suppress splashing with Weber number lower than 300. Basso and Bostwick (Basso and Bostwick 2020) studied water and ethanol drops impacting on soft elastic substrates with a large range of elasticities. They found that soft substrates inhibit droplet spreading after impact. The splashing threshold as defined by K = We 0.5 Re 0.25 , increases as the substrate elasticity decreases, indicating that it is harder to splash on soft substrates. For soft substrate with elasticity lower than 1 kPa, the splashing threshold is lower than 175. Kittel et al. (Kittel et al. 2018) described the deposition/splashing threshold on thin soft elastic surfaces as L = WeRe −0.4 = 16.8 . They also found that the threshold does not depend on the rheological properties of the deformable layer, by studying the impact phenomena of glycerinwater droplets on different thin viscoelastic surfaces.
Although an extensive effort has been devoted to understanding drop impingement on flat and thin soft surfaces tel et al. 2018), 3D-bioprinted droplet impact behaviour on pre-printed thick soft structures ( = h o ∕D o > 1 ) and the corresponding coupling mechanics of liquid-gel interaction still require further study. To fully understand the processes of 3D-bioprinted droplet deposition and fusion, hydrogel droplets were printed and chemically cross-linked using a commercial micro-valve-based 3D bioprinting platform (RASTRUM TM ), provided by Inventia Life Science Pty Ltd. 1 Hydrogels have been used extensively in droplet-based 3D bioprinting due to good printability, good cell compatibility, and capacity to mimick the extracellular matrix (ECM) environment for cellular activities (Gudapati et al. 2016;Hospodiuk et al. 2017;Chameettachal et al. 2019;Unagolla and Jayasuriya 2020;Li et al. 2020). Hydrogel droplets should solidify immediately after landing to help mechanically support the subsequent layer (Hospodiuk et al. 2017;Catros et al. 2011). Solidification occurs by cross-linking of polymer chains in an aqueous medium through various mechanisms such as physical entanglement, ionic interaction, and chemical cross-linking (Unagolla and Jayasuriya 2020). The bioprinting platform was previously reported for the high-throughput production of 3D cell spheroids, providing more invivo realistic models . Sodium alginate bioink and calcium chloride (CaCl 2 ) activator were firstly printed as a tissue-like matrix, which has the structural stability to support gravity-based cell spheroid formation. The tissue-like matrix also supports control over cell spheroid number, size, and shape so that statistically reliable data on drug responses can be obtained in the future (Utama et al. 2020). Four-arm poly(ethylene glycol) maleimide (PEG-4MAL) hydrogels and cell-containing bis-thiol-PEG crosslinker were alternately printed on the top of hydrogel matrix. The combination of matrix support, gravitational forces, and ECM secreted by cells-assisted cell migration, adhesion and proliferation during incubation, leading to cell spheroid formation (Utama et al. 2020. In this paper, the drop impingement on a pre-printed hydrogel matrix was studied. The effect of different bioprinter operating conditions, substrates, and input cell density on droplet impact dynamics were experimentally evaluated using a high-speed imaging system. The droplet impact on the pre-printed soft hydrogel matrix reflects the real impact process in 3D droplet-based bioprinting, considering the surface condition, thickness, and stiffness of the matrix generated from actual prints. The formed 3D cell spheroids were also presented under different conditions, potential improvements in printing fidelity and structural integrity are also discussed.

Ink preparation
Four commercially available ink solutions were used to produce the 3D cell spheroid assay and evaluate the droplet impact dynamics. The alginate bioink was formulated from sodium alginate in Milli-Q water and Dulbecco's buffered saline (DPBS). The hydrogel matrix can be fabricated by printing calcium chloride (CaCl 2 ) activator, a mixture of calcium chloride and Milli-Q water, onto the alginate solutions. The four-arm PEG-based bioink, as a linear polyether compound, was produced by mixing ethylene glycol with Milli-Q water. The corresponding bis-thiol activator, used as the cell-carrier ink during the 3D bioprinting process, contains short chain bis-thiol peptide cross-linker dissolved in DPBS. The actual sequence, concentration and formation process of the inks are proprietary to Inventia Life Science Pty Ltd. The ink solutions were stored at −20 • C. All solutions were sterilised by filtration through a 0.22 μ m syringe filter prior to use.
To study the effect of cells on droplet impact, the cellladen ink used in this study was obtained by suspending 1 × 10 7 cells/ml cell concentration in the blank bis-thiol activator. MCF-7 breast cancer cells were cultured in Dulbecco's minimum essential media (DMEM, Gibco Ⓡ , Australia) supplemented with 10% fetal bovine serum (FBS, Gibco Ⓡ , Australia) and 2% antibiotic-antimycotic (Gibco Ⓡ , Australia) at 37 • C and 5% CO 2 . Cells were screened and passaged every three days. The living cells were harvested from the flasks with initial cell counts achieved using a hemocytometer and the cell pallets with desired cell number were obtained after centrifuging. The blank ink (thiol-containing activator) was mixed with the cell pellets to make the final cell-laden bioinks with a cell density of 1 × 10 7 cells/ml. The cell concentration was checked using a hemocytometer before tests.
The mean fluid density was obtained following a method published by Liu, et al. (Liu and Derby 2019) 1 ml aliquots of the inks were extracted using a 1 ml adjustable-volume pipette and weighed by a laboratory balance. The liquid density was calculated from the measured volumes and weights. The mean liquid viscosity was measured using a vibro viscometer (SV-10A, A &D, Japan) at 25 • C. The pendant drop surface tension measurement technique (Arashiro and Demarquette 1999;Berry et al. 2015) was implemented in this study to measure the surface tension of the inks using a drop shape analyser (DSA30E, KRÜSS ) at 25 • C.

Bioprinting platform
The micro-valve-based 3D bioprinting platform incorporated a substrate stage, a fly-by printhead composed of multiple electromechanical valve dispensers, ink reservoirs, control panels, pressure regulators, a 0.01 m air filter, and a pneumatic back pressure supplier can be seen in Fig. 1i. To eject ink droplets, a constant pneumatic pressure was applied inside of the printing valve, and a step voltage pulse (Fig. 1ii) was applied to activated the electromechanical valve, generating a magnetic field that pulled the plunger upwards from the guarded orifice. Thus, the pressure is applied to the valve only when the valve is activated. This pressure overcomes the forces due ink viscosity and surface tension causing the ink solution to be ejected through the orifice (Gudapati et al. 2016;.
Dosing energy (La) is defined as the integral of the applied pneumatic pressure P(t) over valve opening time dt (Eq.(3)). This parameter has a positive correlation with the resulting droplet volume and velocity (Klinger et al. 2020;Chen et al. 2021;, and can be used to describe the bioprinter's operating condition. The basic unit for dosing energy is Laske (La).
All ink solutions were brought to room temperature prior to printing. The micro-valve-based 3D bioprinting platform was sterilised and rinsed with 70% Ethanol solution (left in the system for at least 20 min) and filtered deionized (DI) water. After sterilization, the sodium alginate bioink (Ink A), CaCl 2 activator (Ink B), PEG-4MAL bioink (Ink C), and bis-thiol activator (Ink D) were pipetted into respective reservoirs. To study the influence of cells on droplet impact, the bis-thiol activator was divided into a blank ink sample and a cell-laden sample with 1 × 10 7 cells/ml input cell concentration.
The bioprinting platform utilized a fly-by printing method using proprietary custom-made software. The dosing energies applied on the four valves were set separately. During fly-by printing, the printhead travelled on the x-axis at a constant velocity. The hydrogel matrix layer was printed first, by initially ejecting a row of sodium alginate bioink (Ink A) drops in one well of the Nunclon TM Delta surface 96-well plate (Sigma-Aldrich, Australia) as the printhead travels on the positive x-axis direction (Fig. 2i). The well plate was placed approximately 20 mm away from the valve orifice. On the return flight, CaCl 2 activator (Ink B) droplets were printed on top of the bioink droplets to initiate the hydrogel formation (Fig. 2ii). Upon contact, gelation occurred instantaneously forming 3D structures (Fig. 2iii). The process was repeated at different y locations until the target well was covered by a continuous hydrogel layer (Fig. 2iv).
A drop of PEG-4MAL bioink (Ink C) was printed at the desired location (Fig. 2v) which was quickly followed by printing a drop of blank or cell-laden bis-thiol activator (Ink D) at the same location to initiate the cross-linking process ( Fig. 2vi and vii). Variation of the size of the 3D-bioprinted hydrogel bead was achieved by altering the dosing energy. The formed 3D hydrogel structures match the mechanical and biochemical properties of different types of tissue, which can provide a physiologically relevant matrix environment for cultured cells Engel et al. 2022).
A dry, flat surface was used as a contrast substrate in this study. Ink C and Ink D were printed directly into the Nunclon TM Delta surface 96-well plate, which can be seen as a plastic surface undergoes Nunclon TM Delta surface treatment, without printing the gel substrate first.
(3) In this study, Ink A (sodium alginate bioink) and Ink B (CaCl 2 activator) were printed under constant dosing energies, aiming to achieve the same hydrogel substrate structure. To investigate the influence of operating conditions on droplet impact, eight sets of the bioprinter operating conditions were tested on Ink C (PEG-4MAL bioink), blank Ink D (bis-thiol activator), and cell-laden Ink D (bisthiol activator), with dosing energy ranging from 1.51 to 3.36 La.
At the completion of the printing process with cell-laden Ink D, 200 l DMEM supplemented with 10% FBS and 2% antibiotic-antimycotic was added manually in the well. The plate was then ready for incubation at 37 • C and 5% CO 2 and visualization of the printed 3D cell structures.

High-speed imaging system
The printing platform was imaged with a high-speed camera system, including a high-speed camera FASTCAM SA-X2 (Photron TM ), a macro lens (55 mm f/2.8, Nikon TM ), and 68 mm extension tubes (Kenko TM ) (Fig. 1i). And a LED illuminator is used for shadowgraphy droplets in-flight and the droplet impingement processes. The high-speed imaging system visualized the droplet impact dynamics in two directions separately: (1) Side view 1, where the camera was pointing at positive x-axis direction and the LED illuminator was pointing at negative x-axis direction and directly facing towards the lens; (2) Side view 2, where the camera was aimed = 20 • below the horizontal at positive y-axis direction to obtain clear images of the droplet spread upon impact. The LED illuminator in Side view 2 was facing towards the negative y-axis. Shadowgraph droplet images were recorded at 50,000 frames per second (fps) frame rate with 256 × 128 pixels image resolution. The resulting image height to pixel ratio (HTPR) was 15.5 m/pixel.
The impact of a droplet on a substrate consists four stages: initial, spreading, contracting and equilibrium (Mallinson et al. 2018) (Fig. 3). Droplet size and falling velocities in the initial stage before impact were analysed from the captured shadowgraph images using a custom image processing program in MATLAB Ⓡ 2018b as previously reported. The image processing program produces a clear droplet edge detection among the diffraction region in the shadowgraph images. The theory of droplet edge detection has been detailed in the previous study (Chen et al. 2021) and is not described here. After applying the edge detection method, the droplet was separated from the background with a clean edge. At the droplet image captured location (20 mm away from the orifice), the droplets coalesce into near spheres due to the effect of surface tension (Klinger et al. 2020) and function imfindcircles detects circular  (Kang et al. 2020). In this manner, the centre position and dimension D o of the droplet based on the assumption of sphericity were obtained directly using this function and the droplet falling velocity v o before impact was calculated using the change in droplet centroids positions between each pair of frame.
where Δz is the distance travelled in the vertical direction calculated from the positions of droplet centroids between consecutive images, Δt is the interval time between consecutive frames. The edge detection program could not be applied to the droplet impact images due to the low contrast between the hydrogel matrix and hydrogel droplet (as shown in Fig. 4i). Therefore, measurement of the droplet spreading diameter, equilibrium diameter, and equilibrium height was conducted manually using the open source program ImageJ with a ± 2 pixel error. The measurement error was used in the subsequent calculation for the deviation of equilibrium droplet volume (Eq. 6).
where the droplet equilibrium volume is assumed to be a spherical cap with height h, and radius a of the base circle of the cap.

Printed 3D cell structure visualization
To investigate the influence of printing conditions on the printed cell-laden 3D structure, bright field images were immediately obtained using an inverted microscope. The next step was to demonstrate the long-term proliferation profile of the printed cells. The printed cell-laden structures were cultured over a period of 7 days inside an incubator. The Hoechst 33342 fluorimetric assay (ThermoFisher, Australia) was used to demonstrate the proliferation profile of printed cells based on staining all cell nuclei (DNA) using a blue fluorescence dye, enabling visualisation of all cells. DPBS was placed in wells before the addition of the Hoechst 33342 fluorimetric assay in the ratio of 2000: 1. A live/dead assay ) was also performed using Calcein-AM (Biotium, USA) and Ethidium homodimer-III (Biotium, USA). Calcein-AM and Ethidium homodimer-III dilution with a ratio of 1: 2000 and 1: 1000 were added in the wells, followed by incubation at 37 • C for 30 min. Calcein-AM is internalised by viable cells and converted to calcein (a green flourescent compound) in the cell cytoplasm. Ethidium homodimer-III only enters dead cells and becomes a red fluorescent compound upon binding to DNA, therefore, the stained green cells represent viable cells, whereas the stained red cells represent dead cells. A fluorescent microscope was used to excite the Hoechst 33342 fluorimetric assay, Calcein-AM, and Ethidium homodimer-III at wavelength of 350, 488, and 594 nm, respectively, for the fluorescence imaging.

Droplet diameter and velocity before impact
To study the effects of dosing energy on droplet impact dynamics, high speed images of droplets just before impingement were captured and analysed to obtain the droplet diameter D o and falling velocity v o . PEG-4MAL bioink (Ink C), was the first to impact on the soft elastic hydrogel matrix, and it was ejected under eight dosing energies: 1. It was found that to achieve the optimum gelation result, the PEG-4MAL bioink and the bis-thiol activator should be printed at 1:1 ratio . At this ratio, the formed hydrogel can mechanically support the 3D structure without collapsing. In droplet ejection, more energy is needed for ink with higher physical properties to overcome the ink viscosity and surface tension at the orifice to achieve  (Gudapati et al. 2016;). Therefore, the printing energy for Ink D should be slightly lower than the ones applied on Ink C, which has higher physical properties than Ink D, to achieve the 1:1 ratio between the size of Ink C and Ink D. The dosing energies applied on Ink C ranged from 1.51 to 3.02 La.
The droplet diameter and falling velocity of printed Ink C, blank Ink D, and cell-laden ink D under eight sets of bioprinter operating conditions are depicted in Fig. 5. In all cases, the droplet diameter increased with increasing dosing energy. The initial droplet diameter D o of the ejected Ink C increased from 362.31 ± 1.50 m under 1.68 La to 439.76 ± 1.09 m under 3.36 La. Blank Ink D had the initial droplet diameter as 346.32 ± 4.44 m under 1.51 La, which was similar to the size of printed bioink droplet for the optimum hydrogel formation outcome. Under 3.02 La, initial droplet diameter of the blank Ink D increased to 427.35 ± 12.66 m. Seeded with a high input cell concentration ( 1 × 10 7 cells/ml), the droplet diameter of Ink D increased from 340.77 ± 4.44 m under 1.51 La, to 466.20 ± 16.09 m under 3.02 La. The average size difference between 0 cells/ml and 1 × 10 7 cells/ml was 17.23 ± 11.63 m under all dosing energies. There is no clear increasing or decreasing tendency with cell concentrations in droplet size. Input cell concentration up to 10 million cells/ml can be seen to have negligible impact on droplet size under the chosen dosing energies in micro-valve-based bioprinting. A similar result was reported by our previous study (Chen et al. 2022).
Droplet falling velocity also has a positive correlation with the applied energy, which is the dosing energy in the micro-valve-based bioprinting. By increasing the applied pneumatic pressure or valve opening time, the dosing energy increases accordingly (Eq. 3). High dosing energy leads to high droplet falling velocity. From 1.68 to 3.36 La, bioink C has a near linear increasing droplet falling velocity raising from 3.8 ± 0.15 to 6.21 ± 0.08 m/s accordingly. The velocities just before the blank Ink D droplet impact increased from 3.44 ± 0.22 to 6.22 ± 0.22 m/s under the corresponding matching dosing energies. Similar to the droplet size, the input cell concentration has negligible impact on the droplet velocity, leading to 3.77 ± 0.22 to 6.55 ± 0.54 m/s in the tested dosing energy range. Cell-laden droplets showed no significant larger or smaller velocity values than the droplets containing no cells. The average velocity difference between 0 cells/ml and 1 × 10 7 cells/ml was 0.3 ± 0.18 m/s under all dosing energies.

Ink physical properties and dimensionless numbers
The viscosity of the blank Ink C and Ink D were measured by Inventia Life Science Pty Ltd, under 75, 225, and 675 1/s shear rate with a constant value. Therefore, both blank Ink C and Ink D can be treated as Newtonian fluids. The viscosity of the cell-laden Ink D was measured at a fixed shear rate ( 10 3 1/s). Ng and Huang (Ng et al. 2022) found that the increasing shear rate results in lower average viscosity for cell-laden inks. The reduction becomes less significant at higher shear rates ( > 10 3 1/s) (Ng et al. 2022). The printing  Table 1 instead.
The density value of the cell-laden Ink D increased by 2.7% compared to the blank Ink D. By adding cells to the ink, the resulting higher frictional force and distorted flow field at the ink-cell interface leads to an increase in the fluid viscosity (Ng et al. 2022). The viscosity of cell-laden Ink D increased 5.7% compared to the blank ink. Theoretically, the higher viscous dissipation during droplet formation process results in a lower overall droplet size and velocity (Xu et al. 2014;Ng et al. , 2022. The increased percentage of the cell-laden ink viscosity was small (5.7%) compared to the blank ink, leading to negligible influence on the droplet size and falling velocity. In contrast, the average surface tension of cell-laden activator decreased 13.4% compared to the blank Ink D, due to the reduction in total free energy of the bioink, because more cells were absorbed to the interface (Xu et al. 2014;). Xu, et al. (Xu et al. 2014) and  have also found that increasing cell concentration results in a decreased surface tension, and an increased density and viscosity.
Although the value of measured density, viscosity, and surface tension of Ink C, Ink D, and cell-laden Ink D cannot be presented in this paper, they were used to calculate the Weber number and Reynolds number to help quantify the study. Table 2 lists the Weber number, We, and the Reynolds number, Re, calculated from the measured droplet size, falling velocity, and physical properties (measured density, viscosity, and surface tension of Ink C, Ink D, and cell-laden Ink D) under eight sets of printing conditions. Due to the difference in ink physical properties, the Weber number and the Reynolds number of cell-laden Ink D was higher than the blank Ink D under all printing conditions. The values of Re and We increased with increasing dosing energy value.

Substrate properties
Two substrates were used in this study: (1) Nunclon TM Delta surface 96-well plate, which can be seen as a flat solid substrate; (2) pre-printed hydrogel matrix, which can be seen as a soft elastic substrate. To generate the hydrogel matrix, the sodium alginate bioink (Ink A), followed by the CaCl 2 activator (Ink B), was printed directly in the well plate. The thickness of the printed hydrogel matrix was h o = 648.73 ± 33.07 m, measured from the obtained images. The obtained maximum initial droplet diameter D o was 466.20 ± 16.09 m, leading to the dimensionless substrate thickness = h o ∕D o > 1.4 . The pre-printed hydrogel matrix can be seen as a thick ( > 1 ) soft elastic structure (Kittel et al. 2018), which mimics the 3D bioprinting conditions in practice. Based on the providers' research, the elastic modulus of the hydrogel matrix generated under this printing condition is slightly over 1.5 kPa (Mahmodi et al. 2021). The average surface roughness R a for the printed hydrogel matrix was 59.30 ± 23.81 m . The average surface roughness was calculated from the surface heights and depths, measured directly from twenty different experiment images. The surface roughness from the pre-printed hydrogel structure is not controllable, which is caused by the chemical properties of the chosen bioink and activator. The droplet impact on the pre-printed soft hydrogel layer with highly rough surface reflects the real impact process in 3D dropletbased bioprinting method in this study.

Spreading factor
In order to investigate the effect of the bioprinter's operating condition (dosing energy) on the impact dynamics, eight sets of dosing energies listed in Table 2 (Fig. 6i). The phenomenon of droplet spreading on a soft elastic substrate (Fig. 6ii) is similar to the drop spreading on a dry solid substrate. The maximum spreading diameter was measured directly from the obtained high-speed images. The spreading factor, as a ratio between the maximum spreading diameter D max and the initial droplet diameter D o , against the Weber number, We, of Ink C impact on two substrates is depicted in Fig. 6. For Ink C, the soft elastic substrate (hydrogel matrix) had generally lower spreading factor than the dry solid substrate (well plate), indicating that soft substrate inhibited the droplet spreading after impact. This is consistent with that proposed by Basso and Bostwick (Basso and Bostwick 2020). The spreading factor of the Ink C/well plate combination showed an increasing trend with the increasing Weber number, while the hydrogel substrate did not have the same increasing tendency. The hydrogel matrix, which can be seen as a thick soft elastic substrate, deformed during droplet impact. The influence of the thick substrate deformation on the rim propagation became significant during spreading when the Weber number is higher than 186.

General impact phenomena
The simplest observation of droplet impact is whether the drop (1) deposits or (2) splashes on the substrate. This distinction is important as the droplet must impact and leave a single isolated drop to achieve high printing resolution and accuracy. Splashing occurs when the liquid inertia overcomes the surface tension forces, which can be defined as either (1) a drop that produces micro-droplets immediately after impact or (2) a drop that exhibits two or more satellite drops that break off from the main drop during impact (Basso and Bostwick 2020). On the well plate, the Ink C droplets spread to the maximum diameter, then receding back to the equilibrium state. As can be seen at 0 ms in Fig. 7, Ink C left single isolated drops under all dosing energies. Therefore, droplet impact on a dry solid substrate causes no splashing at We ≤ 292 , with associated droplet Reynolds number Re ≤ 363.
When the blank Ink D droplet impacted on the preprinted Ink C drop, a bowl-like liquid film was generated upon impact at 112 ≤ We ≤ 254 and finally receded back to single isolated droplets at around 7.7 s after impingement. The bowl-like liquid film did not break into microdroplets, but merged during collapse, resulting in entrapment of several bubbles during the contracting phase. The bubbles were gone at the equilibrium state, leaving a single isolated  Figure 8 shows sequences of droplet impact images on the hydrogel matrix taken from the Side view 2 direction using Ink C under the selected operating conditions (1.68 La, 2.16 La, 2.64 La, 3.12 La, and 3.36 La). The corresponding Weber number values are 90, 134, 186, 246, and 292. On the soft substrate, some of the liquid kinetic energy can be transformed into the elastic energy due to substrate deformation, therefore affecting the impact dynamics and the onset of splashing (Basso and Bostwick 2020). The splashing phenomena on soft substrates was observed at We ≥ 186 , with associated droplet Reynolds number Re ≥ 279 . After the spreading phase, an elongated liquid column was formed, followed by the generation of secondary droplets which pinch off from the main droplet. The residual main drop remained on the substrate, which can be seen as the equilibrium droplet for future evaluation. The satellite droplets may rest on the hydrogel substrate, on the wall of the well, or on the bottom surface of printheads, causing negative effects on printing fidelity. By investigating all dosing energy sets, the splashing phenomena was seen to occur at We = 159 , with a splashing percentage (splashing percentage = number of the tests that have splashing phenomenon / total number of the repeat tests under certain Weber number) of 12.9% over the total 31 repeat tests.
The average surface roughness R a for the printed hydrogel matrix was 59.30 ± 23.81 m . Surface roughness plays an important role in droplet impact on solid substrates. Wang and Qiao (Wang et al. 2021) found that roughness of the solid impact surface ( R a up to 250 m) has a positive effect on the dynamics of splashing droplets. Splashing droplet diameter, velocity, splash angle, splash height, and mass-loss rate of splashing droplets rise with the increase in roughness. Quetzeri-Santiago, Miguel A., Alfonso A. Castrejon-Pita, and J. Rafael Castrejon-Pita (Quetzeri-Santiago et al. 2019) also found that the dynamic contact angle, together with the liquid properties, the average surface roughness R a , and the surface feature mean width, determines the splashing to no-splashing threshold in droplet impact process. When droplets impact on soft matrix, the surface roughness could influence the dynamics of splashing droplets and the splashing threshold. The effects of surface roughness on droplet impact should be discussed in the future work. Figures 9 and 10 show sequences of images taken from the Side view 2 and the Side view 1, respectively, of blank Ink D droplet impact on the hydrogel matrix with pre-printed Ink C drops on top. The hydrogel matrix covered by preprinted Ink C drops can be seen as a wet soft substrate. The blank Ink D was shown to be printed under selected operating conditions (1.51 La, 1.94 La, 2.38 La, 2.81 La, and 3.02 La), with the corresponding Weber number equals to 63, 112, 160, 199, and 254. A splashing phenomenon was observed at We ≥ 199 from both viewing directions. By investigating all eight sets of dosing energies, the splashing phenomena started to occur at We = 160 , with a splashing percentage of 3.7% over the total 27 repeat tests. Compared with the droplet impact processes on the dry soft substrate, the splashing phenomenon occurs on both dry and wet hydrogel substrates at We > 160 . The presence of the pre-printed bioink drop has a negligible influence on splashing.
In the receding phase of droplet impact, droplet retreats after the spreading phase due to the effects of the gelation effect, surface tension of the liquids, surface tension of the substrate, and the interfacial tension between them (Chen et al. 2017). With the hydrogel surface roughness and the gelation effect, the droplet might not retreat evenly. A comparison between the two viewing directions is depicted in Fig. 11. After the blank Ink D droplets impingement on the pre-printed Ink C drops on the well plate, the equilibrium drop diameters were obtained and measured from both viewing directions, at Weber number ranging from 63 to 254. The equilibrium drop diameter increased with increasing Weber number from both viewing directions. The average equilibrium drop diameters obtained from the Side view 1 and the Side view 2 can be seen as consistent, illustrating that the surface roughness or gelation effects has negligible influence on droplet An interesting difference between drop impact on the solid surface and the soft structure can be seen in Fig. 11. On the well plate, the equilibrium drop diameter increased with the increasing Weber number. In contrast, the equilibrium drop diameter on the hydrogel matrix started to decrease after We = 160 . As discussed before, the splashing phenomenon occurred on soft substrates at We > 160 , which can be seen as the main reason causing the decreasing equilibrium droplet size. More results are discussed in the following section.

Influence of substrates on droplet impact
In order to investigate the effect of the substrates on impact dynamics, the general impact processes on the well plate and the hydrogel matrix are presented in Figs. 7,8,9,10. No splashing occurred for We ≤ 292 on both dry and wet solid substrates. With increasing dosing energy, an corresponding increases in Weber number and Reynolds number, droplet spreading diameter and equilibrium diameter increase on both dry and wet solid substrates. The equilibrium drop volume was calculated from the measured equilibrium diameter and height using Eq. 4. The volume increases with the increasing Weber number (Fig. 12). The equilibrium drop volume, after the impact process, increased from 25 ± 7 nl at We = 63 to 93 ± 16 nl at We = 254 . Without splashing, the equilibrium droplet volume is as expected for the printed droplet volume generated by the bioprinter.
On both the dry and wet soft substrates, splashing was observed for We > 160 . The equilibrium drop volume, after the blank Ink D drops impacted on the pre-printed Ink C drops on the hydrogel matrix, increased from 23 ± 5 nl at We = 63 to 43 ± 8 nl at We = 126 . At We > 126 , the equilibrium drop volume decreased from 30 ± 9 nl at We = 160 to 16 ± 5 nl at We = 254.
At We < 159 , with associated Re < 256 , the drop collision on the dry soft substrate (Ink C directly impacting on the hydrogel matrix) led to the deposition without breakup. This was also observed for drop impact on the wet soft substrate (blank Ink C impacts on the pre-printed bioink drops on the hydrogel matrix) at We < 127.36 , with associated Re < 252 . Within this range, the equilibrium drop volume on the soft substrate equalled the total droplet volume applied to the solid substrate. When the Weber number exceeded this value, splashing occurred on the soft substrate. The difference between the equilibrium drop volume on the solid substrate and the droplet size on the soft substrate increased. The printed droplet volume was therefore much lower than the expecting volume, leading to poor printing resolution and reduced structure integrity.
The droplet impact location is another parameter that can directly influence printing fidelity. To investigate the influence of substrates on the droplet impact location, the obtained centre position of the initial droplet before impact was used to compare with the centre position of the equilibrium droplet after impact. On the well plate, the position difference between the initial droplet and the equilibrium droplet was 43.62 ± 18.56 m under all applied dosing energies. It is approximately 11% of the droplet diameter. The position difference remained similar after droplet impact on the hydrogel matrix, with a value of 43.10 ± 15.81 m under all operating conditions. The splashing has negligible influence on the droplet impact location.

Influence of input cells on droplet impact
Compared to the blank Ink D, the cell-laden Ink D had an increasing density and viscosity, and a decreasing surface tension. The initial droplet diameter and falling velocity were not influenced by the amount of input cells in this experiment. The changes in the ink physical properties led to a higher Weber number and Reynolds number upon impact under the same dosing energy. Ink C droplet, which was the first droplet impacting on the soft substrate, had no cells in it. Therefore, the second droplet impact process (the cell-laden Ink D impacts on the pre-printed bioink on the hydrogel matrix) was studied to evaluate the influence of input cells on droplet impact. The comparison of the equilibrium volume of the blank Ink D Fig. 9 and the cell-laden Ink D Fig. 13 impact on different substrates is depicted in Fig. 14. The average equilibrium drop volume obtained from the blank Ink D and the cell-laden Ink D impact on both solid and soft substrates are very consistent, illustrating the input cell concentration has small effects on the printed drop size. Fig. 13 shows the evolution of the cell-laden droplet impact process when the Weber number ranges from 89 to 365. At We ≤ 153 , the cell-laden Ink D impacted on the pre-printed Ink C droplets and combined into single isolated droplets on the soft substrate. Under E d = 2.38La , the corresponding Weber number and Reynolds number of the cell-laden Ink D were calculated to be 199 and 295, respectively. A splashing phenomenon was observed at this Weber number upon second droplet impact, with a splashing percentage of 75% over the total 12 repeat tests. The blank Ink D showed 3% splashing percentage under the same dosing energy with the associated Weber number equals to 160. The difference in calculated splashing percentage between blank ink and cell-laden ink is mainly caused by the different Weber number. Cell-laden ink has higher Weber number under the same applied dosing energy, where liquid inertia overcomes the surface tension forces, leading splashes to occur.
The total splashing percentage, the first drop splashing percentage, and the second drop splashing percentage under two different cell concentrations (0 and 1 × 10 7 cells/ ml) can be seen in Fig. 15. First of all, Ink C, which had no cells in it, remained the same under all conditions. The first drop splashing percentage was therefore having the similar value under both tests regardless of the input cell density in Ink D. Ink C started to splash, with an average splashing percentage of 14.78%, on the dry soft hydrogel matrix, at We = 159 , with the associated Re = 256 . At We = 292 , near 100% of Ink C droplets splashed on the soft substrate in droplet impact process. The increasing Weber number leads to an increasing chance of droplet splashing on the soft substrate.   Fig. 12 The calculated equilibrium drop volume on the well plate and hydrogel matrix. The Weber number for the first droplet impact (Ink C impacts on dry substrates) ranges from 90 to 292. The Weber number for the second droplet impact (blank Ink D impacts on wet substrates) ranges from 63 to 254. Error bars are 95% confidence intervals When a blank Ink D droplet was printed on top of the pre-printed Ink C, there was no splashing at We ≤ 126 , with associated Re ≤ 252 . Under 2.38La, where the blank Ink D has a Weber number of 160, 3% of the blank Ink D splashed on the pre-printed bioink, on top of the soft hydrogel matrix. The splashing percentage for the blank Ink D increased to 41.46% under 2.59La(We = 178) , to 39.29% under 2.81La (We = 199) , to 48.28% under 3.02La(We = 254) . The cell-laden Ink D, on the other hand, illustrated much higher splashing rate under the same applied dosing energies due to its large Weber number. Similar to the blank Ink D, no splashing was generated under 2.16 La. When the applied dosing energy increased to 2.38La, the Weber number of the cell-laden Ink D raised to 199, resulting 75% splashing percentage. The splashing percentage of the cell-laden Ink D kept increasing to 78.26% under 2.59La(We = 210), up to near 100% under 3.02La(We = 365). Mundo et al. (Mundo et al. 1995) have suggested the dimensionless number K = We 0.5 Re 0.25 as an effective metric to quantify splashing. In addition to the K number, Kittel et al. (Kittel et al. 2018) surmised that the splashing condition for drop impact onto soft, deformable substrates can be obtained from the balance of the inertial and surface tension forces in the spreading lamella. The threshold value L is defined by the ratio of the pressure associated with the liquid inertia ( p i = rhov 2 o ) and the capillary pressure on the length scale associated with the residual lamella thickness ( p = The K number and L number of the inks under eight sets of bioprinter's operating conditions for Ink C and blank/cellladen Ink D are listed in Table. 3. Three phases can be used to describe the 3D-bioprinted droplet impact process on the pre-printed soft hydrogel matrix: (1) Droplet deposition/no splashing, where the total splashing percentage is 0%; (2) Partial splashing, where the splashing occurs, while the total splashing percentage is lower than 100%; and (3) Absolute splashing, where the total splashing percentage equals to 100%.

Splashing threshold
On both dry and wet flat solid substrate, no splashing happened under the tested operating conditions, regardless of input cell densities. The splashing threshold for the droplet impact on dry and wet solid substrate is defined by K < 86.19 . This threshold is consistent with the results ( K = 84 ) reported by Kittel et al.(Kittel et al. 2018).
Ink C started to splash on the dry soft hydrogel matrix, at We = 159 , with the associated Re = 256 . To define splashing for Ink C on a thick soft substrate, the critical K and L number is 45.11 and 15.21, respectively, calculated from the experimental results with corresponding We = 134 and Re = 231 . At We = 292 and Re = 363 , nearly 100% of Ink C droplets splashed on the soft substrate. The K and L number that defines the absolute splashing threshold for Ink C are therefore set as 74.53 and 27.61, respectively. The partial splashing phase of Ink C on thick soft hydrogel substrate is bound by these two threshold limiting values.
The blank Ink D started to splash on the wet soft hydrogel matrix, at We = 160 , with the corresponding Reynolds number, K number, and L number as Re = 285 , K = 52.03 ,  Similarly, the cell-laden Ink D started to splash on the wet soft hydrogel matrix, at We = 199 , with the corresponding Reynolds number, K number, and L number as Re = 295 , K = 58.45 , and L = 20.44 . To prevent splashing, the deposition/splashing boundary for the cell-laden Ink D on thick soft substrate should be lower than these values, which are set to be K = 48.98 and L = 16.94 based on the experimental results. At We = 286 and Re = 354 , the total splashing percentage for the cell-laden Ink D impacting on the wet hydrogel substrate reached to 100%. The absolute splashing happens at K = 73.41 and L = 27.36 . The partial splashing phase of the blank Ink C on wet thick soft substrate is bounded by these two threshold limiting values.
Combining the threshold values for all types of ink, input cell densities, and substrate conditions (dry or wet), the deposition/splashing boundary for both the dry and wet soft hydrogel matrix is defined as K = 44.78 and L = 13.85 . The obtained threshold ranges are in agreement with the existing recent theories for splashing threshold ( K = 57.7 , (Mundo et al. 1995, Ng et al. 2022) K < 175 , (Basso and Bostwick 2020) and L = 16.8 . (Kittel et al. 2018)) on soft substrates. The threshold for absolute splashing is defined as K = 73.41 and L = 27.36 . The partial splashing phase is bounded between these two values. This combined threshold should be able to use to achieve high printing fidelity and structure integrity.

Droplet impact influence on bioprinted 3D cell spheroids
Three droplet impact phases (droplet deposit/no splashing, partial splashing, and absolute splashing) on hydrogel matrix have been identified in this study. Figs. 16, 17 are used to illustrate how different droplet impact phases influence the printing outcomes within the droplet-based 3D bioprinting process.
Bright-field images were obtained right after the droplet impact experiment. At We ≤ 154 , both bioink droplets and activator droplets were deposited on the pre-printed hydrogel matrix to form isolated single hydrogel drops. Fig. 16i and ii demonstrates the isolated hydrogel droplets after depositing cell-laden activator Ink D on top of the pre-printed bioink Ink C. The isolated hydrogel droplets indicate potential good outcome for 3D cell spheroids generation. At We > 154 , droplets started to splash on the soft substrate upon impact. The satellite drops caused by splashing around the main hydrogel droplet can be seen in Fig. 16iii, iv and v. Cells that trapped in the satellite drops could not bound with bioink, resulting in extra cells floating in the cell culture media and contaminating the culturing field. Moreover, when a large amount of bioink (Ink C) splashed during impact process (Fig. 16iii), there was not enough bioink left in the main droplet for a good gelation after. The formation of 3D cell spheroids will be negatively influenced.
After 7 days incubation, the fluorescence images of generated 3D cell spheroids can be seen in Fig. 17. Compared to the deposition/no splashing printing results (Fig. 17i, ii, iii, and v), the satellite drops caused by splashing resulted inconsistent printing results. In the absence of splashing, the printed cells formed into isolated spherical structures, which can be used in future experiments. In contrast, the cell-laden droplets that went through splashing did not form into the ideal 3D cell spheroids and cannot be used in the future.

Conclusion
Droplet splashing on pre-printed soft hydrogel substrate has been experimentally investigated using a micro-valvebased 3D bioprinter under different conditions. Droplet impact dynamics was captured by the shadowgraphy method using a high-speed imaging system. The droplet volume, falling velocity, and impact morphology were obtained by analysis of processed images from the camera. The droplet impact morphology was quantified by the spreading factor, Weber number, We, Reynolds number, Re, splashing percentage, and the threshold number K and L. For droplet spreading, the soft substrate can inhibit the spreading after impact. The influence of the thick substrate deformation on the rim propagation became significant during spreading when the Weber number is higher than 186, which inhibit the droplet spreading during impact more. Kittel (Kittel et al. 2018) summarised the splashing threshold K number for droplet impact on flat surfaces smaller than 84. In this experiment, droplet impact on a dry/wet solid substrate causes no splashing with K number up to 86.19. Three phases was used to describe the droplet impact process on thick soft hydrogel matrix: (1) Droplet deposition/no splashing, where the total splashing percentage is 0%; (2) Partial splashing, where the splashing occurs, while the total splashing percentage is lower than 100%; and (3) Absolute splashing, where the total splashing percentage equals to 100%.
The deposition/splashing threshold for droplet impact on both the dry and wet soft hydrogel matrix is defined as K = 44.78 and L = 13.85 , regardless of ink property or input cell density. The obtained threshold ranges are in agreement with the existing recent theories for splashing threshold ( K = 57.7 and L = 16.8 ) (Basso andBostwick 2020, Kittel et al. 2018) on soft substrates. Beyond the threshold, the printed drop volume will be much lower than the expected volume due to splashing, leading to poor printing fidelity and structural integrity. The absolute splashing threshold for the dry and wet soft hydrogel matrix is defined as K = 73.41 and L = 27.36 . The partial splashing phase is bounded between these values. No dependency of the input cell density was observed once the threshold was overcome. Droplet splashing on the soft substrate during impact could significantly influence the printed 3D cell structural accuracy and integrity in 3D bioprinting processes. However, splashing has proven to have negligible influence on the droplet impact location.
Our work provides new insights into droplet deposition and fusion in droplet-based 3D bioprinting. The optimization of printing condition based on the splashing thresholds will aid in achieving high printing fidelity and maintain structure integrity. Future work includes discussing the effects of surface roughness of soft hydrogel matrix 1 mm Fig. 16 Bright-field images of the cell-laden activator Ink D impacts on the bioink Ink D on the top of the hydrogel matrix, at the Weber number of the cell-laden Ink D equals to: i 89 (no splashing); ii 150 (no splashing); iii 199 (partial splashing); iv 286 (absolute splashing); and v 365 (absolute splashing). The satellite droplets generated by splashing are circled by red dashed lines. The main droplets are highlighted by yellow dashed lines on the dynamics of splashing droplets and the splashing threshold.
Acknowledgements The authors acknowledge the Commonwealth's valuable contributions and support of providing the Australian Government Research Training Program Scholarship. The authors would like to express their gratitude for the support provided by the University International Postgraduate Award (UIPA) funded by University of New South Wales. The authors would also like to acknowledge and thank the Inventia Life Science engineering team for supplying the RAS-TRUM TM printing platform.

Author contributions All authors contributed equally to this work
Funding Open Access funding enabled and organized by CAUL and its Member Institutions.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Ethics approval Not applicable
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are Fig. 17 Fluorescence images of 3D cell spheroids generated under different operating conditions, with the corresponding Weber number of the cellladen Ink D equals to: i 89 (no splashing); ii 150 (no splashing); iii 199 (partial splashing -no splashing); iv 199 (partial splashing -splashing); v) 210 (partial splashing -no splashing); vi 210 (partial splashing -splashing); vii 286 (absolute splashing); viii 286 (absolute splashing); ix 365 (absolute splashing); x 365 (absolute splashing); xi 89 (Control set: 2D cell structure, no splashing) included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.