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Yusupov, et al.
Table 1. The relationship between the hydrogel viscosity and ambient temperature.

Hydrogel Viscosity (mPa*s)
Temperature, °С 20 24 28 32 37
Methylcellulose 1% w/v 231±12 194±11 170±12 133±11 104±13
Sodium alginate 1% w/v 76±3 68±2 61±3 56±4 50±5
Hyaluronic acid sodium salt 2% w/v 20±2 18±2 16±1 15±1 13±1

Table 2. The time-dependent hydrogel mass In one study, the authors suggested using the
[61]
changes. inverse number J = 1/Oh. It is shown that jets form
Hydrogel Hydrogel layer weight (% of the well in the range of 0.86 ≤J ≤2.49 at F = 717 ±
initial) 45 mJ/cm . With an increase in fluence, jet formation
2
Time, min 0 2 5 10 30 occurs well at a slightly higher viscosity (lower J).
Methylcellulose1% 100 92.2±0.4 82±2 67±4 35±4 Hydrogel parameters are very important for the
w/v jet formation. The characteristic time Δτ for the
Sodium alginate 1% 100 91.6±0.4 81±2 68±3 32±4 destruction of a cylindrical jet of radius (R) with
w/v
Hyaluronic acid 100 92.1±0.4 82±2 68±3 27±5 the density (ρ) and surface tension σ as a result of
[62]
sodium salt 2% w/v Plateau–Rayleigh instability is :

studied [56,59] . Regarding laser printing methods, ∆τ ≅ 291. ⋅ ρ ⋅ R 3 / σ (2)
they have the best resolution as well as provide
cell survival during the transfer at the level of In the case of R = 50 μm, with σ = 73 × 10 N/m, we
−3
95% or more [10,56] . One of the main difficulties obtain Δτ = 120 μs with a radius of microdroplets
in applying the LIFT technique for biological of ~ 9 R . It was established that at a low gel
[54]
[62]
applications is the need for individual selection of viscosity, the gas bubble does not form and breaks
a large number of parameters for the combination at the initial stage. In this case, the lower working
“hydrogel-transferred object” . For example, two value of the viscosity at which the formation of the
[59]
studies [14,15] on LIFT printing establish the detailed gel jet occurs decreases with decreasing spot size.
relationships between printing parameters, the The We and Oh ranges for optimal printing
regimes of hydrogel jet and droplet formation regimes have already been described in the
using sodium alginate in various concentrations as literature. The works [15,59] present an algorithm in
a model. Moreover, the authors of several research the form of a decision tree that helps to find the
articles [15,60] mainly operate with the (1) Weber optimal printing regimes for specific gels in terms
Number (We), which characterizes the ratio of the We and Oh values. However, in practice,
between inertial force and surface tension, and the usually there is a task of transferring certain bioink
(2) Ohnesorge number (Oh), which describes the with unique physicochemical characteristics at
process of droplet formation. These dimensionless an already-made laser system. Moreover, there
quantities comprehensively characterize printing is also sometimes no possibility of a significant
regimes: change in the viscosity and surface tension of the

hydrogel and adapting them to the parameters
ρ LV 2 η ,
We = , Oh = known in the literature. The task of identifying
σ ρσ L the optimal regime for a given bioink is quite
complicated, and it may require a separate study
where ρ, hydrogel density; L, characteristic using high-speed shooting for the selection of We
length which in many cases is determined by and Oh values [14,15,60] to ensure the optimal transfer
the spot size [14,60,61] ; V, fluid gel speed; σ, surface regime. Therefore, we want to suggest a simplified
tension; η, the shear viscosity of the gel. decision tree based on our results. Following this

International Journal of Bioprinting (2020)–Volume 6, Issue 3 87