A System Approach to Develop New Platforms of Industrial Inkjet Inks

Spreading of Micrometer-Sized Droplets under the Influence of Insoluble and Soluble Surfactants: A Numerical Study

“…The surface tension was evaluated from the surface concentration data obtained with our numerical model and presented in Section 3.1 using the Frumkin equation of state (Equation 9). With the chosen model parameters and the initial surfactant concentration c ∞ = 0.941 mol m −3 in the liquid phase the system shows a similar behaviour compared to the measurements presented by [32].…”

“…Concentration and surface tension data as well as further data presented throughout this article are also available as electronic Supplementary Material. With the chosen model parameters and the initial surfactant concentration c ∞ = 0.941 mol m −3 in the liquid phase, the system shows a similar behaviour compared to the measurements presented by [32]. phase we assume ρ g = 1.2 kg m −3 and µ g = 19 µPa s. The surface tension of UV-curable inkjet inks without surfactant is σ 0 ≈ 35 mN m −1 .…”

“…While dynamic surface tension data and sorption model parameters for aqueous systems are available for a large number of surfactants [25,43], only limited data for other solvents are available. Future works should therefore investigate sorption dynamics of non-aqueous systems, such as, e.g., energy curable inks used in a wide range of inkjet applications [32]. Our numerical model might be helpful in finding optimal sorption and surface tension properties for such processes including droplet impact, collision, or coalescence.…”

“…Only limited data regarding the sorption kinetics for typical surfactants in these systems are available. Bale [32] presented dynamic surface tension measurements using maximum bubble pressure tensiometry of UV-inks with different silicone additives. These measurements show a decrease of the surface tension starting on a timescale of 1 ms and it takes the system several seconds to minutes to reach a stationary equilibrium surface tension σ eq ≈ 23 mN m −1 .…”

“…These measurements show a decrease of the surface tension starting on a timescale of 1 ms and it takes the system several seconds to minutes to reach a stationary equilibrium surface tension σ eq ≈ 23 mN m −1 . Since we are mainly interested in the qualitative spreading behavior, we assumed [33] and D B = 5.3 × 10 −10 m 2 s −1 [34] corresponding to heptanol in water and adjusted σ 0 = 35 mN m −1 as well as the initial surfactant concentrations to fit the initial and equilibrium values of UV-curable ink given by Bale [32]. Even though this can only be a rough approximation, this system shows a dynamic surface tension behavior similar to typical UV-curable inkjet inks.…”