Modeling thermal inkjet and cell printing process using modified pseudopotential and thermal lattice Boltzmann methods

Abstract

Pseudopotential lattice Boltzmann methods (LBMs) can simulate a phase transition in high-density ratio multiphase flow systems. If coupled with thermal LBMs through equation of state, they can be used to study instantaneous phase transition phenomena with a high-temperature gradient where only one set of formulations in an LBM system can handle liquid, vapor, phase transition, and heat transport. However, at lower temperatures an unrealistic spurious current at the interface introduces instability and limits its application in real flow system. In this study, we proposed new modifications to the LBM system to minimize a spurious current which enables us to study nucleation dynamic at room temperature. To demonstrate the capabilities of this approach, the thermal ejection process is modeled as one example of a complex flow system. In an inkjet printer, a thermal pulse instantly heats up the liquid in a microfluidic chamber and nucleates bubble vapor providing the pressure pulse necessary to eject droplets at high speed. Our modified method can present a more realistic model of the explosive vaporization process since it can also capture a high-temperature/density gradient at nucleation region. Thermal inkjet technology has been successfully applied for printing cells, but cells are susceptible to mechanical damage or death as they squeeze out of the nozzle head. To study cell deformation, a spring network model, representing cells, is connected to the LBM through the immersed boundary method. Looking into strain and stress distribution of a cell membrane at its most deformed state, it is found that a high stretching rate effectively increases the rupture tension. In other words, membrane deformation energy is released through creation of multiple smaller nanopores rather than big pores. Overall, concurrently simulating multiphase flow, phase transition, heat transfer, and cell deformation in one unified LB platform, we are able to provide a better insight into the bubble dynamic and cell mechanical damage during the printing process.

Fig. 1.

Calculation of interparticle force on boundary nodes using ghost points (shown in Red).

Fig. 2.

Maxwell construction of Peng–Robinson (P–R) equation of state at various subcritical temperatures.

Fig. 3.

Maxwell construction perdition for P-R EOS versus simulation results of our coupled pseudopotential-thermal model using reduced EOS. The relative density, ρ/ρ_c, are demonstrated in two linear and logarithmic scales at right and left, respectively.

Fig. 4.

Mesh dependency analysis of phase separation at T_init = 0.5T_c. Relative density data along dotted line shown in Fig. 3.

Fig. 5.

Liquid-vapor separation for different reduced parameter. Mesh size is 150 × 150 × 150.

Fig. 6.

Spurious current in lattice unit for various temperatures and reduced parameters. The red stars represent spurious current at k′ = 1 using original pseudopotential formulation by Gong and Cheng [7]. The velocity distribution contours demonstrate unrealistic spurious current at phase interface.

Fig. 7.

Droplet on a surface for different liquid–solid interaction strengths, (a) g_s = 0, (b) g_s = −10, (c) g_s = 10. These simulations are carried out with initial temperature of 0.5T_c with 120 × 240 × 600 lattice nodes. (d) Relative density across dashed line for various liquid–solid interaction strengths.

Fig. 8.

(a) Cross-section of HP60 nozzle plate. (b) Schematics of microinkjet nozzle in computational model. Heating resistor is shown in Red.

Fig. 9.

Relative density distribution during initialization. t_lattice = 7000 marks t = 0s in reference unit

Fig. 10.

Linear variation of reduced parameter versus relative temperature. K′ equals 0.03 at 0.45T_c.

Fig. 11.

Solution process flow chart.

Fig. 12.

Time sequence of droplet injection process at nozzle cross section. Color bar represents relative density.

Fig. 13.

Time sequence of droplet injection process at nozzle cross section. Color bar represents relative temperature.

Fig. 14.

Relative density distribution during nucleation, bubble growth and bubble collapse (a) before and (b) after bubble coalescence. The density data is related to dashed lines shown in Fig. 12 at (a) t = 4μs and (b) t = 13 μs.

Fig. 15.

Comparison of drop head velocity between experiment [43], CFD simulation of Tan et al. [43], and pseudopotential LB method in this study.

Fig. 16.

The history of (a) minimum vapor density and (b) maximum local temperature from pseudopotential LB method.

Fig. 17.

Maximum local pressure derived from pseudopotential LB method in this study compared to vapor pressure used in [11].

Fig. 18.

Time sequence of cell deformation as it get squeezed out of nozzle printer.

Fig. 19.

(a) areal strain, (b) stretching speed, (c) maximum axial stress and (d) maximum shear stress distribution on cell membrane at 6.25 μs. (e) The probability of pore formation R(ε_A) at various stretching speeds [46].