Numerical simulation of evaporation and absorption of inkjet printed droplets

Abstract

Inkjet printing is an important field of research for many industrial applications. In particular, the inkjet-printing technology is widely used in the production of a text or graphics of documents stored in electronic form by printing ink on papers and the manufacturing of microarray slides by printing DNA or protein molecules solved in a liquid on an impermeable or permeable medium. For the latter application, the inkjet printing technology offers a great advantage for the reason that a well-defined droplet can be delivered to the surface without making any contact with the substrate. Consequently, the amount of liquid deposited is not influenced by properties of the substrate surface and contamination of the sample can be avoided. Furthermore, it has been reported that significant better spot morphology has been observed using non-contact printing compared to contact printing. The main topic of the research described in this thesis is to develop a physical model that describes the printing process of a droplet solution for the application of microarray manufacturing. In addition, the same model can also be used to describe the printing process of ink on paper. The printing process starts by propelling a microsize droplet onto a prepared substrate. Following the impact between the droplet with the substrate surface, its kinetic energy will cause spreading and shrinking until it reaches an equilibrium shape. After this initial phase, two phenomena might take place depending on the type of the substrate: evaporation or adsorption. Accordingly, this thesis is divided into two separate topics. In both cases, the dynamics of the fluid determines the behavior of the solute particles and depending on the properties of the substrate, the solute particles have the possibility to bind to the surface or to the pore walls inside a porous substrate. The manner in which a biomolecule binds to the substrate determines the functionality of the biomolecules. Therefore, the nature of the liquid dynamics plays an important role in the quality of the microarray. The physical model, which is developed in this research, describes various processes, which are the dynamics of the solvent, the evaporation process, the absorption process, the convective-diffusive transport of the solute molecules and the adsorption of the solute particles onto or within the substrate. The dynamics of the droplet is modeled by the Navier-Stokes equation in the lubrication approximation. This is done in order to simplify the governing equations and to reduce computational effort. We consider different evaporation models for an impermeable substrate. The evaporation takes place under isothermal conditions, where the mass loss is induced by the gradient of the partial water vapor pressure at the droplet-air interface. For the absorption of the droplet, the flow within the porous medium is described by Darcy’s law and driven by the capillary pressure. The dynamics of the solute particles is modeled by convective and diffusive transport, which are the results of the solute dynamics due to either evaporation or absorption and the concentration gradient, respectively. Furthermore, the adsorption of solute particles is described as an instantaneous process which depends on the local solute concentration. The governing equations for both evaporation and absorption of a sessile droplet constitute a set of coupled nonlinear partial differential equations with the highest order of four. Due to their non-linearity, the governing equations have to be solved numerically. The method of lines, where the spatial derivatives are discretized using a finite volume method, is used in order to transform the partial differential equations into a system of ordinary differential equations. Furthermore, because of the stiffness of this system of equations, the time integration is performed with a combination of a fifth-order accurate Gear method and a first-order accurate implicit Euler method. The numerical method is programmed in Fortran and executed using parallel computing on a shared memory machine with the use of Openmp. The results are validated by a comparison with experimental data provided by literature, with dedicated experiments performed at Wageningen University and Research Center and with simulations from commercial software. In general, the validations give a fair agreement, where the difference in these validations can be explained by the exclusion of some specific physical phenomena from the present model. Hence, in this study some improvements for future work are suggested. Furthermore, a sensitivity analysis is performed by varying the physical properties and an accuracy analysis on the numerical approach is carried out.