Numerical simulation of evaporation and absorption of inkjet printed droplets
Numerical simulation of evaporation and absorption of inkjet printed droplets
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喷墨打印液滴蒸发和吸收的数值模拟
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发表时间：
2012
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通讯作者：
DP Daniel Siregar
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作者：
DP Daniel Siregar
喷墨印刷是许多工业应用的重要研究领域。特别是，喷墨打印技术广泛应用于通过在纸上印刷油墨以电子形式存储的文件的文本或图形的生产，以及通过在不渗透或可渗透的介质上印刷在液体中溶解的DNA或蛋白质分子来制造微阵列幻灯片。对于后一种应用，喷墨打印技术提供了很大的优势，因为可以在不与基材接触的情况下将定义良好的液滴输送到表面。因此，沉积的液体量不受衬底表面性质的影响，并且可以避免样品的污染。此外，据报道，与接触印刷相比，使用非接触印刷可以观察到更好的斑点形态。本论文的主要研究课题是开发一个物理模型来描述微阵列制造应用中液滴溶液的打印过程。此外，同样的模型也可以用来描述油墨在纸上的印刷过程。印刷过程首先将微滴推进到准备好的基材上。随着液滴与基材表面的碰撞，其动能会引起扩张和收缩，直到达到平衡形状。在这个初始阶段之后，根据衬底的类型，可能会发生两种现象：蒸发或吸附。因此，本文分为两个独立的主题。在这两种情况下，流体的动力学决定了溶质颗粒的行为，并且根据基材的性质，溶质颗粒有可能结合到多孔基材的表面或孔壁上。生物分子与底物结合的方式决定了生物分子的功能。因此，液体动力学的性质对微阵列的质量起着重要的作用。在本研究中建立的物理模型描述了各种过程，包括溶剂动力学、蒸发过程、吸收过程、溶质分子的对流-扩散传输以及溶质颗粒在基质上或基质内的吸附。液滴的动力学用润滑近似中的Navier-Stokes方程来模拟。这样做是为了简化控制方程并减少计算工作量。我们考虑不同的蒸发模型为一个不透水的基底。蒸发发生在等温条件下，其中质量损失是由液滴-空气界面部分水蒸气压的梯度引起的。对于液滴的吸收，多孔介质内的流动由达西定律描述，并由毛细压力驱动。溶质颗粒的动力学由对流输运和扩散输运模拟，它们分别是溶质蒸发或吸收和浓度梯度引起的动力学结果。此外，溶质颗粒的吸附被描述为一个瞬时过程，它取决于局部溶质浓度。液滴蒸发和吸收的控制方程由一组最高阶为四的耦合非线性偏微分方程组成。由于控制方程的非线性，必须用数值方法求解。为了将偏微分方程转化为常微分方程组，采用线法，其中空间导数用有限体积法离散化。此外，由于该方程组的刚度，时间积分采用五阶精确齿轮法和一阶精确隐式欧拉法相结合的方法进行。数值方法用Fortran语言编写，并在共享内存机上使用Openmp进行并行计算。通过与文献提供的实验数据、瓦赫宁根大学和研究中心进行的专门实验以及商业软件的模拟，验证了结果的正确性。一般来说，验证给出了一个公平的协议，其中这些验证的差异可以通过从当前模型中排除一些特定的物理现象来解释。因此，本研究对今后的工作提出了一些改进建议。此外，通过改变物理性质进行了灵敏度分析，并对数值方法进行了精度分析。
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.