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A study of the evaporation of a solvent from a solution-Application to writing ink aging

机译：从溶液中蒸发溶剂的研究-在书写墨水老化中的应用

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When writing ink is placed on a substrate, a drying process begins. This process is dependent on the composition of the ink and of the substrate. Lociciro et al. [1] provide an equation that describes the drying process based on models developed by earlier investigators. The work given here develops an equation for the drying process that is based on a different and rather simple model. This model considers the evaporation of a solution in an opened vertical container (e.g., a beaker) and consists of a volatile, non-hygroscopic solvent with a non-volatile solute dissolved in it. Three assumptions are made: (a) the rate of evaporation is proportional to the vapor pressure of the solution and to the solution's exposed surface area, (b) this solution vapor pressure is proportional to the solvent vapor pressure with the proportionality constant being the solvent mole fraction (Raoult's law), and (c) a small fraction of the solvent remains trapped in the solute after evaporation ceases. What results is a differential equation, which, when solved, gives the solvent weight W(t) as an implicit function. What emerges naturally from this treatment is the fact that the function W(t) can have a point of maximum acceleration. Prior to this point the drying process is fast and after this point, the drying process is slow. An approximation to W(t) is taken to be the sum of two exponential functions, one describing the fast drying region and the second describing the subsequent slow drying region. Upon including an additive constant, this approximation turns out to be similar to, but not the same as that provided by Lociciro et al. [1]. However, their equivalence is shown and then tested using the two inks examined by Lociciro et al. [1] (the drying of a Bic and a Staedtler blue ballpoint ink).The examples of (solvent. +. solute) systems (" inks" ) given here consist of the solvent (2-phenoxyethanol) and a solute such as a dye (crystal violet) or a polymer resin such as synthetic resin SK or polyvinyl butyral. In the case of polymers, the Raoult's law assumption is replaced with one developed by the Flory-Huggins theory of solutions. Saturation and film formation, both of which slow the evaporation rate, are also discussed.
机译：将书写墨水放在基板上时，干燥过程开始。该过程取决于油墨和基材的组成。 Lociciro等。 [1]提供了一个基于早期研究者开发的模型描述干燥过程的方程。此处给出的工作基于不同而简单的模型为干燥过程开发了一个方程式。该模型考虑了在打开的立式容器（例如，烧杯）中溶液的蒸发，并且由挥发性，非吸湿性溶剂以及溶解于其中的非挥发性溶质组成。做出三个假设：（a）蒸发速率与溶液的蒸气压成正比，与溶液的暴露表面积成正比;（b）该溶液的蒸气压与溶剂中的蒸气压成比例，比例常数为溶剂摩尔分数（拉乌尔定律），以及（c）蒸发停止后，一小部分溶剂仍留在溶质中。得到的结果是一个微分方程，当求解时，给出溶剂重量W（t）作为隐函数。从这种处理中自然得出的事实是，函数W（t）可以具有最大加速度。在此之前，干燥过程较快，而在此之后，干燥过程较慢。 W（t）的近似值是两个指数函数的总和，一个描述快速干燥区域，第二个描述随后的慢速干燥区域。包括加性常数后，该近似值与Lociciro等人提供的近似但不相同。 [1]。但是，显示了它们的等效性，然后使用Lociciro等人检查过的两种油墨进行了测试。 [1]（Bic和Staedtler蓝色圆珠笔墨水的干燥）。此处给出的（溶剂+。溶质）体系（“墨水”）的示例包括溶剂（2-苯氧基乙醇）和溶质，例如染料（结晶紫）或高分子树脂，例如合成树脂SK或聚乙烯醇缩丁醛。对于聚合物，拉乌尔定律假设被弗洛里-哈金斯解决方案理论发展的假设所取代。还讨论了饱和和成膜，这两者都会减慢蒸发速度。

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