Advances in computational technology and high-throughput modeling software have given rise to the tailored design of products that require accurate mathematical relationships for their assessment. Industrial emulsion-based products, ubiquitous to everyday life, are complex systems driven by interfacial phenomena that require quick property-prediction tools for their commercialization. In this work, by means of a multiscale approach, mathematical relationships to model oil-in-water emulsions and that can be applied to any commercial emulsion-based product are proposed. The energy consumption during the emulsification process (, which transitions from monotonic increase to exponential growth at 80% ), a parameter responsible for finished product performance, was linked to final product properties at three different levels: (i) molecular, through the dynamics of the interdroplet interactions given their distribution and structure at a microscopic level; (ii) microscopic, through average droplet size yielding an inversely proportional exponential relationship (); and (iii) macroscopic, through the plateau value of the elastic modulus and the flow behavior index leading to inversely proportional quadratic relationships ( and , respectively). These relationships are valid at dispersed phase concentrations beyond the 60%  threshold where the packing of the droplets changes the emulsion’s microscopic structure giving rise to Van der Waals forces-driven phenomena. Finding this threshold allowed expanding the concentration ranges of previously reported models. The main expectation is that these results will aid researchers and process/product designers to optimize their work in different industrial applications.

中文翻译：

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基于水包油乳液的产品设计和处理的多尺度方法

计算技术和高通量建模软件的进步催生了量身定制的产品设计，这些产品需要准确的数学关系进行评估。基于乳化剂的工业产品在日常生活中无处不在，是由界面现象驱动的复杂系统，需要快速的性能预测工具对其进行商业化。在这项工作中，通过多尺度方法，提出了对水包油乳液模型进行建模的数学关系，并可以将其应用于任何基于乳液的商业产品。在乳化过程中（能量消耗，其从转变为80％单调增加至指数生长 ）是负责成品性能的一个参数，它在三个不同的水平上与最终产品的性能相关：（i）分子，通过小滴间相互作用的动力学（在微观水平上给出了它们的分布和结构）；（ii）通过平均液滴尺寸产生微观关系，产生反比例的指数关系（）; （iii）在宏观上，通过弹性模量的平稳值和流动行为指数导致反比例的二次关系（ 和 ，分别）。这些关系在分散相浓度超过60％时有效 液滴堆积改变乳液的微观结构的阈值，产生范德华力驱动的现象。找到这个阈值可以扩大以前报道的模型的浓度范围。主要期望是这些结果将有助于研究人员和过程/产品设计人员优化其在不同工业应用中的工作。