Abstract One of the most widely used techniques for evaluating the wettability of powdered foods is the capillary rise method, in which the contact angle is usually estimated using the classical Washburn model. However, this model does not take into account the effect of the dissolution of the particle bed in the rising process, which is an important limitation for its application to many powdered foods. This work presents a new mathematical model for the analysis of capillary rise data considering the partial dissolution of the particle bed. As in the case of the classical Washburn model, the proposed model, designated Dissolution-Modified Washburn Model (DM-Washburn), was obtained by the integration of the Navier-Stokes equation, but introducing a dependency of the capillary diameter as a function of meniscus position and time as a strategy to quantify the dissolution effects. The comparison between the DM-Washburn and the classical Washburn models in terms of quality of fit was performed using experimental data of capillary rise in d -(+)-glucose and lactose using as wetting liquids pure water and aqueous solutions of these two materials with concentrations up to saturation. The DM-Washburn model provided better fit to the height versus time data, with mean relative deviation (MRD) values lower than 5% for all tested conditions. Further, the estimates of contact angle obtained with the DM-Washburn model showed to be independent of the carbohydrate concentration in the wetting liquid, differently from what was observed using the classical Washburn model. Additionally, tests with microcrystalline cellulose (MCC), a water insoluble material, showed the consistency of the DM-Washburn model in conventional capillary experiments, i.e., without significant dissolution of the particle bed. The obtained results indicate that the model has great potential for evaluating the wettability of soluble materials.

中文翻译：

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部分可溶颗粒床中液体毛细上升的数学模型

摘要 评估粉状食品润湿性最广泛使用的技术之一是毛细管上升法，其中接触角通常使用经典的沃什伯恩模型估计。然而，该模型没有考虑颗粒床在上升过程中溶解的影响，这是其应用于许多粉状食品的重要限制。这项工作提出了一种新的数学模型，用于分析考虑颗粒床部分溶解的毛细管上升数据。与经典的沃什伯恩模型一样，所提出的模型，称为溶出修正沃什伯恩模型 (DM-Washburn)，是通过纳维-斯托克斯方程的积分获得的，但引入毛细管直径作为弯液面位置和时间的函数的依赖性作为量化溶解效应的策略。DM-Washburn 模型与经典 Washburn 模型在拟合质量方面的比较是使用 d -(+)-葡萄糖和乳糖的毛细管上升实验数据进行的，使用纯水和这两种材料的水溶液作为润湿液浓度达到饱和。DM-Washburn 模型更好地拟合了高度与时间的数据，所有测试条件下的平均相对偏差 (MRD) 值都低于 5%。此外，使用 DM-Washburn 模型获得的接触角估计值表明与润湿液体中的碳水化合物浓度无关，这与使用经典 Washburn 模型观察到的不同。此外，使用微晶纤维素 (MCC)（一种水不溶性材料）进行的测试表明，DM-Washburn 模型在常规毛细管实验中具有一致性，即颗粒床没有显着溶解。所得结果表明该模型在评价可溶性材料的润湿性方面具有很大的潜力。