Particle migration and alignment in slot coating flows of elongated particle suspensions

Abstract

We analyze slot coating flows of elongated particle suspensions and investigate particle concentration and average orientation at the coated film. Shear‐induced particle migration is described by the Diffusive Flux Model, and particle orientation is given by the principal direction of the particle conformation tensor. The conformation evolution and the constitutive equation for the resulting complex liquid are adapted from classical models that describe the behavior of suspensions of cylinders and fibers and polymeric solutions of almost rigid rod‐like molecules. The proposed fully coupled model is applied to slot coating flows, and is solved using the DEVSS‐TG/SUPG finite element method. The results show that the wet coated film is highly nonuniform. Particle concentration and orientation vary along the film thickness and are a strong function of the operating parameters of the process, such as the film thickness‐to‐coating gap ratio and the capillary number of the flow. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3187–3198, 2017

Microstructure evolutions in lithium ion battery electrode manufacturing

“…电极制造技术 [38] ，直接对活性颗粒、黏结剂、导电剂粉末进行混合，其中黏结剂是以纤维状存在， 活性颗粒与导电剂之间接触紧密，电极密度大、导电性好、容量高 [39,40] 。但干法电极在粉末混合 工艺上仍需解决大分子量黏结剂开发、多组分电极材料均匀分散、高强度剪切作用下活性颗粒完整 性等关键问题，才能有望实现工业大规模应用 [41] 基础上，还研发出"金属导电层-高分子支撑层-金属导电层"三明治结构复合集流体，具有"高安 全、高比能、长寿命"等优势。目前常用的电极涂布方法包括辊涂、刮刀涂、狭缝挤压涂布等，其 中狭缝挤压式涂布是一种高精度预计量涂布技术，具有速度快、精度高等特点 [43] ，成为于锂电池 极片涂布的主流工艺 [44] 。 在挤压涂布过程中，高固含量(＞40wt%)的浆料通过狭缝挤出流动成形，电极涂布间隙小(＜ 200 μm) [45] 、剪切速率高(＞1000 s -1 ) [45] 、活性颗粒尺寸(如负极球状石墨 d50≈20.4 μm) [46] 相对涂布 间隙与涂层厚度(60~150 μm)较大、且形态复杂(片状石墨、球形磷酸铁锂等)。在流场剪切作用下， 活性颗粒易发生迁移，从而形成非均匀分布的孔隙结构。研究表明，宏观涂布流场剪切诱导的介观 活性颗粒易迁移会导致孔隙大小分布不均匀，严重时甚至会导致涂层缺陷 [45] 。然而高固含量的浆 料呈现非牛顿流体特性，导致涂布中颗粒迁移行为与孔隙结构形成过程十分复杂。尽管颗粒迁移在 平板泊肃叶流动、库艾特流动等简单流场中的迁移行为已被广泛研究 [47] ，并通过电容层析成像 [48] 、 光学相干层析成像 [49] 与超声测量方法等技术直接观测颗粒浓度分布，但受限于狭缝挤出涂布空间 限制、非牛顿流动特性、模腔封闭且不透明等原因，仍然无法通过现有检测方法进行在线检测，通 过简单宏观流场分析或者直接试验测量分析孔隙结构的演化过程仍然十分困难。 现有研究多采用数值模拟分析宏观涂布流场中的介观颗粒迁移行为，如 Carvalho 研究组 [50,51] 系统地分析了颗粒初始浓度、颗粒形态与涂层湿厚等参数对宏观涂布流场中颗粒浓度分布的影响规 律，由于欧拉法将颗粒处理为分散相，仅考虑了低固含量(<10%)颗粒在宏观涂布流场中的流动行为， 忽略颗粒的实际大小，这与实际电极浆料体系存在一定偏差。当颗粒固含量偏高时，利用欧拉法将 颗粒处理为分散相会引起过大的预测误差，需要采用拉格朗日法精确地跟踪介观颗粒的迁移行为。 A c c e p t e d https://engine.scichina.com/doi/10.1360/TB-2021-1069 采用拉格朗日法跟踪介观颗粒迁移的难度在于：在受限空间、高固含量条件下，宏观流场与介观颗 粒迁移演化过程是高度耦合的，介观颗粒迁移依赖于宏观涂布流场的剪切作用，颗粒迁移又会导致 浆料浓度与黏度变化 [50] 。在宏观流场与介观颗粒迁移的共同作用下，涂层中会形成非均匀分布的 组分结构。因此，高固含量浆料在宏观涂布流场中介观活性颗粒的迁移行为仍有待深入研究。 当宽幅高速涂布时，为保证涂层组分的均匀性，就需要综合考虑涂布速度、流速、真空压力、 涂布间隙、浆料黏度和表面张力等多因素影响 [43] 。现有研究主要采用理论模型、流体动力学仿真 等方法建立涂布窗口，如最早由 Ruschak 等人 [52] 根据真空压力下涂布液珠破裂的临界条件提出了 毛细管模型，并建立最低压降与最薄涂层厚度控制的涂布工艺窗口(图 3a, b)。此后，Higgins [53] 、 Jang [54] 、Lee [55] 、Bhamidipati [56] 等人大量研究者在此基础上建立了考虑表面张力、黏性力、黏弹性 作用的黏性/黏弹性等毛细管模型，适用于牛顿、非牛顿等具有复杂流变特性的电极浆料体系。但 上述理论模型简化了实际的浆料流动行为，并假设上下弯月面固定在模唇边角，导致与实际涂布工 艺窗口存在一定误差。如 Schmitt 等人 [45] 采用实验研究了高黏度石墨负极浆料的最小涂覆厚度，结 果表明在不同涂布速度下，大颗粒引起的团聚可能引起下游弯液面的破裂，这与理论模型存在一定 误差，并且涂层表面粗糙度随涂覆厚度降低而增大(图 3c)。同时，除了由涂布液珠破裂/泄露引 起的涂布失稳外，还有由颗粒团聚、集流体移动、浆料黏弹性等因素引起的涂布缺陷，包括规律竖 /横条纹、厚边、橘皮、划痕等(图 3d)。此外，涂覆过程中工艺参数的波动、外界扰动引起涂层 厚度不均匀也是研究与工业生产关注的重点，其中工艺参数波动主要包括进口流量、真空压力、背 辊精度引起的涂覆间歇波动等。Romero 等人 [57] 采用数值模拟方法研究了周期性扰动对浆料流速与 涂层厚度的影响，发现响应是施加的扰动频率和模具几何形状的函数，通过优化模具几何形状可以 减小涂层厚度的波动。Lee 等人 [58] 采用黏性毛细管模型与流体动力学模拟方法研究了不同扰动对涂 层厚度波动的影响，发现对于牛顿流体，涂布间歇扰动对波动的影响在高频时显著增大，而对于非 牛顿流体，低频时流量和涂布速度扰动对振幅影响较大，高频时受涂布间歇和涂布压强扰动影响更 大。 A c c e p t e d https://engine.scichina.com/doi/10.1360/TB-2021-1069 图 3 电极涂布工艺窗口与缺陷. (a) 单层狭缝涂布液珠 ...…”

Computational study of planar extrudate swell flows with a viscous liquid–gas interface

“…The method has been successfully used to study different free surface flows of Newtonian liquids, 9,17-21 viscoelastic polymer solutions, [22][23][24][25][26] and particle suspensions. [27][28][29][30][31] We present a brief review of the overall numerical scheme in this section. The interested reader can find more details elsewhere (e.g., see Pasquali 32 and the references therein).…”

Shear-induced particle migration in the flow of particle suspensions through a sudden plane expansion

“…In addition to that, the singularity of the particle transport equation as the local shear rate approaches zero was treated using the non-local contribution to the shear stress [29][30][31]. This version of the DEVSS-TG formulation together with finite element basis functions has been successfully used in recent studies of particle migration in complex flows of particle suspensions and more details can be found elsewhere [33][34][35][36].…”

“…Another problem is related to its numerical implementation, since the model becomes singular as the local shear rate approaches zero, as occurs near the symmetry plane of pressure-driven flows through tubes and channels [29,30]. However, because of its relative simplicity, good accuracy and low computational cost, the diffusive flux model has been extensively used to study particle migration in many different problems involving complex flows, such as flows through two-and three-dimensional bifurcations [31,32], free-surface flows [33,34], and flows of suspensions with non-spherical particles [35,36]. Alternative approaches have also considered variations of the diffusive flux model to study particle migration in suspensions with a non-Newtonian continuous phase [37,38].…”