The freezing process of a sessile nanofluid droplet has been reported to behave differently from a pure sessile water droplet in terms of freezing dynamics and the final shape of the ice droplet. When nanoparticles are added to the water droplet, instead of forming a pointed tip on the top, the completely frozen droplet exhibits a flat plateau shape. To investigate this unique scenario, we developed a lattice Boltzmann (LB) model that combines the multiphase solidification model (MSM) with the immersed boundary method (IBM). The MSM is based on our previous work of simulating the freezing of a pure droplet, while the IBM is used to handle the interaction forces between the suspended particles and the different phases in the freezing droplet. Using this LB model, we succeeded in simulating the formation process of the frozen plateau shape. The simulation takes into account the dynamics of the dispersed particles, including their expulsion from the propagation freezing front and their segregation, which brings the liquid water to the edge. We compared the simulated freezing shape profiles with the experimental images and found that the shape forms in a similar manner. We then used the developed model to explore more cases, considering the effects of droplet contact angles and particle volume concentration. Results show that the distribution of particles and final droplet height depend on the surface wettability, as the freezing front exhibits a concave/convex shape on hydrophilic/hydrophobic surfaces, resulting in different particle separation distributions on the freezing front interface. Furthermore, our simulation results confirm the experimental conclusion that the plateau size on the frozen top increases with particle concentration and appears to be independent of the initial droplet contact angle.

据报道，固着纳米流体滴的冷冻过程在冷冻动力学和冰滴的最终形状方面与纯固着水滴的行为不同。当纳米颗粒添加到水滴中时，完全冻结的水滴不会在顶部形成尖头，而是呈现出平坦的平台形状。为了研究这种独特的情况，我们开发了一种晶格玻尔兹曼 (LB) 模型，该模型将多相凝固模型 (MSM) 与浸入边界法 (IBM) 相结合。MSM 基于我们之前模拟纯液滴冻结的工作，而 IBM 用于处理悬浮颗粒与冻结液滴中不同相之间的相互作用力。利用该LB模型，我们成功地模拟了冰冻高原形状的形成过程。该模拟考虑了分散颗粒的动力学，包括它们从传播冻结前沿的排出以及它们的分离，这将液态水带到了边缘。我们将模拟的冻结形状轮廓与实验图像进行比较，发现形状以类似的方式形成。然后，我们使用开发的模型探索更多案例，考虑液滴接触角和颗粒体积浓度的影响。结果表明，颗粒的分布和最终液滴高度取决于表面润湿性，因为冷冻锋面在亲水/疏水表面上呈现凹/凸形状，导致冷冻锋面界面上不同的颗粒分离分布。此外，