The bubble-particle detachment interaction is critical to the flotation of coarse (composite) particles which has attracted significant research interest in recent years. It is principally controlled by the capillary forces arising from the deformation of the air–water interface that has been quantified employing the single-particle models. However, these single-particle models can be far away from the detachment in the actual flotation process in which the bubble surface is covered by many attached particles. Here, we investigate the effect of the presence of nearby (attached) particles on the interfacial deformation, thereby influencing the particle detachment from the laden interface. Specifically, the detaching force and the deformed interface shape were simultaneously recorded for a floating sphere at the center of a hexagonal lattice unit that comprised six spheres fixed at an initially planar air–water interface. The 3-dimensional Young–Laplace equation was numerically solved to determine the interface deformation, quantify the detachment process, and validate the model prediction for the detaching force. The results show that the effect of nearby particles called the constraint effect on the interface deformation and the detaching force is significant. The nearby particles confine the interface deformation around the test particle, thereby restricting the movement of the three-phase contact line (TPCL) on the particle surface, leading to smaller changes in the TPCL radius and displacement into the liquid phase during the detachment interaction than those in the absence of nearby particles. However, the change in the contact angle and polar angle of TPCL on the test particle is insignificant. The constraint effect reduces the tenacity which is critical to the stability of bubble-particle aggregates and was not expected. The results of this work provide useful details about the detachment and floatability of particles at the particle-laden interface, which is relevant in many industrial applications, including flotation separation.

气泡-颗粒脱离相互作用对于粗（复合）颗粒的浮选至关重要，近年来引起了重大研究兴趣。它主要由气-水界面变形产生的毛细管力控制，已使用单粒子模型进行量化。然而，这些单粒子模型可能与实际浮选过程中气泡表面被许多附着粒子覆盖的脱离相去甚远。在这里，我们研究附近（附着）颗粒的存在对界面变形的影响，从而影响颗粒从负载界面的脱离。具体来说，同时记录了六边形晶格单元中心的浮动球体的分离力和变形的界面形状，该单元由六个固定在初始平面空气-水界面的球体组成。对 3 维 Young-Laplace 方程进行数值求解以确定界面变形，量化分离过程，并验证模型对分离力的预测。结果表明，附近粒子对界面变形和分离力的影响称为约束效应。附近的颗粒限制了测试颗粒周围的界面变形，从而限制了颗粒表面三相接触线（TPCL）的运动，导致在脱离相互作用期间 TPCL 半径的变化和位移到液相中比没有附近颗粒时的变化更小。然而，TPCL在测试颗粒上的接触角和极角的变化是微不足道的。约束效应降低了对气泡颗粒聚集体稳定性至关重要的韧性，这是意料之中的。这项工作的结果提供了有关颗粒负载界面处颗粒分离和可漂浮性的有用细节，这与许多工业应用相关，包括浮选分离。约束效应降低了对气泡颗粒聚集体稳定性至关重要的韧性，这是意料之中的。这项工作的结果提供了有关颗粒负载界面处颗粒分离和可漂浮性的有用细节，这与许多工业应用相关，包括浮选分离。约束效应降低了对气泡颗粒聚集体稳定性至关重要的韧性，这是意料之中的。这项工作的结果提供了有关颗粒负载界面处颗粒分离和可漂浮性的有用细节，这与许多工业应用相关，包括浮选分离。