Abstract In this work, a new model is introduced to determine the crossflow velocity required to dislodge permeating oil droplets at the surface of a membrane. Oil droplets at the surface of a membrane face either of four fates; namely, pinning, permeation, rejection, or breakup. The conditions at which the first three fates are realized have been, to a large extent, satisfactorily explored. The conditions for the breakup, however, do not seem to be very well defined. Although there exist few attempts to define conditions for breakup by crossflow field, they seem insufficient and lack consistency with the physics. It is, therefore, the aim of this work to provide elaborate analysis based on a clear understanding of the physics involved and the forces contributing to the breakup. A mathematical formula is developed to estimate that critical crossflow velocity at which break up occurs. This formula is derived based on the balance of torques that are generated by the interplaying forces. These forces are essentially surface tension forces and drag force. When the droplet encounters a pore opening it forms an interface and if the pressure across the opening is larger than the entry pressure, the interface advances inside the pore. When the receding interface of the droplet reaches the pore opening, the droplet pauses and anchors itself by that portion of the droplet in the pore. The droplet then continues to deform in accordance with the interplay of the imposed drag force and the generated surface force. The droplet wraps around the pore opening and the central angle of encounter increases per the imposed drag force. When the central angle of encounter reaches π radians, this represents the critical configuration beyond which the droplet breaks down to two parts. As the droplet deforms while anchored in its place, the contact line around the pore opening uncover the surface and starts to contribute towards the torque about the pivoting point. The balance of torques generated by the drag force and the interfacial force at that portion of the contact line, which makes a central angle of π radians, is used to determine that critical velocity beyond which the droplet breaks up. Several verification exercises are conducted using computational fluid dynamics (CFD) analysis to build confidence in the derived formula of the critical crossflow velocity. Based on the comparisons, the newly derived formula compares very well with the data obtained using CFD analysis.

中文翻译：

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横流过滤中渗透油滴在膜表面破裂的开始研究：新模型和 CFD 验证

摘要 在这项工作中，引入了一种新模型来确定驱除膜表面渗透油滴所需的错流速度。膜表面的油滴面临四种命运之一：即钉扎、渗透、拒绝或分手。实现前三种命运的条件在很大程度上已得到令人满意的探索。然而，分手的条件似乎并不十分明确。尽管很少有尝试定义横流场破裂的条件，但它们似乎不够充分并且与物理学缺乏一致性。因此，这项工作的目的是基于对所涉及的物理学和导致分裂的力量的清晰理解，提供详细的分析。开发了一个数学公式来估计发生破裂时的临界横流速度。该公式是根据相互作用力产生的扭矩平衡推导出来的。这些力本质上是表面张力和拖曳力。当液滴遇到孔隙开口时，它会形成一个界面，如果穿过开口的压力大于进入压力，则该界面会在孔隙内前进。当液滴的后退界面到达孔口时，液滴会暂停并通过孔中的那部分液滴将自身锚定。然后液滴根据施加的阻力和产生的表面力的相互作用继续变形。液滴环绕孔隙开口，并且遇到的中心角随着施加的阻力而增加。当相遇中心角达到 π 弧度时，这代表了液滴分解成两部分的临界构型。随着液滴在固定在其位置时变形，孔口周围的接触线露出表面并开始对围绕枢轴点的扭矩做出贡献。由阻力和接触线那部分的界面力产生的扭矩的平衡，使中心角为 π 弧度，用于确定液滴破裂的临界速度。使用计算流体动力学 (CFD) 分析进行了几次验证练习，以建立对临界横流速度推导公式的信心。根据比较，新推导出的公式与使用 CFD 分析获得的数据非常吻合。