We present a semianalytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of the quality factor of the two-dimensional (2D) cross-section resonance mode. This axial variation is determined analytically based on the numerical solution to the eigenvalue problem in the 2D cross section. The analysis is developed in two steps: First, we generalize a recently published expression for the 2D standing-wave resonance modes in a rectangular cross section to arbitrary shapes, including the viscous boundary layer. Second, based on these 2D modes, we derive analytical expressions in three dimensions for the acoustic pressure, the acoustic radiation and trapping force, as well as the acoustic energy flux density. We validate the theory by comparison to three-dimensional numerical simulations.

中文翻译：

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毛细管中微粒的声捕获理论

我们提出了一种半解析理论，用于在毛细管内具有任意横截面和在壁上进行超声激励的粘性流体中的声场和颗粒捕获力。我们发现，声场在长度尺度上轴向变化，该尺度与二维（2D）截面共振模式的品质因数的平方根成比例。该轴向变化是基于二维截面中特征值问题的数值解而解析确定的。该分析分两个步骤进行：首先，我们将矩形截面中2D驻波共振模式的最近发布的表达式推广到任意形状，包括粘性边界层。其次，基于这些2D模式，我们导出了三维的声压解析表达式，声辐射和捕获力，以及声能通量密度。我们通过与三维数值模拟进行比较来验证该理论。