A capillary surface bound by a solid rectangular channel exhibits dynamic wetting effects characterized by a constitutive law relating the dynamic contact-angle to the contact-line speed through the contact-line mobility \(\Lambda \) parameter. Limiting cases correspond to the free (\(\Lambda =0\)) and pinned (\(\Lambda =\infty \)) contact-line. Viscous potential flow is used to derive the governing integrodifferential equation from a boundary integral approach. The spectrum is determined from a boundary value problem where the eigenvalue parameter appears in the boundary condition. Here we introduce a new frequency scan approach to compute the spectrum, whereby we scan the complex frequency plane and compute the system response from which we identify the complex resonant frequency. Damping effects due to viscosity and Davis dissipation from finite \(\Lambda \) do not attenuate signal response, but rather shift the response poles into the complex plane. Our new approach is verified against an analytical solution in the appropriate limit. We identify the critical mobility that maximizes Davis dissipation and the critical Ohnesorge number (viscosity) where the transition from underdamped to overdamped oscillations occurs, as it depends upon the static contact-angle \(\alpha \). Our approach is applied to a rectangular channel, but is suitable for a myriad of geometric supports.

由实心矩形通道包围的毛细管表面表现出动态润湿效应，其特征在于通过接触线迁移率\(\Lambda \)参数将动态接触角与接触线速度相关联的本构定律。限制情况对应于自由（\(\Lambda =0\)）和固定（\(\Lambda =\infty \)) 联络线。粘性势流用于从边界积分方法导出控制积分微分方程。频谱由边界值问题确定，其中特征值参数出现在边界条件中。在这里，我们引入了一种新的频率扫描方法来计算频谱，从而扫描复频率平面并计算系统响应，从中我们可以识别复谐振频率。由于粘性和戴维斯耗散从有限\(\Lambda \)引起的阻尼效应不会衰减信号响应，而是将响应极点移动到复平面中。我们的新方法在适当的限度内针对解析解进行了验证。我们确定了使戴维斯耗散最大化的临界迁移率和临界 Ohnesorge 数（粘度），其中发生从欠阻尼到过阻尼振荡的转变，因为它取决于静态接触角\(\alpha \)。我们的方法适用于矩形通道，但适用于无数几何支撑。