For the analysis of falling film mass transfer such as gas absorption in liquid phase flowing over a vertical wall, conventionally an infinite penetration depth for penetrating component has been assumed. This assumption is originated from the fact that magnitude of diffusion depth is too small relative to the film thickness as if the mass transfer into the liquid film is taking place in a semi-infinite geometry. Despite its validity in the most engineering applications, it is still an unanswered question that ‘to what physically meaningful extent the diffusion may occur or the mass transfer boundary layer into the liquid film could progress alongside the wall, and consequently how it might affect the mass transfer characteristics’. We addressed such concern here by considering a finite depth of penetration into the film, derived governing equations for the continuity of mass and solved it analytically and numerically. The progress of penetration depth over the vertical coordinate i.e. flowing direction of falling film is observable as it approaches the film thickness far down the wall. The method gives the opportunity to examine the progress of the penetration depth with mass transfer properties such as diffusivity, average liquid velocity and etc. which have not been touched before.

为了分析降膜的传质，例如在垂直壁上流动的液相中的气体吸收，通常假设渗透组分的渗透深度是无限的。该假设源自以下事实：扩散深度的大小相对于膜厚度太小，就好像质量转移到液体膜中是在半无限的几何形状中进行的。尽管它在大多数工程应用中都是有效的，但仍然没有一个悬而未决的问题，即“扩散可能发生到什么物理上有意义的程度，或者传给液膜的传质边界层可能会沿着壁前进，因此，它如何影响质量？传输特性”。我们在这里通过考虑有限的渗透深度来解决这种担忧，推导了质量连续性的控制方程，并进行了分析和数值求解。可以观察到穿透深度在垂直坐标（即降膜的流动方向）上的进展，因为它接近壁深处的膜厚。该方法提供了检查渗透深度的进展的机会，该渗透深度具有诸如传质，平均液体速度等以前从未接触过的传质特性。