We propose a new method for finding the exact analytical solution in Laplace domain for the problem where a particle is diffusing on a flat potential in the presence of a rectangular sink of arbitrary width and height. In our model, diffusive motion is described by the Smoluchowski equation. Our method with this sink of rectangular shape is very general and can be used to deal with other potentials. We have derived exact analytical expression for rate constants using our model. This is the first model where the exact analytical solution in closed form is found in the case of a sink of arbitrary width. This model is more realistic for understanding reaction–diffusion systems that all other existing models available in literature.

对于存在任意宽度和高度的矩形水槽的情况下，粒子在平面势上扩散的问题，我们提出了一种在拉普拉斯域中找到精确解析解的新方法。在我们的模型中，扩散运动由Smoluchowski方程描述。我们使用这种矩形水槽的方法非常通用，可用于处理其他电位。我们使用我们的模型得出了速率常数的精确解析表达式。这是第一个模型，在任意宽度的水槽情况下，都可以找到封闭形式的精确解析解。与文献中所有其他现有模型相比，该模型对于理解反应扩散系统更为现实。