When a liquid drop spreads on an adaptive substrate the latter changes its properties what may result in an intricate coupled dynamics of drop and substrate. Here we present a generic mesoscale hydrodynamic model for such processes that is written as a gradient dynamics on an underlying energy functional. We specify the model details for the example of a drop spreading on a dry polymer brush. There, liquid absorption into the brush results in swelling of the brush causing changes in the brush topography and wettability. The liquid may also advance within the brush via diffusion (or wicking) resulting in coupled drop and brush dynamics. The specific model accounts for coupled spreading, absorption and wicking dynamics when the underlying energy functional incorporates capillarity, wettability and brush energy. After employing a simple version of such a model to numerically simulate a droplet spreading on a swelling brush we conclude with a discussion of possible model extensions.

当液滴散布在自适应基质上时，后者会改变其特性，这可能导致液滴与基质的复杂耦合动力学。在这里，我们为此类过程提供了一个一般的中尺度流体力学模型，该模型被写为基础能量函数上的梯度动力学。我们为在干聚合物刷上散布的液滴的示例指定模型细节。在那里，液体吸收到刷子中导致刷子膨胀，从而导致刷子的形貌和润湿性改变。液体还可以通过扩散（或芯吸）在刷子内前进，从而导致液滴和刷子动力学耦合。当基本的能量功能结合了毛细作用，可湿性和电刷能时，该特定模型说明了耦合的扩散，吸收和芯吸动力学。