A model for capillary rise in micro-tube restrained by a sticky layer

Fluid transport in a microscopic capillary under the effects of a sticky layer was theoretically investigated. A model based on the classical Lucas-Washburn (LW) model is proposed for the meniscus rise with the sticky layer present. The sticky layer consists of two parts: a fixed (located at the wall) and a movable part (located on the inside of the capillary), affecting the micro-capillary flow in different ways. Within our model, the movable layer is defined by the capillary radius and pressure gradient. From the model it follows that the fixed sticky layer leads to a decrease of capillary radius, while the movable sticky layer increases flow resistance. The movable layer thickness varies with the pressure gradient, which in turn varies with the rising of the meniscus. The results of our theoretical calculation also prove that the capillary radius has a greater effect on the meniscus height, rather than the additional resistance caused by the movable layer. Moreover, the fixed sticky layer, which affects the capillary radius, has a greater influence than the movable sticky layer. We conclude that the sticky layer causes a lower imbibition height than the LW model predicts.