Imbibition of Liquids through a Paper Substrate in a Controlled Environment

The physics of liquid spreading has become more complex when the surface is porous like paper or fabrics due to the evaporation of the liquid and swelling of the fibres. We have performed liquid imbibition experiments on paper strips in a controlled environment. The experimental results are compared to the existing analytical models that account for each effect separately. The existing models were found to be inaccurate in predicting the experimental results. We developed new analytical models by modifying existing models to predict the capillary rise of the liquid through the paper substrate accurately. Different effects, such as the barrier, evaporation, and swelling, are considered simultaneously while developing the models to mimic the exact practical situation. The modified models predict the experimental results more accurately than the existing models with a maximum prediction error of 10%. Finally, experiments with volatile (water) and non-volatile (silicon oil) liquids at various temperatures and under various relative humidity conditions are conducted to validate the analytical results.