Modelling of a Capillary Rise Height of Biochar by Modified Lucas–Washburn Equation

Lucas–Washburn equation is a fundamental expression which is used to describe capillary rise in porous materials according to average pore radius, liquid viscosity, surface tension, contact angle and time. However, a traditional equation is overestimating a real capillary rise height of liquid in the material, since it models pores as straight and circular capillaries, though in reality porous materials, such as biochar, have tortuous capillaries with different aperture forms. It is also known that cellulosic materials are characterised by their swelling capacity, which also can affect the process of capillary rise. Therefore, a modified model including a parameter describing the pores’ form and swelling parameters (volumetric swelling, energy loss coefficient and radius of swelled capillary) was developed. Experiments of water capillary rise in the biofilter tubes were conducted: the biochar made from different primary feedstocks, size of particles and modifications with steam of the biomedia. It was shown that the model is suitable for the prediction of short time (until 5 h) water capillary rise process in biochar due to low relative maximum error. Both experimental and modelling results showed that higher biochar porosity, average capillary radius, volumetric swelling and wettability govern higher velocity of capillary rise. Meanwhile, liquids with higher surface tension and dynamic viscosity lower the capillary rise speed in the biochar.