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.

Lucas-Washburn 方程是一个基本表达式，用于根据平均孔径、液体粘度、表面张力、接触角和时间来描述多孔材料中的毛细管上升。然而，传统方程高估了材料中液体的真实毛细管上升高度，因为它将孔模拟为直毛细管和圆形毛细管，但实际上多孔材料（如生物炭）具有不同孔形式的曲折毛细管。还已知纤维素材料的特征在于它们的溶胀能力，这也会影响毛细管上升过程。因此，开发了包括描述孔隙形状和膨胀参数（体积膨胀、能量损失系数和膨胀毛细管半径）的参数的修改模型。进行了生物过滤管中水毛细管上升的实验：由不同的主要原料制成的生物炭、颗粒的大小和生物介质的蒸汽改性。结果表明，由于相对最大误差较低，该模型适用于预测生物炭中短时间（直至 5 h）水毛细管上升过程。实验和建模结果都表明，较高的生物炭孔隙率、平均毛细管半径、体积膨胀和润湿性控制着较高的毛细管上升速度。同时，具有较高表面张力和动态粘度的液体会降低生物炭中的毛细管上升速度。结果表明，由于相对最大误差较低，该模型适用于预测生物炭中短时间（直至 5 h）水毛细管上升过程。实验和建模结果都表明，较高的生物炭孔隙率、平均毛细管半径、体积膨胀和润湿性控制着较高的毛细管上升速度。同时，具有较高表面张力和动态粘度的液体会降低生物炭中的毛细管上升速度。结果表明，由于相对最大误差较低，该模型适用于预测生物炭中短时间（直至 5 h）水毛细管上升过程。实验和建模结果都表明，较高的生物炭孔隙率、平均毛细管半径、体积膨胀和润湿性控制着较高的毛细管上升速度。同时，具有较高表面张力和动态粘度的液体会降低生物炭中的毛细管上升速度。