Influence of the Pore Radius on the Penetration Depth of Inks in Binder Jetting—A Modification of the Washburn Equation

In binder jetting (BJ), an ink is inserted layerwise into a powder bed to selectively bond the particles in the cross-section of a part. By predicting the penetration depth of the ink, the ideal layer thickness for BJ can be set. Each layer should be penetrated with ink. Insufficient penetration will result in a poor layer bond and a low strength of the part; over-penetration will impede a dimensionally accurate production, as the ink will leak from the sides of the part and unintentionally solidify the powder in these areas. The Washburn equation has been used for the calculation of the penetration depth in various fields, such as hydrology or with loose powders. However, a transfer to the BJ process is difficult due to the preferably compact powder bed and the fine particles. In more compact powder beds, the small radii with their greater capillary pressure and their distribution in the layer have a high influence on the penetration depth. This work shows an adaptation of the Washburn equation for powder beds in BJ and a new approach to determine the effective pore radius for calculating the penetration depth. A weighted pore radius was introduced, which accounts for the spatial distribution of the pores in the powder bed and the acting capillary pressure. The validation was performed with two different powders by experimentally simulating the BJ process through the infiltration of a drop into a powder bed. The weighted radius was used in the Washburn equation to calculate the penetration depth. The results were compared with those models from the literature and experimental data, and a good agreement between the calculation and the experiment was found