Varying microfluidic channel cross-sectional geometry can dramatically alter fluid flow behavior, particularly for capillary-driven flow. Most fabrication techniques, however, are planar and therefore incapable of providing depth-dependent variations in width. We introduce an ultrafast laser ablation technique that enables the fabrication of microchannels with arbitrary triangular cross sectional geometry. Triangular channels were fabricated with widths ranging from 45 to 116 mu m and aspect ratios between 0.7 and 1.9. This experimental platform was utilized to observe two-phase flow and evaluate the capillary pressures required to initiate flow within triangular capillaries. Applying Mayer, Stowe and Princen (MS-P) theory, critical drainage capillary pressures were predicted for varying cross sections and compared to experimental observations. Results indicate the capability to predict capillary pressures inside triangular channels with perfectly water wet surfaces, providing the first instance of experimental validation of the theory for arbitrary triangular cross sections. This work was extended to intermediate wet conditions, which provides an insight into the prediction of capillary pressure under more realistic conditions. The fabrication techniques and validation of predictive frameworks presented here provide an approach to microfluidic experimental design that will impact a wide range of fundamental and applied technology areas. (C) 2017 Elsevier Inc. All rights reserved.