The liquid in foam forms an interconnected network, which is composed of Plateau borders, nodes, and films. One of the dominant pathways for foam drainage is flow through Plateau borders, and we use confocal microscopy to obtain experimental results for the flow fields inside individual Plateau borders. For three types of surfactants detailed comparisons are made with a model based upon the influence of surface viscosity at free boundaries between the gas in the bubbles and the liquid in the Plateau borders. The model describes the flows well, and we find good agreement between the surface viscosity predicted by this model and representative values found in the literature. We also give a qualitative description of the flow in the nodes.