Possibly the following slime flux, but that is not something I could be sure it is from your description.
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http://shadetreeexpert.com/tree-diseases/
Curiously, wetwood and the associated slime flux help protect the infected tree. The bacterial growth creates conditions in the wood and slime that inhibit wood decay organisms. Furthermore, if the slime flux continues to flow over a number of years, the liquid that is toxic to other organisms can discolor the bark, kill moss and lichens on the bark and even kill grass at the base of the tree. The stain on the bark can be either light or dark color. There is no treatment for slime flux but that fact may not stop insistent garden center sales clerks from selling homeowners "a cure" anyway. In the past arborists would insert a tube in the tree to allow the slime flux to flow more freely and drip onto the ground. But this technique is no longer recommended because it doesn't improve the problem and the hole for the tube is just one more injury to the tree.
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Disease and Fungus
Be on the lookout for bark diseases in globe willow. One of the worst is slime flux disease. Symptoms include a smelly, frothy slime that oozes from branch bark. The ooze is from bacterial activity inside the branch, which forces sap out under pressure. There's no cure for slime flux. All you can do is make sure the tree gets enough water, and prune away the dead and diseased wood wherever you can. Clean pruning tools after use to avoid transmitting disease to other trees.
https://www.hunker.com/13428992/natural-problems-of-globe-willow-trees
https://www.hunker.com/13428992/natural-problems-of-globe-willow-trees
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