Walnut trees do have spring sap flows. Did you have the tree pruned recently? Otherwise you probably had some branches break during spring storms and that is the cause.  Any pruning is best left to early through midsummer to prevent this.  Pruning weak branches then may help to prevent breakage in spring and subsequent sap flows. Hopefully they are done dripping sap for the season.  An onsite visit from an arborist can confirm this and offer pruning recommendations. 
1. https://extension.umn.edu/planting-and-growing-guides/how-hire-tree-care-professional
2. https://www.treesaregood.org/
 
Taping walnut trees for syrup is done but probably wouldn’t prevent this if you have a lot of branch breakage from spring storms.  The websites give an in-depth explanation of how to tap walnut trees if you are interested. 1.https://cdn.future.edu/wp-content/uploads/2022/09/Walnut-Research-Paper.pdf
2. https://smallfarms.cornell.edu/2016/01/tapping-walnut-trees/

I don’t see a lot of broken branches and we haven’t pruned lately. Is the dry weather a possible factor?

Margaret



This could be a factor, especially if it is primarily the north side of the trees.  What happens is that lack of sufficient water in the fall means that trees overwinter in a moisture deficit.  Then spring comes and without rains to push the water to the tree branches they don’t really wake up and have the usual sap flow until later. There is probably some other factor like frost cracks, or insect damage or storm damage that would push the sap out.  
Another possibility is that the tree is infested with pests like aphids.  They produce a sticky substance called honey dew.  Aphids are easy to get rid of. A strong water spray knocks them out of the trees and because they can’t fly, they stay mostly on the ground.   other pests may produce cankers that would allow sap leaks.

Without pictures of the tree and possible insects we cannot accurately assess what is causing this. Your best strategy is to have an onsite visit by a tree professional who can look for possible insects and different types damage.

The leaves of the black walnut trees are covered with stickiness just like the furniture on the deck.  

Margaret



Just the lower leaves or all the leaves?  What does the sticky material smell like? Is it black or dark colored? Can you get a pair of binoculars and check for areas along the branches that are sunken? These are the kinds of things an onsite professional would be able to assess.