is it possible to dye a nylon backed gortex membrane?
The Goretex® itself is a porous PTFE membrane, the same material as is in Teflon®. It cannot itself be dyed, but this is not an issue since the fragile membrane is always covered by another fiber, such as nylon in your case. The problem is that, typically, the fabric surrounding the Goretex has been treated with a water-resistant finish, generally known as a DWR (Durable Water Repellent) coating. Why? The Goretex itself is water resistant, but it cannot let water vapor out with any degree of efficiency if the outside of the fabric is coated with water. In addition, the weight of the water that wets the fabric can be sufficient to be quite uncomfortable. Any coating which prevents dye from reaching fabric will cause your colors to come out pale and/or splotchy. This means that chances are not particularly good that you can successfully dye your jacket. Even old DWR coatings can often be revived by drying in a hot dryer, so it probably has not worn off enough to allow for good dyeing. In
