To flow or leak out or emit something slowly
The tears continued to seep down Julie's cheeks but she didn't sob.
Slowly the facts were beginning to seep through the layer of shock.
When I looked over at my wife I could see a tear seep down her cheek.
Silicone cleaners can seep into the finish and create a barrier that won't allow a stain or lacquer to bond with the furniture, making it impossible to refinish or touch-up.
Contact dermatitis is an allergic reaction to something that irritates the skin and is manifested by one or more lines of red, swollen, blistered skin that may itch or seep.