I used Procion dyes to dye the rayon part and my usual Alter Ego dyes for the silk part. I wanted to achieve different colors or at least different shades for a two-color effect.
The most successful result was by first dyeing the rayon with Procion dyes in the microwave. I used an indigo blue volor dye.
Then I dyed the silk part with Turquoise Alter Ego dyes on the stove in the usual way. The result was not quite what I was looking for because the Turquoise dye also colored the alredy-dyed rayon part so it is not as bright and dramatic.
Looks like more experimenting is in my future.