What will happen to the earth when the sun turns into a brown giant?

Given that the sun’s size will increase, though not its mass, would the earth maintain its current orbital path, be sucked up by the sun, or would it move farther away? Would the sun evaporate the earth’s water? Would the process be swift once the main sequence is ended, or gradual over hundreds of millions of years?

PS I am also aware that the sun has billions of years of life left in her yet!