Assuming that the second hard disk has a directory mount point: /data, which is usually the data disk.
First stop the running docker:
sudo systemctl stop docker
Moving data to a second hard disk
sudo rsync -aP /var/lib/docker/ /data/docker
Rename the old directory (just in case, you can leave it alone):
sudo mv /var/lib/docker /var/lib/docker_old
Creates a connection symbol:
sudo ln -s /mnt/vdb/docker /var/lib/docker
Restart the Docker service:
sudo systemctl start docker
Validation:
docker info
Cleanup, can be done without:
sudo rm -rf /var/lib/docker_old