How to use actors for database access and DDD?
Usually DB reading operations (cRud) can be performed directly by any actor. There is no need to make any special handling in most cases. Just a simple round-robin to balance the load.
As for update operations (CrUD), they can be split into non intersecting domains/shards. For instance, all operations with a single account should be preferably processed by a single actor. One may have N almost independent processing actors and a router that routes commands to one of them based on account.hashCode % N, for instance. Thus operations will be distributed between actors more or less evenly and every account will be processed sequentially.
P.S. Slick seems to be a descent db library for Akka applications.