We examine the challenges and advantages of using an actor framework for programming and execution of scientific workflows. The following specific topics are studied: implementing workflow semantics and typical workflow patterns in the actor model, parallel and distributed execution of workflow activities using actors, leveraging event sourcing as a novel approach for workflow state persistence and recovery, and applying supervision as a fault tolerance model for workflows. In order to practically validate our research, we have created Scaflow, an Akka-based programming library and workflow execution engine. We study an example workflow implemented in Scaflow, and present experimental measurements of workflow persistence overhead.