Del. Code tit. 25, § 5710

Where triable issues of fact are raised, they shall be tried by the court. At the time when an issue is joined, the court, at the application of either party and upon proof to its satisfaction by affidavit or orally that an adjournment is necessary to enable the applicant to procure necessary witnesses or evidence or by consent of all the parties who appear, may adjourn the trial, but not more than 10 days, except by consent of all parties.