29 C.F.R. § 102.36

(a) An Administrative Law Judge may withdraw from a proceeding because of a personal bias or for other disqualifying reasons. Any party may request the Administrative Law Judge, at any time following the Judge's designation and before filing of the Judge's decision, to withdraw on grounds of personal bias or disqualification, by filing with the Judge promptly upon the discovery of the alleged facts a timely affidavit setting forth in detail the matters alleged to constitute grounds for disqualification. If, in the Administrative Law Judge's opinion, the affidavit is filed with due diligence and is sufficient on its face, the Judge will promptly disqualify himself/herself and withdraw from the proceeding. If the Administrative Law Judge does not disqualify himself/herself and withdraw from the proceeding, the Judge must rule upon the record, stating the grounds for that ruling, and proceed with the hearing, or, if the hearing has closed, the Judge will proceed with issuance of the decision, and the provisions of § 102.26, with respect to review of rulings of Administrative Law Judges, will apply.

(b) If the Administrative Law Judge designated to conduct the hearing becomes unavailable to the Board after the hearing has been opened, the Chief Administrative Law Judge, Deputy Chief Administrative Law Judge, or an Associate Chief Administrative Law Judge, as the case may be, may designate another Administrative Law Judge for the purpose of further hearing or other appropriate action.