A surgical drain device includes an adhesion matrix of biodegradable polymer material and a plurality of drain tubes attached to the matrix. The device is implanted within a surgical wound to treat the presence of seromas, for example, and is used to promote drainage, tissue adhesion, and wound closure. The drain tubes converge into a common collection tube that leads wound fluid outside the body under gravity feed or negative pressure applied to the collection tube. The matrix contains an array of apertures that allow tissue contact across the device. The device also can include a coating of surgical adhesive and a tissue anchoring system of hooks or barbs. The device and systems containing the device are particularly useful to promote the healing of surgical wounds from abdominal surgery.