The Ospreys are coming off an away loss to Leeds Tykes, while Edinburgh produced the upset of the first round with a thrilling win over defending Heineken Cup champions Toulouse.
Ospreys assistant coach Sean Holley said: "We were bitterly disappointed by the loss in Leeds last weekend.
"At the very least we thought the performance deserved a bonus point, which was taken away by the last kick of the match. However, on review of the game it is clear that we have lots of positives, including several missed opportunities to score tries.
"The players and coaching staff are still in a positive frame of mind about Friday's game, although Edinburgh will pose a completely new challenge. They will be revelling in their win over champions Toulouse, but we are determined to put things right on Friday night."
Ospreys fullback Gavin Henson is out for another three weeks with a broken hand, but he has had the cast removed and should be available for the Scarlets match on January 2.
Wales prop Duncan Jones has a fracture to the lower leg and some resulting cartilage damage. His recovery is progressing well and he is on track to also be available to face the Scarlets.
Paul James has a prolapsed disk injury and will have surgery in the new year. He will out of action for about four months
Neath-Swansea Ospreys; A Durston; S Terblanche, D Tiueti, S Gibbs (capt), S Williams; S Connor, A Williams; A Millward, H Bennett, A Jones, A Newman, L Tait, G Llewellyn, Gavin Thomas, J Thomas
Replacements; B Williams, P Jones, N Bonner-Evans, S Tandy, P Horgan, Matthew Jones, E Seveali'i.
Edinburgh Rugby;D Lee; C Joiner, M Di Rollo, B Laney, H Southwell; C Paterson, M Blair; A Jacobsen, D Hall, C Smith, N Hines, S Murray, T Blackadder (capt), A Hogg, S Taylor
Replacements; C Di Ciacca, R Mathieson, A Kellock, A Dall, G Burns, A Warnock, A Dickson.
Referee; David Pearson (England)