1. In a large pot, cook bacon over medium heat until crisp. Remove bacon and set aside, leaving the drippings in the pot.
2. Add onions and celery to the pot and cook until softened, about 5 minutes.
3. Stir in potatoes and cook for another 5 minutes.
4. Pour in clam juice from the cans, add enough water to cover the vegetables, and bring to a boil. Reduce heat and simmer until potatoes are tender, about 15 minutes.
5. Add clams, milk, and heavy cream. Heat through but do not boil.
6. Season with salt and pepper to taste. Serve hot, garnished with the cooked bacon.