If I understand you correctly Anne, the thick egg white is opaque? The eggs from my
chickens have always had two "kinds" of egg white. A very thick part that appears to be surrounding the yolk, and a thinner runnier more liquid like outer egg white. The amount of these in my chickens eggs vary. When I crack them into the frying pan in the morning, sometimes it's mostly the thick part, appearing to hold a 1/4" high blob around the yolk, and other eggs I crack into the pan just run everywhere covering almost a quarter of my 12"
skillet. The albumen in my chickens eggs always seems transparent, though I have come across cloudy egg whites from other farm eggs I've purchased in the winter when my chickens aren't laying.