What causes frothing in a radiator when the car is running?

The head gasket is gone or the block/head is cracked. Water is mixing with oil. If you remove the valve cover and the head or the intake manifold you may notice a fluid of a deep battleship gray color. This is due to grinding metal fillament mixing with the water and lubricant due to failed lubrication because chances are that you are losing oil if the block is cracked and engine coolant is mixing with water and oil or the head gasket, or the manifold seal is broken and may need to be replaced. An oil leak doesn't always mean that the block is cracked-- your problem could just be a broken head or manifold gasket. This is easy enough to replace but requires extensive dismantling of the top of the motor.