Lime water turns milky due to formation of CaCO3
Ca(OH)2 + CO2 → CaCO3 + H2O
Milkiness will disappear if continuously exhaling i.e., CO2 is passed due to formation of calcium bicarbonate.
CaCO3 + CO2 + H2O → Ca(HCO3)2
Milkiness will reappear if heating is done due to formation. CaCO3