a fuel injection system for gas turbines is described including a pair of high pressure pumps. The pumps provide fuel and a carrier fluid such as air at pressures above the critical pressure of the fuel. A supercritical mixing chamber mixes the fuel and carrier fluid and the mixture is sprayed into a combustion chamber. The use of fuel and a carrier fluid at supercritical pressures promotes rapid mixing of the fuel in the combustion chamber so as to reduce the formation of pollutants and promote cleaner burning