The main reason for the roux is to keep the flavours in a less diluted form. We want the sauce to adhere to the food so we can have a better taste of the food and to prevent the showing of the dry nature of the food. We can have reduction which does not involve flour. The sugar in the reduction process would thicken the sauce to its desirable state. 

Since we are talking about thickening agent, we can examine other thickening agents. Besides from flour, we can use oil and of course eggs. The sauce made from eggs and clarified butter forms the next group of Hollandaise sauces. The same as before, we have 

Clarified butter + egg yolks + lemon juice = Hollandaise

Since eggs are mainly protein and they do not react well with high heat, we use steam to warm up the egg yolks and we temper the eggs with warm clarified butter. We simply put the bowls with the eggs onto of another bowl with water at low heat. The steam would keep the eggs warm while we whip them frothy. We use another pan / pot to keep the clarified butter warm as well before we dripped the butter into the egg yolks while we continuously whip up the mixture. The result is a warm, luscious, golden sauce that compliment so well with vegetables, seafood, fish and also food of egg nature. 

Please use caution when you are whipping the eggs so you would not over whip. The temperature of the butter has to be lukewarm or else it would cook the egg yolks instantly and you ended up with scrambled eggs. Tempering means to even out and tone down the temperature with small amount before mixing everything together. An electric mixer would be helpful at this stage. 

Eggs Benedict with Hollandaise sauce!