The mixing of ingredients in a cake or bread is initially a mixture. When heated these ingrediaents react, releasing CO2 which makes the batter rise up. Most of the mixing moisture is driven out of the dough and leaves a soft spongy mass filled with little gas pockets. The cake dough has been transformed by the application of heat to form a compound
that is generally referred to as carbohydrate - starch
Pulling metal splinters from an eye is not a process of separation of one element or compound from another. It is not accomplished by a chemical process. The metal and organic material of the eye have not 'Mixed" as such. The metal is a foreign body imbedded in living tissue. The use of a magnet is purely a mechanical process to remove that object. IF - the metal is left there the tears will reduce it to rust which will then stain the cornea.
An air filter removes particulate matter from the air by making the passages through the filter smaller than the particals that you want to remove. Filters come in sizes measured in microns - referring to the size of the airborn particles that the filter will remove. Filters are not 100% in that if there is a hole for air to pass through a particle smaller than that hole will go through as well.
Osmosis deals with materials passing through a membrane. The pores in this membrane can act as a filter. Reverse osmosis is used in water filters to remove salt to make drinking water. It requires extreme high pressure and is a relatively slow - therefore - expensive process.
Less expensive - New techniques using less energy are being developed. You cannot get something for nothing. Any process that consumes energy for pumps, heating, cooling or any other process involving machinery will cost money. Processes that involve evaporation and natural condensation are basically free after you build the containment vessels. But as they rely on sun and temperature differentials - they are not reliable in volume of output.
Soaps are used to emulsify grease making it able to be absorbed by the water and removed. Different types of soaps or detergents are involved depending on the type of grease, the amount and whether manufactured or natural - like body oils or animal fat. Some chemicals are used to deliberately emulsify oils so they will stay in suspension in water. The mixtures are used to lubricate metal working machinery to prevent wear. Grease can be removed by solvents - that is material based on petroleum compounds that will dissolve the grease into a lighter, less dense fluid with a viscocity that enables it to flow away easily. Grease has a high viscosity that enables it to cling to virtually all surfaces. It is removed by breaking the bonds between the grease and the surface it is clinging to. You cannot "Separate" grease from steel since they have not mixed. The grease is a coating on the surface of the steel. Separation would be a method of removing the grease from the solvent by mechanical or chemical means.
It is the same as the steel splinter in they eye. The steel has not become part of the eye it is encapsulated within the eye - or a splinter in your finger. Foreign object and no mixing is involved as would be with solvent and grease. But not grease with steel - the two don't mix
I believe alcohol is used as a vehicle in perfume. It evaporates quickly leaving the oils and other scent essences on the skin. Remember that alcohol is miscible and can mix with either oil or water without changing the essential structure of the other fluid.
Because cold liquids will dissolve gas much better that warm liguids. The gas molecules are packed between the molecules of the soda. When the liquid gets warm the molecules separate and let the gas out easily. Pour some Coke or Pepsi carefully in a glass. Put one glass in referigerator and leave the other out for 30 minutes. The warm glass will be flat and the cold glass will still have some carbonation.
Acidic - You should know that. Certainly a car battery if filled with sulfuric acid. Otherwise there is nothing in common with the other two items. The bee sting is acetic acid and the Pineapple is ascorbic.