I have very little experience in fluxing, and have practically no experience in assay, although I have tried playing with these a little.
Flux a broad term to describe a mix of materials added to a melt (or to welding, brazing or even soldering), flux came from the word to flow, it can have different properties depending on what we are trying to do with it, I wont describe welding or soldering here, as we are more concerned with melting metals and other gangue material like Ore, or in this case polishing waste which contains values.
Normally we will start with a basic flux, which will normally contain some basic chemicals, chosen because of how they can help to make our melt "flow" or to become fluid, and also provide us with a molten glass slag (silicates that will absorb metals into this glass).
A basic flux normally will contain three main ingredients such as suggested by Hokes:
5 parts soda ash (sodium carbonate Na2CO3, also called washing soda),
4 part borax glass (Sodium tetraborate Na2B4O7),
2 parts Ground glass (window glass or quartz silica...)
I will try to tell some of why these are in the basic flux.
With flux we want to help make the melt flow or to become fluid, this is important for the melt to mix, as what we are doing is a chemical reaction with in this melt, and we want the reaction to be able to mix the ingredients in our chemical reaction, we want metals and acids or bases to combine, oxidizers to oxidize some and reducers to reduce others, we want unwanted metals to oxidize and the acid glass silicates to form a glass slag of metal oxide silicates, we want the more precious metals, or metals we are using as collectors to combine with the values, or just metals we are trying to reduce back to metal to combine in the melt and reduce to molten metals. The flux being fluid is important for the mixing and combining of chemicals and metals, and for the metals once combined to be able to combine and sink in the melt by gravity, and for the metals to become oxidized and to form glass silicates (slag that can float to the top of the melt), fluxes can also help in changing the temperature at which things will fuse or melt, than they may otherwise.
The three ingredients above can help to make the melt fluid, and the have other properties to list some:
Borax can help to protect the melting crucible from metals adhering, help the melt to flow, it can act as an acid flux, and help in slagging, can act as a shield to help keep out atmospheric oxygen or oxygen from the torch or furnace burners and so on, it is also helpful with iron, magnesia, zinc oxides...
Sodium carbonate, A basic flux, when melted with silica gives off CO2, to help form make the silicates more fusible, and to help form the sodium silicate compounds (slag glass) important to form or absorb the base metals oxides as silicates in the glass slag, soda ash can also act as a desulfurizer (important for many Ores).
Crushed glass, (SiO2) silica (such as white sands) or quartz provide the main ingredient for our slag, to help form silicate base metal glass slag,
SiO2 silica is a very strong acid flux which combines with metal oxides to form silicates (slag’s, or metal slag glass), silica can also help to protect crucibles from attack from other ingredients in a flux chemistry (such as litharge which will dissolve the crucible), silica can aid in fusion of things.
Using way too much silica can also cause loss of values in the Matte; it is an acid flux that can also act as an oxidizer.
Also your material you are melting can be high in silica so you may not need to add much as flux.
The above just gives us some basic ingredients to our flux; we may need some other chemicals or ingredient added to help the chemistry of our melt depending on the material we are melting.
First we may need to know, or understand some of the chemistry of what it is we are melting, in an assay they will test the material they will assay to get an idea of what its chemistry may react in a melt, is it oxidizing or reducing in nature, like will it oxidize lead to litharge, or will it reduce litharge to metal lead, this can be important to know as if the material is an oxidizing nature it can easily oxidize base metals, or if it is reducing can reduce base metals, it can also react with our basic flux changing the properties of flux.
Remember we are not just melting a chemical mix of flux but our Ore (as an example) or polishing sweeps also have a chemistry they add to the melt, this chemical reaction is done at high heat, and can be acidic or caustic, oxidizing or reducing, basically a chemical reaction, with our material being a very big part of the chemistry as well as the chemistry we choose for the flux, we adjust the chemistry of our flux to get the desired results or reaction with our Ore or whatever we are melting.
Litharge lead oxide PbO, is a strong oxidizer (it can even oxidize our crucible), with silica can form a lead silicate (lead glass Pb2SiO4), or act as a collector of other metals like precious metals of gold and silver, litharge can also act as a desulfurizer, litharge readily gives up oxygen and can act as an oxidizer to oxidize base metals, lead as stated above can act as a collector.
In a melt other metals can act as collectors of values, or help to reduce the melting points of other metals, some collectors like silver or copper bismuth...
Carbon, sugar, flour, charcoal, wood... these are carbon sources which act as reducing agents, or to offset the chemical reaction of oxides, the use of flour in flux is very common, the carbon can take oxides from metals in a melt, offset an oxidizer in the melt or flux. Carbon and oxygen normally burn off as CO2 gas (CO if not enough oxygen involved), carbon can also help to lower the oxygen absorbed into a melt from air or oxygen in the torch or used in the burner of the furnace...
Say we are using litharge as a collector in a melt, and the Ore (or material we are melting) like red rouge (Fe2O3) polishing waste that may contain many other oxides aluminum oxide (Al2O3) from the grinding wheels or chromium Oxide (Cr2O3) in buffing grinding compounds) and our melt is of such an oxidizing nature, that we cannot get the litharge (PbO) to reduce back to lead (it will not collect gold), we may need to add flour or another carbon source to reduce the oxides (and to reduce the lead to metal where it can pick up the fine gold in the melt)...
There are several other reducing agents used in fluxes.
Sometimes we need an Oxidizer to the flux or melt, to help oxidize base metals to get them to dissolves as silicates in the slag glass, such as potassium nitrate KNO3.
Sometime sulfur may be a problem and Iron can help in the melt as a desulfurizer or collector.
Salt, or carbon is sometimes used as a cover.
Fluorspar or cryolite used as fluidizers to help with fluidity and with some materials in a melt...
Flux can use many things, or combination of things to help change the chemical properties of the melt...
Basically you are melting (doing a a chemical reaction with high heat) your flux is mixed to help to get what you want back out of this chemical reaction.
Also since this is a chemical reaction how you perform the melt can also be a very be important part of this chemical equation, the melting environment can be oxidizing or reducing (in the furnace), a torch may not get the melt hot enough for the melt to mix well or can also be oxidizing or reducing, a furnace where you can get a good hot melt to get the melt fluid, and keep it fluid for metals and flux to react, and have more control on temperature of the melt...
A torch melt would not work well for most procedures we are looking at here.