## 1 Introduction  
Fluorite ores are attracting attention due to the wide range of novel applications that this mineral possesses [1; 2; 3; 4]. However, applications require acid grade fluorite of at least 97% purity. To achieve this level of purity, froth flotation is shown to be the most efficient and economically viable technique. However, treating fluorite ores by froth flotation is a complex process. The process is influenced by a range of different factors [5]. Froth flotation is a heterocoagulation process where target mineral particles within an aqueous pulp selectively attach to air bubbles, forming particle-bubble aggregates, which are subsequently transported out of the pulp into a froth phase. As the air bubbles mainly differentiate between hydrophobic and hydrophilic surface properties, selectivity is essentially based on differences in wetting properties of the solid particles suspended in the pulp [6]. With economic factors driving the production of acid grade fluorspar, common gauge minerals must be reduced to the minimum allowed in such a pure concentrate. The ultimate goal of all fluorite concentrate producers is to improve grade to a point where they have a marketable product, while also maintaining recovery. Roughing, as the first step in froth flotation, has to achieve the maximum metallurgical recovery leading to a metallurgical grade. There are numbers of operation variables affecting the rougher process [7]. Particle size is a crucial physical factor in order to achieve high grade purities because it has to be small enough to ensure the liberation of minerals [8]. Otherwise, particle size smaller than 20 microns is less efficient in froth flotation process due to the formation of slime coatings. As the particle size decreases the specific surface area increases making necessary the augmentation of reagents dosage when slime coatings are presented in froth flotation [9; 10]. In a flotation cell, entrainment occurs simultaneously along with true flotation. Unlike true flotation, entrainment is not chemically selective and it occurs without a direct attachment of particles to bubbles. This issue can be solved by applying enough agitation energy to the flotation process [11]. Depressants in fluorite flotation, which are used for decreasing the floatability of calcite and silica, mainly include some inorganic salts. Sodium silicate commonly known as water glass and its solution with inorganic salt ions, are often applied in fluorite flotation to depress silica [12; 13]. Otherwise, tannins are presented as strong depressants of the carbonated gangue, in this way quebracho tree stands out as especially energetic tannin in the calcium carbonate depression [14]. Reagents such as starch are particularly effective for reducing common gangue constituents in fluorspar ores [15]. When slime coatings are present in the flotation process, dispersants as sodium silicate have an important role upgrading the depressant action [16]. Fatty acids and their soaps are often used as collectors in flotation for non-sulfide ores such as bauxite, hematite, apatite, scheelite, and fluorite. Oleic acid, linoleic acid, and linolenic acid have been and are commonly used as collectors. Additionally, they have low temperature resistance [17; 18]. Most recent research in fluorite flotation focuses on the study of new collectors [19] and new depressants [20; 21]. However, to our knowledge, no data have been published on the interaction between different reagents involved in the fluorite flotation process. Some authors have used the technique of design of experiments (DoE) to optimize some chemical and physical variables of flotation process, for example [22] use this technique to optimize the dosage of collector in the flotation of apatite and [23] Use DoE to study some hydrodynamic aspects in column flotation. On the other hand, only [24] used a mathematical modeling to study some physical and chemical variables in fluorite flotation process.