Correlations for the attainment of optimum formulation

A similar correlation was reported for systems containing non-ionic surfactants of the polyethoxylated alkylphenol or alcohol type [25]. 

In these expressions, S is the salinity of the aqueous phase (in wt.% NaCl) and In S its neperian logarithm, ACN is the alkane carbon number which characterises the oil phase, cr is a characteristic parameter of the anionic or cationic surfactant which increases linearly with the length of the lipophilic tail, as well as a which is characteristic of the lipophilic group of non-ionic surfactants, EON is the average number of ethylene oxide groups per polyethoxylated surfactant molecule and T is the temperature, k, b, a-x and ct are constants which depend on the kind of system particularly the surfactant head group and electrolyte nature [23-25]. For ethoxylated non-ionics, the characteristic parameter (3 = a - EON is sometimes introduced./(A) and (A) are function of the alcohol type and concentration which could be written in first approximation as 

Crude oils were found to behave as an equivalent alkane as far as the attainment of optimum formulation was concerned. The equivalent alkane carbon number or EACN was then introduced to characterise pure hydrocarbons or mixtures [26]. The EACN of an oil phase is defined as the ACN of the alkane that results in the satisfaction of the correlation in the same conditions of surfactant, salinity, alcohol and temperature. EACN has been experimentally determined for n-alkanes mixtures, resulting in a linear mixing rule on a molar fraction basis, namely 

The EACN was found to depend on the oil molecular structure. Branching was not found to alter it significantly unless it is extensive, but cyclisation tends to cut it down definitely. EACN was found to be 3.5 for cyclohexane and (3.5 + n) for alkyl cyclohexanes with n carbon atoms in their alkyl chain benzene EACN was initially found to be close to 0 alkylbenzenes were found to have an EACN equal to the number of carbon atoms of their alkyl chain [4]. Recent findings with extremely pure surfactants tend to indicate that these results for aromatic oils might be erroneous, or at least misleading, because these solvents 

The salinity effect of different salts, particularly divalent cation salts, is expressed through the term bS in the correlation for non-ionic surfactants of the polyethoxylated phenol or alcohol type. No information is available yet on the salinity effect on other non-ionics such as alkyl-polyglucosides. The salinity effect on ionic surfactant systems is a more complex issue because the surfactant itself is also a (more or less) dissociated electrolyte. Its degree of dissociation is paramount as far as its hydrophilicity is concerned. For instance sodium salts of alkyl sulphonic acids are essentially completely dissociated, hence they act as the sulphonate ion, and it is essentially the same with the salt of potassium or ammonium. The presence of multivalent anions produces an interference with the monovalent anionic surfactant ion, such as an alkyl benzene sulphonate, but it is essentially an ideal mixing rule. 

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