There is widespread interest in improved oil recovery by the low salinity effect (LSE) and a pressing need to better predict the likely response and its relation to wettability change. A LSE in kaolinite-bearing sandstones can arise from detachment of crude oil, by its peeling from rock surfaces due to increased oil/rock repulsion, and/or by detachment of mineral fines with adhering oil, due to increased fines/rock repulsion. In a mixed wet sandstone reservoir, oil is typically in close contact with an extremely small fraction of total rock surface, a key component of which are asperity tips such as at edges of kaolinite platelets. An Integrated pH Ion Surface Electrostatics (IpHISE) model is used to predict speciation and interactions of oil surfaces and kaolinite edges across NaCl and CaCl2 solutions of variable pH in sandstones. At pH < 5, a LSE can arise by weakened oil adhesion due to fewer positively charged oil base groups adsorbed to kaolinite edges. At higher pH, the electrostatics is dictated by competition between negatively and positively charged acid groups produced by respectively deprotonation and calcium binding. The LSE is predicted to be strongest in a narrow range around pH 56 in which salinity reduction switches the oil/kaolinite edge interaction to repulsive. At pH > 6, the interaction becomes increasingly repulsive at all salinities. There, a LSE can only arise from the extended range of repulsion, both between oil and kaolinite edges and between the latter and the underlying rock. The existence and cutoff values of these pH ranges depend sensitively upon the oils acid number/base number, salt concentrations, and the pH shift caused by injection of low salinity fluid.