Membrane desalination is associated with significantly increased ion concentration of rejected sparingly soluble salts (commonly of calcium, magnesium, barium, etc) right at the membrane surface, leading to undesirable membrane scaling. Optimization of desalination membrane-plant design and its operation strategy requires quantification of scaling evolution phenomena, through appropriate mathematical models involving experimentally determined system parameters. In recent years, a modeling approach based on heterogeneous nucleation-growth theory was developed for this purpose, and proven to be successful in the case of non-stirred dead-end desalination experiments but not in the case of cross-flow and stirred dead-end desalination. To resolve this inconsistency, new results from numerous sets of improved dead-end non-stirred experiments (some with controlled changes of imposed pressure difference during testing) are reported that provide useful quantitative information and insights regarding incipient scaling. The previous modeling approach is generalized considering non-classical nucleation. Moreover, the likely scatter of local membrane-surface properties is considered in a parameter estimation approach. The new modeling approach leads to estimation of a range of scaling-model parameters consistent with the experimental data. Such parameters can be employed in comprehensive modeling tools of membrane-modules, to simulate their operation for the particular type of membrane for which parameters are extracted. (C) 2016 Elsevier B.V. All rights reserved.