Abstract There is no known controlled mechanism to produce exact replicates of titanium (Ti) surfaces containing multi-scale roughness, as “preferred” by bone cells. Such a mechanism would allow to, at least: (a) carry out robust statistical analyses of the actual roughness features preferred by bone cells, and (b) advance of the state-of-the-art on implant technology. With that overarching goal in mind, this works derives and suggests the form of a numerical model to predict surface roughness based on the thermo-chemical behavior of the etching of Ti surfaces with sulfuric acid (H2SO4). The test variables studied are acid molarity (4 M, 9 M and 18 M), temperature (40, 60, and 90℃), and exposure time (5 min, 10 min, 15 min, 30 min, 1 h, 3 h, and 8 h). Characterization is carried out using scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). Numerical methods and the bond graph approach are used in the analysis. An empirical numerical model is constructed for prediction of both mass etching and surface roughness. The average roughness, Ra, is found to be of the form: R a = C 1 + C 2 1 - e - C 3 , where C1 is related to the pre-treatment condition of the surface, C2 is a function of temperature (T), solubility limit, and oxygen concentration of surroundings, and C3 is a function of time (t), T, and acid concentration. It is suggested that the empirical equations proposed be expanded to include other surface parameters, which could extend the prediction capabilities to smaller scales. Additionally, it is found that while submicron-scale roughness can be predicted using thermo-chemical parameters, grain size can restrict micro-scale roughness. The numerical model for surface roughness developed contributes to the on-going investigation to develop a multi-step controlled technique for producing the aforementioned types of surfaces. It is expected that the form of the numerical model developed can be extended to other etching agents on Ti.