In the flamelet framework for premixed turbulent combustion, a transport equation for the flame surface density commonly known as the H-equation, can be formulated but requires closure assumptions. We have applied an aqueous autocatalytic reaction, which produces a self-propagating chemical surface (liquid flame) with characteristics closely matching many of those assumed by flamelet models to extract full spatial statistics relating to the Bray-Moss-Libby model. The present work reports, for the first time, measurements of some unclosed terms in the S-equation using liquid flames in a nearly isotropic turbulent flow field. The three-dimensional form of nearly stationary isotropic turbulence was generated near the core region between a pair of vibrating grids in a chemical tank, as verified by laser-Doppler velocimetry. Visualization of propagating surfaces is via a high-speed, successive planar chemically reacting, laser-induced fluorescence technique to extract flame surface density, vector normal to the front, and curvature. Unlike gaseous flames, liquid flames with essentially constant laminar propagating (burning) velocity are approximately free of thermal expansion and heat loss effects and thus may be useful for developing a very basic understanding of the interrelationship between production by hydrodynamic straining and destruction by propagating effects in the S-equation, relevant to flamelet models. It is found that the propagation term is negligible and the curvature term has three different modes across the turbulent front brush, respectively (1) mainly negative, (2) positive/negative: production at the reactant side/destruction at the product side, and (3) mainly positive. The first two modes constitute nearly 90% of all possible modes found for a typical aqueous propagating front, indicating that the curvature behavior is more complicated than that generally assumed by flamelet models (mode 1 only) and that of direct numerical simulation and gaseous V flame results (mode 2 only). Two simple schemes are included to explain these results. Finally, measurements of the total propagating surface area production (flame stretching) suggest that the collisions or reconnections of flamelets may be important for the coexistence of these three different curvature modes.