Confinement induced topological fluctuations in a system with internal surfaces

The lamellar phase between two parallel walls, in the water, oil, surfactant system, exhibits strong topological fluctuations. As we change the distance between the walls we observe the formation of two layers, then the microemulsion between two layers, and finally four layers. The transition is marked by the peaks in the average Euler characteristics and in its variance. The topological fluctuations may be responsible for attractive background force found in force apparatus measurements of the system.