In this paper we demonstrate the combination of supported membranes and so-called flat microfluidics, which enables one to manipulate liquids on flat chip surfaces via ``inverse piezoelectric effect''. Here, an alternating external electric field applied to the inter-digital transducers excites a surface acoustic wave on a piezoelectric substrate. Employing lithographic patterning of self-assembled monolayers of alkoxysilanes, we successfully confine a free-standing, hemi-cylindrical channel with the volume of merely 7 µL. The experimentally determined maximum flow velocity scales linearly with the acoustic power, suggesting that our current setup can drive liquids at the speed of up to 7 cm/s (corresponding to a shear rate of 280 s(-1)) without applying high pressures using a fluidic pump. After the establishment of the functionalization of fluidic chip surfaces with supported membranes, we deposited asymmetric supported membranes displaying well-defined mannose domains and monitored the dynamic adhesion of E. Coli HB101 expressing mannose-binding receptors. Despite of the further technical optimization required for the quantitative analysis, the obtained results demonstrate that the combination of supported membranes and flat fluidics opens a large potential to investigate dynamic adhesion of cells on biofunctional membrane surfaces with the minimum amount of samples, without any fluidic pump.