(a) air liq U d h (b) (d) (b) (e) (c) (a) dewetting spreading 0 1 0 1 x t 0 T L (x) (t) FIG. 1: (color online) (a) Sketch of a film of dielectric liqui d of thick- ness h ( x ) in a capacitor of gap width d and voltage U ( x, t ) . The relative dielectric constants of the liquid and air are ε liq and ε $_{air}$, re- spectively. (b) Sketch of a drop on a vibrating inclined substrate. The frequency and angle of the vibration with the substrate normal are ω and β , respectively. The inclination angle of the substrate is α . FIG. 2: (Color online) Panels (a) to (c) illustrate the working princi- ple of a fluidic ratchet based on a switchable wettability tha t causes dewetting-spreading cycles. (d) illustrates the spatially asymmetric periodic interaction profile Φ( x ) responsible for the wettability pat- tern and (e) indicates the time dependence Ω( t ) of the switching in relation to the dewetting and spreading phases in (a) to (c). II. LONG-WAVE FILM PROFILE EVOLUTION EQUATION We are here particularly interested in three cases: (i) For a liquid film in an external electrical ratchet potent ial on a horizontal substrate one has and F = 0 . The disjoining pressure Π$_{vdW}$ comprises the ef- fective interactions between the liquid-gas interface and the substrate, i.e. the wettability properties [18, 20, 21]. We as- sume that a dielectric oil forms a film in a capacitor of gap width d . The oil wets the lower plate and does not wet the upper plate corresponding to We restrict our attention to a two-dimensional system and consider films/drops on lengthscales in the micrometer rang e. P ( h, x, t ) = Π$_{vdW}$( h ) + Ω( t ) Φ( x ) Π$_{el}$( h ) (2) Π$_{vdW}$ = ( A$_{l}$ h 3 + A$_{u}$ (1 − h ) 3 ) (3) In the present contribution we will restrict our attention to one-layer films (i.e. liquid under gas) and formulate the thin film model that applies to both driving types – an ex- ternal ratchet potential and the vibration (Section II). Then we present selected results for the external electrical ratchet potential in Section III. Section IV discusses drop transport by an oblique vibration of the substrate (cf. [15]), whereas Section V describes results for the recently investigated case where the drop moves as a reaction to a phase shift between decoupled horizontal and vertical vibrations [17]. Finally, we conclude and give an outlook in Section VI. As mass is conserved (no evaporation is considered), the time derivative of the film thickness profile equals the divergenc e of a flow. The flow results from a pressure gradient and a lateral force and is proportional to a mobility Q ( h ) . The pres- sure contains the Laplace or curvature pressure and a term P ( h, x, t ) that stands for all other pressure contributions as, e.g., disjoining pressure (wettability), hydrostatic pressure, electrostatic pressure and so on. The pressure P might de- pend on position and time. The lateral driving force F may include gravity (drop on incline), thermal or wettability gradi- ents and other. Depending on the particular effect included it might as well depend on h . The decisive element in both presented systems – the ratchet capacitor and the vibrated drop – is the interaction of the external periodic forces with capillarity and wettabil- ity. With other words the nonlinearity that is necessary for a net motion results from interface effects. One may call this class of ratchets, “interfacial flow driven ratchets”. As th ey are dominated by interface effects they become more effec- tive the smaller the involved scales are. This implies that they are good candidates for micro- or even nano-fluidic actuator s. observed net motion of the drop. A second experiment does not employ an oblique vibration but decouples the normal and parallel vibrations entirely [17]. On a horizontal substrate a net transport may be induced in either direction depending on the phase-shift and amplitude ratio of the two harmonic vibra- tions. Note, that in Ref. [17] both vibrations have the same fre- quency. In both vibration experiments the phenomenon might be seen as a rocked self-ratcheting [1] of the drop as it is the drop itself that introduces the local time-reflection asymm e- try in the response to the time-periodic driving of the sliding motion. The behaviour is then controlled by the interplay of the time- periodic external force (and its spatial modulation), wetta- bility and capillarity. In the limit of small surface slopes (small contact angles) it can be well described using an evo- lution equation for the film thickness profile h ( x, t ) that is derived from the momentum transport equations with ade- quate boundary conditions employing long-wave approxima- tion [18, 19]. In dimensionless form we find 2 ∂$_{t}$ h = − ∂$_{x}$ { Q ( h ) ∂$_{x}$ [ ∂$_{xx}$h + P ( h, x, t )] + Q ( h ) F ( t ) } . (1)