origin of the reversal. 6 0 5 10 15 h 70 400 0.1 0.2 0.3 0.4 x/L 0 5 10 15 0.1 0.2 0.3 0.4 T t=0 t=T/4 t=T/2 t=3/4T 0.4 0.6 0.8 1 x/L 0 2 4 6 8 h 0 T/4 T/2 3/4T T FIG. 10: Drop profiles at various times of the cycle as indicat ed in upper right corner of each plot for various vibration periods T as indicated in the legend. T = ∞ indicates the low frequency limit. Remaining parameters are V = 384 , L = 256 , α = 0 , β = 0 . 1 , a 0 = 10 , G = 0 . 001 . FIG. 8: (color online) Shown are several drop shapes during one vibration cycle for an obliquely vibrated horizontal substrate at V = 192 , G = 0 . 001 , a 0 = 10 , α = 0 , T = 400 , L = 128 and a relatively large vibration angle β = 1 . -0.4 -0.2 0 <v>/$^{β}$ a 0 $_{2}$ [10-3$^{]}$ 10 0.1 7.5 0.1 5 0.1 10 0.05 10 0.15 10 0.2 0.01 0.1 -0.1 -0.05 0 <v>/L 1.67  [10 -5$^{]}$ 64 128 192 256 L a$_{0}$ a b 0 0.2 0.4 0.6 0.8 1 t/T 8 10 12 14 16 h max 70 150 400 1000 T FIG. 11: Variation of the maximal drop height during one vibration period for different vibration periods as indicated in the legend. Re- maining parameters are as in Fig. 10. FIG. 9: Scaled mean velocity depending on the vibration frequency ω for drops on a horizontal substrate. Panel (a) gives the master curve for the scaled mean velocity 〈 v 〉 /βa 2 0 for sets ( a $_{0}$, β ) as given in the legend. The horizontal dashed line indicates the result in the low frequency limit. Remaining parameters are as in Fig. 6. Panel (b) gives the scaled mean velocity 〈 v 〉 /V 1 $^{.}$67 for drops of different volume as given in the legend. Remaining parameters are a 0 = 10 . 0 , β = 0 . 1 , α = 0 . 0 , G = 0 . 001 . To this end we show in Fig. 10 a superposition of drop pro- files obtained at frequencies above and below ω$_{c}$ at selected times during the vibration cycle. The profiles in the low fre- quency limit are per definition ideally in-phase with the sub - strate vibration. At T = 400 ( ω = 0 . 016 < ω$_{c}$ ≈ 0 . 05 , cf. Fig. 9(b)) the profiles near the times of maximal acceller - ation (i.e., t ≈ T/ 4 and t ≈ 3 T/ 4 ) strongly resemble the ones in the low frequency limit, although the variation in their shape is already smaller. For T = 1000 they are nearly in- distinguishable (not shown). However, around t = 0 and T = T/ 2 where the accelleration changes sign the conver- gence to the low frequency limit is much slower as there even small phase lags are very important (cf. Fig. 11). The overall behaviour can be well appreciated in Fig. 11 where the depen- dence of the maximal drop height on time is shown for one vibration cycle for several different periods. With decreas- ing period we observe a continuous increase of the phase shift w.r.t. the curve for the low frequency limit. The curves of finite frequencies lag behind the one for zero frequency and show a less pronounced variation of the drop heights. morphological changes. It can transform between a spherical cap-like drop via a drop with a backwards shoulder to a fi- nite film with a capillary rim [30]. We do here, however, not investigate this regime further. For smaller vibration angles β morphological transitions do not occur (at reasonable accellerations a$_{0}$ ). This allows for ’universal’ behaviour, i.e., one finds that scaling laws tha t are discovered in the low frequency regime hold in part in the en- tire frequency range studied. In particular, one finds in thelow frequency regime a scaling 〈 v 〉 ∼ βa 2 $_{0}$L 1 . $^{67}$. Fig. 9(a) shows that for drops of identical volume the scaling 〈 v 〉 ∼ βa 2 0 does hold very well as it is possible to ’collaps’ curves for a range of parameter pairs ( a$_{0}$, β ) on a single master curve. The scal- ing with volume does, however, not hold [see Fig. 9(b)]. In- terestingly, one finds a flux reversal at high frequencies, i. e., above a critical frequency ω$_{c}$ the drops move on average to the right. Fig. 9(b) further indicates that for larger drop volume the reversal is more pronounced and occurs at lower frequen- cies ω$_{c}$ . We will end this section with an investigation of the