| The displacement of liquid interfaces in natural reservoirs involves the motion of contact lines of systems with finite static contact angle hysteresis. Already in the case of perfectly wetting liquids different models for the dynamic law are proposed, while more general cases are still under debate. In the limit of small capillary numbers, we numerically investigate the impact of different laws on the global shape of liquid drops near the depinning transition. The transition from stationary to steady moving solutions is found to be continuous or discontinuous depending on the specific protocols to vary the driving force. Quantitative analysis of the drop shapes can provide additional benchmarks to discriminated between different models when compared to experiments. The present study can be extended to the motion on chemically heterogeneous and smoothly corrugated substrates, as well as systems of spheres and fibers. |
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