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The hydrodynamics of a liquid-vapour interface in contact with anheterogeneous surface is largely impacted by the presence of defects at thesmaller scales. Such defects introduce morphological disturbances on thecontact line and ultimately determine the force exerted on the wedge of liquidin contact with the surface. From the mathematical point of view, defectsintroduce perturbation modes, whose space-time evolution is governed by theinterfacial hydrodynamic equations of the contact line. In this paper we derivethe response function of the contact line to such generic perturbations. Thecontact line response may be used to design simplified 1+1 dimensional modelsaccounting for the complexity of interfacial flows coupled to nanoscaledefects, yet offering a more tractable mathematical framework to includethermal fluctuations and explore thermally activated contact line motionthrough a disordered energy landscape.

A one dimensional modal approach for flows controlled by contact line motion