The moving contact line on a smooth solid surface

Abstract A mathematical model for the advancing contact-line motion on a smooth solid surface is proposed. It is shown that in the spreading of liquids over solid surfaces, the flow causes a surface tension gradient along the liquid-solid interface which influences the flow and, in the case of small capillary and Reynolds numbers, determines the dynamic contact angle and the force between the liquid and solid in the vicinity of the contact line. The model: (a) eliminates the shear-stress singularity of the classical model; (b) describes the fluid motion as rolling, in complete agreement with direct experimental observations; (c) determines the dynamic contact angle and the tangential force dependence on the contact-line speed; (d) explains the existence of the maximum contact angle values

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