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When is it energetically favorable for a rivulet of perfectly wetting fluid to split?

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When is it energetically favorable for a rivulet of perfectly wetting fluid to split?

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We determine when it is energetically favorable for a thin rivulet of perfectly wetting fluid (i.e., a thin rivulet with zero contact angle) on the underside of a planar substrate to split into two or more subrivulets.

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