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A dense suspension of the cornstarch flowing on a very inclined wall finallyforms some ridge-like patterns of the free surface. The onset of patternformation is the primary target to elucidate the mechanism. In this work, basedon the continuity of fluids and the force balance, we show that the flat freesurface is unstable when the second normal stress difference $N_2$ isnegatively proportional to shear stress and the gravity component perpendicularto the wall is weak enough. Such instability is inevitable to grow into aridge-like surface profile oriented parallel to the flow direction. We use theinstability criterion to predict the critical slope angle for the formation ofridge patterns. The estimated critical angle was found to be in agreement withexperimental observations for a cornstarch suspension.

Ridge instability in dense suspensions caused by the second normal stress difference