Steep wave fronts on extrudates of polymer melts and solutions: lubrication layers and boundary lubrication

Steep wave fronts tend to develop in many regimes of lubricated, slipping flows in which waves appear. Problems of slip, spurt, fracture and extrudate distortion can be framed in terms of lubrication theory with paradigms arising from the lubrication of heavy oil with water for some problems and concepts from the theory of boundary lubrication for others. In water lubricated pipelines, high pressures are produced at the front side of a wave on the oil when water is forced through the wavecrest and the wall; low pressures develop at the back of the wave where the gap opens. The steep waves which develop on cores of heavy oil lubricated by water are irregular and look like melt fracture. Direct numerical simulation of regular periodic waves give rise to sharkskin solutions in which the wave length decreases with the wave amplitude as the gap size decreases, preserving the steep wave front. Wave steepening seems always to occur in extrusion when the polymers slip, in the abrasion of rubber samples and in Schallamach’s waves of detachment. 1 Lubrication layers and slip Slipping of extrudates is just one special case of slipping of one material on another, a topic in the well-developed subject of friction, lubrication and wear. In the case of extrudate slip, I divide the subject into two categories, “wet” slip and “dry” slip. In problems of wet slip a lubricating layer of soft material is between the extrudate and the wall; in these problems ideas from theory of hydrodynamic lubrication and lubricated pipelines ought to be important. “Dry” slip is a concept which makes sense when the asperities on the extrudate and the pipe wall make touching contact, and here also there is an excellent theory of boundary lubrication which can be applied (see, for example, Bowden and Tabor [7] or Roberts [34]). The concept of “dry slip” should be carefully examined since two bodies which slip either have a substance between or nothing between. “Nothing” would imply a vacuum or else that the two materials weld at touching asperities. Even in the case of welded asperities, the two materials are not joined everywhere and one may consider the effects of the substance between.