Abstract
We consider the Newtonian Poiseuille flow in a tube whose cross-section is an equilateral triangle. It is assumed that boundary slip occurs only above a critical value of the wall shear stress, namely the slip yield stress. It turns out that there are three flow regimes defined by two critical values of the pressure gradient. Below the first critical value, the fluid sticks everywhere and the classical no-slip solution is recovered. In an intermediate regime the fluid slips only around the middle of each boundary side and the flow problem is not amenable to analytical solution. Above the second critical pressure gradient non-uniform slip occurs everywhere at the wall. An analytical solution is derived for this case and the results are discussed.
Similar content being viewed by others
References
Denn MM (2001) Extrusion instabilities and wall slip. Annu Rev Fluid Mech 33:265–287
Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:381–411
Neto C, Evans DR, Bonaccurso E, Butt HJ, Craig VSJ (2005) Boundary slip in Newtonian liquids: a review of experimental studies. Rep Prog Phys 68:2859–2897
Hatzikiriakos SG (2012) Wall slip of molten polymers. Prog Polym Sci 37:624–643
Navier CLMH (1827) Sur les lois du mouvement des fluides. Mem Acad R Sci Inst Fr 6:389–440
Sochi T (2011) Slip at fluid-solid interface. Polym Rev 51:309–340
Damianou Y, Georgiou GC, Moulitsas I (2013) Combined effects of compressibility and slip in flows of a Herchel-Bulkley fluid. J Non-Newton Fluid Mech 193:89–102
Spikes H, Granick S (2003) Equation for slip of simple liquids at smooth solid surfaces. Langmuir 19:5065–5071
Estellé P, Lanos C (2007) Squeeze flow of Bingham fluids under slip with friction boundary condition. Rheol Acta 46:397–404
Ballesta P, Petekidis G, Isa L, Poon WCK, Besseling R (2012) Wall slip and flow of concentrated hard-sphere colloidal suspensions. J Rheol 56:1005–1037
Ebert WE, Sparrow EM (1965) Slip flow in rectangular and annular ducts. J Basic Eng 87:1018–1024
Majdalani J (2008) Exact Navier-Stokes solution for pulsatory viscous channel flow with arbitrary pressure gradient. J Propuls Power 24:1412–1423
Wu WH, Wiwatanapataphee B, Hu M (2008) Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary. Physica A 387:5979–5990
Wiwatanapataphee B, Wu YH, Hu M, Chayantrakom K (2009) A study of transient flows of Newtonian fluids through micro-annuals with a slip boundary. J Phys A, Math Theor 42:065206
Wang CY (2012) Brief review of exact solutions for slip-flow in ducts and channels. J Fluids Eng 134:094501
Wang CY (2003) Slip flow in a triangular duct—an exact solution. Z Angew Math Mech 33:629–631
Kaoullas G, Georgiou GC (2013) Newtonian Poiseuille flows with wall slip and non-zero slip yield stress. J Non-Newton Fluid Mech 197:24–30
Kalimeris K, Fokas AS (2010) The heat equation in the interior of an equilateral triangle. Stud Appl Math 124:283–305
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Georgiou, G.C., Kaoullas, G. Newtonian flow in a triangular duct with slip at the wall. Meccanica 48, 2577–2583 (2013). https://doi.org/10.1007/s11012-013-9787-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-013-9787-7