Pressure-driven flow in thin domains
John Fabricius, Elena Miroshnikova, Elena Miroshnikova, Afonso Fernando Tsandzana, Afonso Fernando Tsandzana, Peter Wall, Peter Wall · Asymptotic Analysis · 2019
We study the asymptotic behavior of pressure-driven Stokes flow in a thin domain. By letting the thickness of the domain tend to zero we derive a generalized form of the classical Reynolds–Poiseuille law, i.e. the limit velocity field is a linear function of the pressure gradient. By prescribing the external pressure as a normal stress condition, we recover a Dirichlet condition for the limit pressure. In contrast, a Dirichlet condition for the velocity yields a Neumann condition for the limit pressure.