We study the shape differentiability of a cost function for the steady flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design.

We consider the motion of a viscous compressible fluid confined to a physical space with a time dependent kinematic boundary. We suppose that the characteristic speed of the fluid is dominated by the speed of sound and perform the low Mach number limit in the framework of weak solutions. The standard incompressible Navier-Stokes system is identified as the target problem.

This Letter describes a quasistationary breakup of an immiscible, inviscid fluid at low capillary numbers. The breakup proceeds in a coflowing, viscous liquid, in a confined geometry of a long and narrow orifice. In contrast to the capillary instability in an unbounded fluid, the collapse proceeds through a series of equilibria, each yielding the minimum interfacial energy of the fluid-fluid in...

Chemical reactions inside carbon nanotubes can yield unusual outcomes. Molecular dynamics simulations show that within the confined space of carbon nanotubes, the 1,4-exo adduct of a Diels-Alder cycloaddition may be produced instead of the 9,10-adduct, which is favoured in bulk. The likely product is highly dependent on the nanotube radius and reactant size.

Magnetic colloids adsorbed at a fluid interface are unique model systems to understand self-assembly in confined environments, both equilibrium and out of equilibrium, with important potential applications. In this work the pearl-chain-like self-assembled structures superparamagnetic fluid–fluid under static time-dependent actuations investigated. On one hand, it is found that generated by fiel...

We develop a theory for stick-slip motion in ultrathin liquid films confined between two moving atomically flat surfaces. Our model is based on the hydrodynamic equation for flow coupled to the dynamic order parameter field describing the ‘‘shear melting and freezing’’ of the confined fluid. This model successfully accounts for the observed phenomenology of friction in ultrathin films, includin...

Anodic bonding was used to fabricate a 10 mm diameter × 640 nm tall annular geometry suitable for torsion pendulum studies of confined 3He. For pure 3He at saturated vapor pressure the inertia of the confined fluid was seen to be only partially coupled to the pendulum at 160 mK. Below 100 mK the liquid’s inertial contribution was negligible, indicating a complete decoupling of the 3He from the ...

Nonlinearity in finite-Reynolds-number flow results in particle migration transverse to fluid streamlines, producing the well-known "tubular pinch effect" in cylindrical pipes. Here we investigate these nonlinear effects in highly confined systems where the particle size approaches the channel dimensions. Experimental and numerical results reveal distinctive dynamics, including complex scaling ...

a new mathematical model for identifying pollution sources in aquifers is presented. the model utilizes lagrange constrained optimization method (lcom) and is capable to inversely solve unsteady fluid flow in saturated, heterogeneous, anisotropic confined and/or unconfined aquifers. throughout the presented model, complete advection-dispersion equation, including the adsorption as well as retar...