Lubrication theory

About: Lubrication theory is a research topic. Over the lifetime, 1713 publications have been published within this topic receiving 50261 citations. The topic is also known as: Fluid bearing.

Two-phase viscous fingering of immiscible thixotropic fluids: A numerical study

Abstract: The effects of a fluid’s thixotropic behavior is investigated on the viscous fingering phenomenon in a rectangular Hele-Shaw cell assuming that the displacing fluid is Newtonian while the displaced fluid obeys the Moore model for thixotropic fluids. Lubrication theory is used to simplify the gap-averaged governing equations in which the interfacial tension is treated as a body force. It is shown that the shapes of the fingers are dramatically affected by the displaced fluid’s thixotropic behavior. For highly thixotropic fluids, a chaotic behavior, accompanied by a blowup at prolonged times, is predicted to occur for certain set of parameter values. The viscosity ratio of the Moore fluid is also predicted to influence the shapes of the fingers provided that the zero-shear viscosity of the displaced fluid is higher than the viscosity of the displacing fluid. It is shown that the amplitude and wavenumber of the initial perturbation plays a crucial role on its time evolution. Also, a partial slip of the displaced and/or the displacing fluid is predicted to have a stabilizing effect on the viscous fingering phenomenon.

Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

Abstract: A lubrication theory has been developed for the electro-osmotic flow of non-uniform buffers in narrow rectilinear channels. The analysis applies to systems in which the transverse dimensions of the channel are large compared with the Debye screening length of the electrolyte. In contrast with related theories of electrokinetic lubrication, here the streamwise variations of the velocity field stem from, and are nonlinearly coupled to, spatiotemporal variations in the electrolyte composition. Spatially non-uniform buffers are commonly employed in electrophoretic separation and transport schemes, including iso-electric focusing (IEF), isotachophoresis (ITP), field-amplified sample stacking (FASS), and high-ionic-strength electro-osmotic pumping. The fluid dynamics of these systems is controlled by a complex nonlinear coupling to the ion transport, driven by an applied electric field. Electrical conductivity gradients, attendent to the buffer non-uniformities, result in a variable electro-osmotic slip velocity and, in electric fields approaching 1kV cm -1 , Maxwell stresses drive the electrohydrodynamic circulation. Explicit semi-analytic expressions are derived for the fluid velocity, stream function, and electric field. The resulting approximations are found to be in good agreement with full numerical solutions for a prototype buffer, over a range of conditions typical of microfluidic systems. The approximations greatly simplify the computational analysis, reduce computation times by a factor 4-5, and, for the first time, provide general insight on the dominant fluid physics of two-dimensional electrically driven transport.

Wetting failure and contact line dynamics in a Couette flow

Abstract: Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.