Publication

Studying Droplet dynamics by depth-averaged simulation

2012
Talks

Abstract

Droplets in flat micro channels are deformable, avoid obstacles, interact with one another and undergo separation and coealescence. For the simulation of these micro fluidic two-phase flows we propose a depth-averaged model derived from the Stokes equation, the so called Brinkman equation. This equation is solved by the Boundary Element Method, which leads to a meshless numerical algorithm. A flow solver based on the depth-averaged model computes the dynamic evolution of the droplet in the 2D flow plane and retains the dominant effects in the thin/depth-averaged direction. In addition we developed a set of modified boundary conditions that account for 3D effects like film formation, droplet break-up or capillary action on cavities. We present results for droplet breakup in flow focussing devices and interaction between two droplets. In both cases the numerical results show a good agreement with experiments. The reduction from 3D to 2D by depth averaging and 2D to 1D by transformation of the equations to boundary integrals leads to a significant simplification. Yet the model reproduces essentially the physics to describe these confined two-phase flows.

Official source

https://infoscience.epfl.ch/entities/publication/1d3a58f3-ee38-4c6f-bce3-6e4aa87f6eb0

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2012
Talks

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1d3a58f3-ee38-4c6f-bce3-6e4aa87f6eb0

About this result

Related concepts (32)

Boundary layer

In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Boundary element method

The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), fracture mechanics, and contact mechanics. The integral equation may be regarded as an exact solution of the governing partial differential equation.