By Nam-Trung Nguyen

Quite a lot of functions in chemistry and biochemistry are using the speedy improvement of microfluidics. This booklet focuses its awareness on an enormous subtopic of microfluidics; blending in microscale. It offers the basics of shipping results in microscale together with molecular diffusion, convection, and chaotic advection. The technology and expertise of microfluidics disguise a large spectrum and the science Read more...

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Sample text

A small change in Rayleigh number leads to a large change in the solution. 2 Dean Flow in Curved Pipes The flow field inside a curved pipe was first derived by Dean [28]. For a more detailed review of flow in curved pipes, see [29]. The following detailed derivation was given by Gratton [30]. The model for the flow in a toroidal pipe is depicted in Fig. 16. The pipe has the form of a toroid of a radius of R. 16 Model of Dean flow in a toroidal pipe. diameter is a. The coordinate system for this model is based on cylindrical coordinates, where s is the coordinate of the toroid’s centerline q.

There are few terminologies related to visualization of an Eulerian velocity field. The first and most common terminology is the pathline, also called trajectory of a fluid particle in the flow field. In experiments, pathlines, orbits, or trajectories can be obtained by a long time exposure image of a fluorescent fluid particle. If the particles are idealized so that they are small enough not to disturb the flow, but large enough so that molecular diffusion is neglected, they can move passively with the flow.

The distance done by each step is equal, and  The direction from one point to the next is random. Following these rules, a random walk of a particle can be realized with a simple programe. Considering a one-dimensional random walk on a line, the particle has a random choice of two directions for each of its steps. The distance done by each step is assumed to be s. 23) i¼1 where si is a random step, which can take a value of either þs or Às. 24) i¼1 The proportionality comes from the assumption that the same amount of time is take to make each step (t / n).

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