Team:SDU-Denmark/project-m

Modeling

[[Physical Modelling]]

What we want to do here is to create a model with which the effects of changing certain parameters in the system can be estimated. Since the model should be able to run on an ordinary computer we have to simplify how a flagella works in our system. A flagellum creates propulsion by spinning around in a helical shape. Many who models a single flagellum considers this shape rigid and then calculate a flowfield from the spinning helix. Our system consists of many flagella and modelling every single flagellum in this way would take to much time. The overall result of the spinning flagellum is that the bacteria moves in an almost straight line. We will therefore consider the forces created by the flagellum to be simply a force pointing in the direction of the flagellum. The size of this force can be approximated by calculating drag on a swimming bacteria.If the bacteria is considered almost spherical the drag force can be calculated by using the following formula: <math> F_d = -6 \pi \eta r v </math> where η is the viscosity of the fluid in which the bacteria is swimming, r is the radius of the bacteria and v is the speed.

Using the following data

<math> r = 0.4*10^-6 m </math> <math> v = 50*10^-6 m/s </math> <math> \eta = 8.94*10^-4 Pa*s </math>

The dragforce and thereby the force created by the flagella (all the flagella) of a e. coli is <math> F_d = 3.37*10^-13 N </math>

First, we will make a model consisting of a 1D-grid, afterwards we will expand it to 2D.

1D-model indsæt billede her

What we do from here is that we neglect the body of the bacteria. Instead we imagine that the flagella are glued to the surface off the pipe in such a way that they

<math>\coprod_{i=1}^N x_i</math>

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