This project is the extension work of the paper published in JFM: Marangoni circulation by UV light modulation on sessile drop for particle agglomeration.

This project is used to calculate the Marangoni flow stream function as well as the velocity field in a spherical cap droplet of various contact angle based on Stokes flow assumption. Streamlines folder contains all the codes needed to calculate and plot stream function and folder Velocity contains codes calculating velocity field in droplet based on Spherical coordinates or Toroidal coordinates.

For calculating the stream function and streamlines, run the main program GaussianTensionStreamFunction.m. The main program calculate the stream function values at 100X100 nodes and return a *.mat file. Four different patterns of surface tension is considered and correspond N2(Gaussian).m, N2(Step).m, N2(MultipleGaussian).m and N2(Concentric).m, which are discribed below:

When using the code for calculation, the proper N2(***).m should be picked and suitable modifications should be made to match the surface tension profile one is dealing with, and rename it to N2.m to overwrite the original N2.m file.

Note that PSI.m file implements parallel computing by calling spmd() in matalbe. One should also change the value of nodes to match the number of CPUs used in the calculation. The number of CPUs should also be put in the main program in parpool($number of CPUs).

The Streamlines folder also contains 2 codes for ploting streamlines. StreamFunctionPlot.m create a draft plot for adjusting the contour value list and StreamFunctionPlot_Final.m plots the refined contour.

A sample result is also included in this folder as StreamFunction_b37.8_s200_p0.2_t900.mat.

For calculating the velocity field in droplet, either Spherical coordinates (folder Velocity_by_Spherical_Coordinates) or Toroidal coordinates (folder Velocity_by_Toroidal_Coordinates) can be used. The patterns of surface tension considered are same as the four patterns discribe in Streamlines, thus, the modification for N2.m is exactly the same as in streamline calculation. Parallel computing is also implemented for velocity calculation:

The main program is Velocity_of_Spherical_Coordinate.m.

dpsid.m needs to be modified for nodes value to match the number of CPUs used.

The main program is VelocityInToroidalCoordinates.m.

Ualpha1.m, Ualpha2.m, Ubeta1.m and Ubeta2.m need to be modified for nodes value to match the number of CPUs used.