I intend to simulate transport of one particle representing an insulin molecule in a macro-scale fluid flow ~cm using lattice-Boltzmann coupling. I notice that in tutorials values for friction coefficient and particle mass are close to unity. In this case, the user is able to vary time step value in a reasonable range. I assume this is because the friction coefficient and particle mass which are on both sides of the coupling equation would be roughly of the same order of magnitude. This would allow the user to vary the value for time step without causing any numerical issues for the integration procedure.
In my simulation, I set values for Boltzmann constant times temperature parameter, gamma, and particle mass based on Stokes-Einstein's relation in SI units. I calculate the gamma according to the diffusivity value of the insulin molecule. For the particle's mass, I set it to be equal to the mass of one insulin molecule. In this manner, the value of gamma and particle's mass would be significantly different as they are 2.85e-11 [kg/s] and 9.64e-24 [kg], respectively.
Under this condition, I cannot increase the time step value to be over 5e-13 [s], otherwise, the jupyter notebook kernel would die. Since I am interested in studying transport of this molecule in larger time/length scales for instance in tens of seconds, I need to be able to increase the time step value significantly. I would really appreciate your thoughts on the applicability/possibility of increasing the time step.
All the best,
Benyamin
----------------------------------------------------------
Benyamin Naranjani; PhD candidate
Department of Pharmacy
Uppsala University
Sweden