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Re: [ESPResSo-users] Educated guess about gamma in Langevin thermostat

From: Stefan Kesselheim
Subject: Re: [ESPResSo-users] Educated guess about gamma in Langevin thermostat
Date: Mon, 14 Jan 2013 14:03:35 +0100
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:17.0) Gecko/17.0 Thunderbird/17.0

Dear everybody,
sorry, I assumed, you wanted to use LB.
But it seems you don't, and the Ulf is right :-). And you should remember: High friction makes all processes slow, including relaxation towards thermodynamic equilibrium.

On 01/14/2013 10:32 AM, Stefan Kesselheim wrote:
I have one very small remark:
The combination of viscosity and (apparent -- see Ahlrichs 98) friction determines the effective size of the particles. The radius acts as the prefactor of the hydrodynamic interactions (see e.g. literature on Stokesean Dynamics). Sometimes this length scale (compared to other length scales in the system) must be matched. Especially in low Re conditions matching this can sufficient, as long as the Schmidt number is high enough. The hydrodynamic particle size remains constant as long as visc/friction is held constant, and it can not be much larger than the LB lattice size (this is because the coupling is point--like).

On 01/11/2013 05:40 PM, Ulf Schiller wrote:
Hi Salvador,

On 12/19/2012 06:34 PM, Salvador H-V wrote:
I am doing some simulations for a two-dimensional  hard-sphere
The interaction potential is the purely repulsive Lennard-Jones (WCA)
using the rigid_bond feature to constraint the bond in the dimers.

I would like to choose a value of the the friction coefficient (gamma = 6.0*Pi*dynamic_viscosity*sphere_radius / mass ) in the Langevin thermostat
such as is representative of the solvent experimental viscosity.

Using the experimental data, I obtain the following
M ~ 4.4x10^(-15) kg
T ~ 293.15 K
tao = sigma * ( mass / kbT)^1/2 ~ 2.08x10^-3 s
viscosity ~ 0.001002 Pa * s
sigma = 2x10^-6 m

Then, gamma_langevin = 6 * Pi * viscosity * radius / mass
and in reduced units  gamma / tao = gamma_reduced ~ 8930

If my above simple calculations are right and if I understood well,
accordingly to previous post in the mail list,  we have to use a value
of time_step
such as:  gamma_reduced * dt  / 2.0 is < 1 and preferably around  0.1.

Then, I should use a time_step <= 0.00002 that is very small and will
require very long simulations to obtain the experimental time window.

I was wondering if somebody could provide suggestions of how to reduce
the value of gamma (so, i can increase the time_step) but still
representing the solvent viscosity.

I think that depends on what physics you want to look at. If inertial effects can be neglected in your system, you could try to use an artificial mass instead of matching the experimental mass. Keep in mind that a too high value of gamma will also affect the accuracy of the integrator (the Verlet algorithm with velocity dependent forces is first order only).

Another possibility is to think whether you really need the exact value of the viscosity. It might be enough to match dimensionless quantities such as the Reynolds number, Peclet number, etc. One can then typically scale the simulation parameters to obtain reasonable values. The details depend again on what you want to simulate/measure.

Hope this helps,

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