Approximations to be made to model Vincent's flow
Evgenii Rudnyi
http://www.msc.univ-paris-diderot.fr/~vincent/portailmaths.html
and small comments are below.
To solve a CFD problem in general one should consider the continuity,
momentum and energy equations. If we are not interested in the
temperature distribution, say assuming the constant temperature, then
the energy equation can be neglected. After that the problem can be
divided to compressible and incompressible flows. Basically the
assumption for incompressible flow is that the density is constant.
However, this approximation is quite good for the flows with the low
Mach number, so it can be applied to somewhat a more general class of
problems.
For incompressible flow the continuity equation becomes that the
divergence of velocity is zero
http://en.wikipedia.org/wiki/Incompressible_flow
Well, it is also necessary to solve the Navier-Stokes equation
http://en.wikipedia.org/wiki/Navier_Stokes_equations
The next approximation is related to viscosity. When one can neglect it,
then we obtain inviscid incompressible flow and then there are some more
subdivisions there. Say when one can additionally neglect vortices in
the flow, there is a theory of potential flow (irrotational
incompressible inviscid flow).
Alternatively when one leaves the viscosity under consideration but
neglects the inertial forces (velocities are small and viscosities are
high), one obtains the Stokes flow
http://en.wikipedia.org/wiki/Stokes_flow
and I guess that this is what Vincent considers. Here it would be good
to mention that this is valid for Newtonian fluid only. If fluid is
non-Newtonian, then the life will be harder. Finally one should
understand that this concerns one phase flow without surface effects and
fluid structure interactions.
Best wishes,
Evgenii
Richard Gordon
re:
Fleury, V. (2010). Chaining the Evolution of Chordates from
Cephalochordates to Amniotes via the Physical Morphogenetic Flow
[PowerPoint presentation]. Silver Bog, Second Life®, Embryo Physics
Course.
Fleury, V. (2010). Chaining the physical events in tetrapod
embryogenesis: Soft macles, visco-elasticity and vortex flows in
embryogenesis [PowerPoint presentation]. Second Life®, Embryo Physics
Course.
Dr. Evgenii Rudnyi
CADFEM GmbH
use...@rudnyi.ru - Other
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eru...@cadfem.de - Work
Germany
http://evgenii.rudnyi.ru/ - Home
http://groups.google.com/group/mor4ansys - Work
Dear Evgenii,
Yes, these are hard problems. I attach:
Nouri, C., R. Luppes, A.E.P. Veldman, J.A. Tuszynski & R. Gordon
(2008). Rayleigh instability of the inverted one-cell amphibian embryo
[Invited: "Physical Aspects of Developmental Biology" special issue,
Guest Editor Shane Hutson, Vanderbilt University]. Physical Biology
5(1), 015006.
in which our assumptions were:
1. Two fluids of different densities, with an interface, to
approximate a single, initially stratified fluid.
2. Newtonian behavior, when we know viscoeleasticity is present.
Much research in CFD (computational fluid dynamics) will be needed to
overcome making such approximations. I would like to move this on to a
combined CFD/MD (molecular dynamics) simulation incorporating the
cortical microtubules as both flow aligned and exerting forces on the
fluids. We started generating such code under a one shot contract, and
could use help to bring it to fruition. Thanks.
Yours, -Dick
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Evgenii Rudnyi
> Nouri, C., R. Luppes, A.E.P. Veldman, J.A. Tuszynski & R. Gordon
> (2008). Rayleigh instability of the inverted one-cell amphibian embryo
> [Invited: "Physical Aspects of Developmental Biology" special issue,
> Guest Editor Shane Hutson, Vanderbilt University]. Physical Biology
> 5(1), 015006.
Thanks for the paper. It looks very interesting.
> in which our assumptions were:
>
> 1. Two fluids of different densities, with an interface, to
> approximate a single, initially stratified fluid.
> 2. Newtonian behavior, when we know viscoeleasticity is present.
>
> Much research in CFD (computational fluid dynamics) will be needed to
> overcome making such approximations. I would like to move this on to a
> combined CFD/MD (molecular dynamics) simulation incorporating the
> cortical microtubules as both flow aligned and exerting forces on the
> fluids. We started generating such code under a one shot contract, and
> could use help to bring it to fruition. Thanks.
Well, you might also think of some mesoscale theory, say Dissipative
Particle Dynamics.
Some time ago at IMTEK, we have made lectures for MST engineers on
molecular simulation:
http://evgenii.rudnyi.ru/teaching.html#md
It could be considered as a starter for not specialists. In the second
part of the last lecture Chemometrics and Applications, there are some
slides on multiscale.
Best wishes,
Evgenii
Evgenii Rudnyi
> Nouri, C., R. Luppes, A.E.P. Veldman, J.A. Tuszynski & R. Gordon
> (2008). Rayleigh instability of the inverted one-cell amphibian embryo
> [Invited: "Physical Aspects of Developmental Biology" special issue,
> Guest Editor Shane Hutson, Vanderbilt University]. Physical Biology
> 5(1), 015006.
>
> in which our assumptions were:
>
> 1. Two fluids of different densities, with an interface, to
> approximate a single, initially stratified fluid.
> 2. Newtonian behavior, when we know viscoeleasticity is present.
I have finally read the paper more carefully. I find it very
interesting. I would never think that a rotation of an amphibian egg
could influence its development.
I lack however the knowledge about the phenomenology of an egg, say an
amphibian egg. What reading could you recommend as a starter with the
goal to learn the terminology and basic processes that happens in the
egg during the development?
Best wishes,
Evgenii