# Can kerolox or SRB soot particles grow too large too quickly; not accelerated in expanding exhaust leading to a loss of mass-specific impulse?

In this answer to Is methyl silane CH6Si ever considered as fuel in rocketry? I argue that there's no huge loss in mass-specific impulse (Isp) when producing sand (and by extension soot) in the exhaust as long as the particles are small enough that they behave similarly to a gas in that they speed up to the exhaust velocity during expansion and so are effective carriers of momentum.

If they formed and grew extremely quickly, there may be a risk of them getting so large that they are not accelerated to the full speed of the exhaust gas, which we remember is quickly expanded to match the ambient pressure, which is pretty low in space. That low-pressure gas may be ineffective in accelerating large particles.

However, I have no idea what "quick" and "large" mean quantitatively in this context, so I'd like to ask:

Question: Can kerolox or SRB soot particles grow too large too quickly so that they are not sufficiently accelerated in expanding exhaust leading to a significant loss of mass-specific impulse?

• If you have a lot of soot forming, that means combustion is very far from stoichiometric and you're losing a lot of potential chamber pressure already. Sure soot may be an extra nail to the coffin but this seems like a problem that will fix itself as soon as you fix the root problem (way too little oxidizer or very bad mixing). – SF. Apr 24 at 1:12
• @SF. In addition to "quick" and "large" it also remains to be seen quantitatively what "a lot" means. – uhoh Apr 24 at 1:47

Partial answer for solid motors:

Fundamental Aspects of Solid Propellant Rockets (Williams, Barrere, and Huang, ~800 pages, 55 MB) says that if combustion products condense into solids inside the motor, the effect can be detrimental.

From Sections 3.2.6 (page numbered 78):

Typical results show substantial performance losses for particle diameters above 2 microns

(in this graph, $$e$$ is the mass flow fraction of the condensed phase, and "lag" refers to the condensed particles slowing down in the flow)

($$e$$ = 0.5 seems like a lot to me, especially since "We retain the approximation that the condensed phase occupies a negligible fraction of the total volume" but solids are not my field so my intuition is lacking)

• I've downloaded the pdf and will try to read, but you might already know this; is there a place where it states that the reason that the particulates are "not accelerated in expanding exhaust leading to a loss of mass-specific impulse?" In other words, is it a this particular causal relationship, or a different one, or just an observed correlation? – uhoh Apr 24 at 14:04
• @uhoh I assumed it's just because the solid particles don't experience the "natural" acceleration though the De Laval nozzle that gasses do, but that is just an assumption. space.stackexchange.com/questions/18904/… – Organic Marble Apr 24 at 14:34
• In case of gasses, flow is approximated as one-dimensional compressible fluid flow of an ideal gas. This cannot be applied on solid particles. My opinion is that acceleration of solid particles should be related to square to cube law and particle density because solids are accelerated when gasses act on particle surface and acceleration is related to the mass of the particle which also depends on its volume and density. For the same particle size i think that carbon has lowest effect C<SiO2<Al203 – WOW 6EQUJ5 Apr 28 at 11:50
• Given that solids are a lot denser than gasses, it seems perfectly plausible to me that a large portion of the mass flow could consist of solids and still make up only a tiny proportion of the volume of the exhaust. – Vikki - formerly Sean May 29 at 0:03