Proxima Centauri b seems to be the closest exoplanet in its habitable zone. At a distance of $4.2$ lightyears, travel to this planet within a human lifetime is not impossible prima facie, however doing so requires a mean velocity that is an appreciable fraction of the speed of light, i.e. around $0.1 c \approx 3 \times 10^4 \text{km/s}$.
My questions concern the problem to travelling at this speed posed by the presence of an interstellar medium due to (1) the damage caused by collisions with microscopic particles and (2) the loss of momentum to the interstellar medium.
Firstly the problem of collisions. At this speed it is plausible that collisions with even microscopic particles pose a problem. A crude equation of the incident kinetic energy with energy of required to raise steel to its boiling point from absolute zero, suggests that a collision of a dust particle $1\text{mg}$ ($\approx$ a grain of sand) travelling at $0.1c$ would be enough to vaporize about $0.6\text{kg}$ of steel from the surface of a spacecraft, $$ \frac{(1\text{mg})\cdot(0.1 c)^2}{2 \cdot (420 \, \text{kJ} \cdot\text{kg}^{-1} \cdot\text{K}^{-1})\cdot (1643 \text{K})} = 0.65\ldots \text{kg} $$ and transfer about the same momentum as a bowling ball thrown from a moving car. Collisions with objects that are hard enough to start to penetrate steel before vaporising are potentially even more serious problems with the penetration depth of a hard hypervelocity projectile growing proportional to the incident kinetic energy (see e.g. Walker 2001).
Interstellar medium is of course very empty. However to be empty enough that such collisions could be neglected requires that dust particles large enough to do damage have a number density $n \ll 10^{-19} \text{m}^{-3}$, (roughly the inverse of the volume traced out by a small ($10\text{m}$ by $10\text{m}$) spacecraft travelling $4.2\text{ly}$. Is the density of potentially damaging particles in the interstellar medium low enough to permit interstellar travel at speeds $0.1c$?
The second problem is the problem of viscosity. Neglecting the potentially damaging nature of collisions with larger particles, the fact space is not empty implies that work must be done against it to maintain a constant velocity. Does presence of a viscous interstellar medium place any practical restrictions on the speed of interstellar travel?