This is the second in a series of papers on the effects of dust on multifluid , magnetohydrodynamic shock waves in weakly-ionized molecular gas .
We investigate the influence of dust on the critical shock speed , v _ { crit } , above which C shocks cease to exist .
Chernoff showed that v _ { crit } can not exceed the grain magnetosound speed , V _ { gms } , if dust grains are dynamically well coupled to the magnetic field .
Since \mbox { $V _ { gms } $ } \simeq 5 km s ^ { -1 } in a dense cloud or core , the potential implications for models of shock emission are profound .
We present numerical simulations of steady shocks where the grains may be well- or poorly coupled to the field .
We use a time-dependent , multifluid MHD code that models the plasma as a system of interacting fluids : neutral particles , ions , electrons , and various “ dust fluids ” comprised of grains with different sizes and charges .
Our simulations include grain inertia and grain charge fluctuations but to highlight the essential physics we assume adiabatic flow , single-size grains , and neglect the effects of chemistry .
We show that the existence of a phase speed v _ { \phi } does not necessarily mean that C shocks will form for all shock speeds v _ { s } less than v _ { \phi } .
When the grains are weakly coupled to the field , steady , adiabatic shocks resemble shocks with no dust : the transition to J type flow occurs at \mbox { $v _ { crit } $ } \approx 2.76 \mbox { $V _ { nA } $ } , where V _ { nA } is the neutral Alfvén speed , and steady shocks with \mbox { $v _ { s } $ } > 2.76 \mbox { $V _ { nA } $ } are J shocks with magnetic precursors in the ion-electron fluid .
When the grains are strongly coupled to the field , \mbox { $v _ { crit } $ } = \min \left ( 2.76 \mbox { $V _ { nA } $ } , \mbox { $V _ { gms } $ } \right ) .
Shocks with \mbox { $v _ { crit } $ } < \mbox { $v _ { s } $ } < \mbox { $V _ { gms } $ } 
have magnetic precursors in the ion-electron-dust fluid .
Shocks with \mbox { $v _ { s } $ } > \mbox { $V _ { gms } $ } have no magnetic precursor in any fluid .
We present time-dependent calculations to study the formation of steady multifluid shocks .
The dynamics differ qualitatively depending on whether or not the grains and field are well coupled .