  Several mechanisms have been identified that create dense particle clumps in
the solar nebula. The present work is concerned with the gravitational collapse
of such clumps, idealized as being spherically symmetric. Calculations using
the two-fluid model are performed (almost) up to the time when a central
density singularity forms. The end result of the study is a parametrization for
this time, in order that it may be compared with timescales for various
disruptive effects to which clumps may be subject. An important effect is that
as the clump compresses, it also compresses the gas due to drag. This increases
gas pressure which retards particle collapse and leads to oscillation in the
size and density of the clump. The ratio of gravitational force to gas pressure
gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans
parameter with the sound speed replaced by an the wave speed in a coupled
two-fluid medium. Its use makes the results insensitive to the initial density
ratio of particles to gas as a separate parameter. An ordinary differential
equation model is developed which takes the form of two coupled non-linear
oscillators and reproduces key features of the simulations. Finally, a
parametric study of the time to collapse is performed and a formula (fit to the
simulations) is developed. In the incompressible limit $J_t \to 0$, collapse
time equals sedimentation time. As $J_t$ increases, the collapse time decreases
roughly linearly with $J_t$ until $J_t \gtrsim 0.4$ when it becomes
approximately equal to the dynamical time.
