In the gas drag regime the dissipative force (per unit mass) would be given by:

Where rp is the particle radius, \rho_gas is the density of the gas, and mp the particle mass) and v is the relative velocity of the satellite with respect to the gas-disk.  With the assumption that the test particles are spherical and have an average density \rho_sat, the equation becomes:

(Units of distance are in AU in our system).  The problem is to determine the relative velocity and how the density of the gas changes as a function of the particle position.   Following Beauge` and Ferraz-Mello's approach (Icarus 103, pp. 301-318)) we assume that the relative velocity can be expressed as:

Where \alpha is a parameter that gives the difference in velocity between the disk velocity and the particle's (= 0.995 Adachi et al. 1976) and n is the angular velocity vector of the disk ([0,0,\sqrt(G*Mplan/r3)]).
For the density of the disk I followed the approach of Cuk and Burns (Gas-assisted capture of Himalia's family, submitted to Icarus), i.e.:

Where H is the height of the disk, assumed equal to 0.05*r (Lubow et al. 1999).   rho0 is the central density of the gas-disk, and r0, r1, and r2 are parameters of the disk, that are related to the position where the density is equal to \rho0, and what are the lower and outer edge of the parabolic cutoff.
In the following figures we report two  simulations, courtesy of Matija Cuk, that involve test particles under the effect of gas-drag and without drag.  Without gas drag the particle is lost with a timescale of 50000 yrs.  With gas-drag the particle is captured in the libration island and becomes a Kozai resonator.  The oscillations with period of ~48,000 yrs are associated with the s₆ frequency of Saturn.
 

The images below represent the orbital evolution of test particles under gas-drag, integrated bacwards in time, under the effect of jupiter alone (no s₆ perturbations are present in this case).  These particles were captured in the Kozai resonance as well.