You can achieve this by using Forces to direct the particles to your mesh surface. The key is to change the shape of the field to "Surface" :
Here the cube has a Force Field added, with the type set to Force, Shape of 'Surface' and a negative strength. This will draw all affected particles towards the surface.
Note that particles aren't affected by forces applied to their own mesh - so you need to create a separate mesh to generate the particles. However, this could be in the same location as the mesh - so that it appears that the particles are spawned by the same mesh - if that is a requirement.
I also added a couple of fource fields to affect the particles - a 'Drag' field to slow them down (with Quandratic set to 2.0 to slow fast moving particles more than slow-moving ones) and a Turbulance field to move them about a bit. You could also add a Self Effect force on the particles themselves to push them gently away from each other. You'll need to play with the relative strengths of those forces for your situation but I used -5 for my 'surface' effect, 0.005 for the particle self-effect repulsion force, Linear 1.000 and Quadratic 2.000 for the Drag field and 7.4 for the Turbulence field to give them some 'jiggle'.
I also added Collision to the mesh so as to affect the particles when they do hit the surface - to effectively 'grab' them and slow them a bit - by increasing Stickiness to 0.7, Damping to 1.000 and Friction to 0.25.
This produces the following effect :