Two colliding dust particles can stick, bounce, fragment, melt, or vaporize upon collision, depending on the relative velocity and material parameters. We have theoretically modeled the microphysics of the coagulation process in the collision of two, smooth, elastic, spherical grains. It is shown that sticking will occur when the relative collision velocity is less than a critical velocity, v(cr), which depends on the grain size and the elastic properties and surface energy of the material. Critical relative velocities for coagulation have been evaluated as a function of grain sizes for silicate, icy, and carbonaceous grains. We find that v(cr) varies as R-5/6 where R is the radius of curvature of the colliding particles. Micron-sized quartz particles are able to coagulate at collision velocities of less than congruent-to 10(2) cm s-1, while centimeter-sized grains require velocities below 10(-2) cm s-1. Critical velocities also depend on the material properties (interface energy and elasticity) of the particles; thus small icy grains stick better than small quartz grains (v(cr) is congruent-to 2 x 10(3) cm s-1 vs. 10(2) cm s-1 for 1000 angstrom grains). Realistic interstellar grains may be nonspherical and have core mantle structure and rough surfaces. In addition, plastic flow may also be of importance. The role of these effects in the coagulation process is examined. It is concluded that nonsphericity has only a minor effect. Surface irregularities can limit coagulation considerably. For submicron-sized ice grains this may reduce the critical velocity by a factor congruent-to 3. For silicate and graphite grains this reduction may be much larger. While plastic deformation is very important in the collision of centimeter-sized metal spheres, micron-sized grains have a much higher yield strength, and their sticking will not be affected much. Finally, we briefly examine sticking in the collision of fluffy agglomerates. Coagulation of interstellar grains in dense clouds is briefly discussed. We conclude that efficient coagulation requires coverage of grain cores by an icy grain mantle. Even then, coagulation will lead to only a doubling of the mass of a large (a > 1000 angstrom) grain within a dense core lifetime. Smaller grains can, however, be efficiently removed from the cloud by coagulation. Thus, coagulation can have a dramatic effect on the visible and, particularly, the UV portion of the extinction curve in dense clouds and on their IR spectrum.
