Dynamics of coalescence and spreading of liquid polymeric particles during coating formation

Processes of agglutination, coalescence and spreading of polymeric powder particles during coating formation are considered using methods of mathematical modeling. The relationships to evaluate time of particles agglutination, velocity of coalescence and spreading of material on the surface of a treated body are given. Recommendations on intensification of the given technological stages are presented.

Particles agglutination occurs in the deposition process of polymeric powder particles on a treated surface and after completion of this technological stage, in the following stagecoalescence, spreading, and finally, coating formation [1,2]. Peculiarity of agglutination stage is that in the course of its implementation the certain connections are set between particles of the same materials in contact. In adhesion theory this case is called autohesion [3]. It is assumed that material of the particles in the contact region is not mixed; boundary surface of particles is retained.
In the next stagecoalescence stage of powder particles provided that their material is in the fluid (liquid) state the boundary surface of the particles unnoticeable. Over time, in the absence of external factors the two merging particles under the action of capillary forces form one particle close in shape to a sphere.
It should be noted that these two processes can occur, primarily, between softened particles of thermosetting materials as well as between fritted or melted thermoplastics particles.

Agglutination of polymeric powder particles
In order to mathematically describe the agglutination process of powder particles in an applied layer let us move from real porous medium of this layer to fictitious [4] and such that its voids are identical gaseous cavities of spherical shape uniformly distributed over the volume. It is easy to assure that in case of rhombohedral laying of spherical particles the diameter of these pores 2 1/3 (6sin 1 cos / ( (1 cos )) 1) Here щcorrection factor, surface tension coefficient (surface tension) at the contact boundary Slightly different evaluation of the agglutination dynamics of polymeric powder particles can be obtained by considering an ideal model [4] of the layer instead of the named above fictitious model. At the initial time using the Kozeny formula we define the channel radius of an ideal porous medium by the formula: or by the relationship: where kpermeability coefficient of the applied layer of the medium [4,5]. Further, assuming that dependence (4) where the bubble radius a is replaced by the channel cross-section radius r  acts in a circular cross-section of the pore channel we find: (9) Substituting dependence (3) in the equation (9), we approximately obtain: The coalescence process of the polymeric powder particles is typical, in our opinion, for the particles the material of which is in slow-flowing state or close to it, for example, in a plastic state. In this case with respect to the processes occurring in the applied powder layers we will assume that particles coalescence is the stage that follows the agglutination when as a result of heating of material up to a certain temperature * T TT  ( * Tlimiting temperature, probably, decomposition temperature of the polymeric material) the surface tension, viscosity decrease and its fluidity increases. Considering a layer of liquid polymeric particles on the body surface we can identify, firstly, a layer of particles in contact with the body; secondly, layer of particles in contact with the ambient gaseous medium and, finally, a plurality of particles located in the inner region of the layer. For the latter it is typical that each of them is surrounded by other particles.
It should be expected that coalescence processes of liquid particles in the selected areas of the applied layer will be slightly different from each other. The near-border particles, their coalescence will of course be under a certain influence of both the solid body and ambient gaseous medium (air).
Let us consider further as the most interesting from a practical point of view coalescence of polymeric powder particles that are located on the surface of a treated body. Considering the regularities of spreading liquid on the solid surface [6][7][8] we adopt the following assumptions as the initial ones. Let us assume that liquid and gas media are incompressible; process of deformation, form changing of particles, pores is slow (quasi-stationary), isothermal; pressure in material of particles Due to the fact that at coalescence of adjacent particles the tangent EQ ( fig. 3) must be parallel to the axis Ox center of the circle C is located on the line DQ we get: where angle /2    .    along the body, it is quite possible that when shifting the point P the value of angle  will be changing. Considering this fact we can write: