# Photopolymerization of Ceramic Resins by Stereolithography Process: A Review
## 4 Ceramic Suspensions and Effects on the Process  
Effects of suspension's solid loading influence several aspects of the process. Primarily parameters such as yield stress or flow index change, rheological behavior is predominantly influenced by the number of solid particles in suspension. In ceramic suspension for SLA, maximum solid loading possible is often desired for different reasons, from the ease of green parts post-process to a more controllable shrinkage effect. Krieger-Dougherty analytical formulation is frequently used to obtain a model for relative viscosity (\(\eta_{r}\)) of suspensions (Equation (2)):  
\[\eta_{r}=\frac{\eta_{s}}{\eta_{d}}=\left(1-\frac{\phi}{\phi_{m}}\right)^{-B \cdot\phi_{m}} \tag{2}\]  
where \(\eta_{s}\) and \(\eta_{d}\) are respectively viscosity of suspension and dispersion medium, \(\phi\) is the solid loading of suspension, \(\phi_{m}\) is the maximum solid loading obtainable, \(B\) is the Einstein coefficient. \(B\) and \(\phi_{m}\) depend on the shape and size of particles, so a fit model to determine them is necessary [17; 26]. In literature, differences between Krieger-Dougherty model and experimental data are quite low, demonstrating a good reliable of analytical formulation. Figure 5: Shear stress vs. strain rate for Newtonian and non-Newtonian fluid. Several studies confirm a raise of relative viscosity with solid loading incrementation, in addition to a deviation from Newtonian behavior [13; 18; 19; 26; 44; 45]. It is well known that particle size in ceramic suspensions is one of the most influential aspects of fluid behavior and optical characterization. Larger particles are more difficult to disperse in monomeric base than finer ones, it is due to a lower surface energy (lower specific surface). Previously, the effect of particle size on suspension's stability has been investigated: Wan der Waals interactions and Brownian's motion cause an agglomeration of particles as finer they are. [PERSON] et al. [46] studied effects of nanoparticles (40 nm) addition to micro-particles (15 \(\upmu\)m) silicon carbide (SiC) suspension, an interesting result has been found. The viscosity of suspensions is heavily influenced by nano-particles addition, while curing thickness showed a decrease. The influence of nano-particles addition on stability of suspension is one of the most interesting aspects, because experimental tests on sedimentation behavior showed a positive effect. Nanoparticles are arranged in the interstices of micro-particles, making agglomeration, and consequently sedimentation, more difficult. The creation of bimodal suspensions has a positive effect also in delaying shear thickening behavior [47]. When a light source hits an object, different optical phenomena take place. The scattering effect (Figure 6) is usually matched with absorption in energy transformation of the source, competing for the attenuation light beam [48]. Optical phenomena in which SLA ceramic suspensions are involved depend on different aspects: solid loading, particle size, RI of particle, RI of the medium, PIs and dyes percentage, energy dose. The scattering effect occurs every time a solid particle dispersed in a medium deviates a beam. A common approach is to consider the scattering coefficient which quantifies the decrease of penetration depth (\(D_{p}\)) due to light deviation of particles. The absorption model introduced by [PERSON] and [PERSON] [50] considers the two different contribute of scattering effect and absorption in evaluating the reciprocal of \(D_{p}\) (Equation (3)):  
\[\frac{1}{D_{p}}=S+A-\phi\cdot A=A_{d} \tag{3}\]  
where \(S\) is the scattering coefficient, which depends on particles size and distribution, the difference between medium RI and particles RI. This coefficient is the reciprocal of scattering  
Figure 6: Light scattering and absorption phenomena in a media charged in ceramic particles. Adapted from [49]. length, which is defined as the dimensional value over which photon propagation becomes randomized [51].