# Critical Review of Techniques for Food Emulsion Characterization
## 4 Emulsion Fractionation and Characterization Methods
### Capillary Hydrodynamic Fractionation (CHDF)  
Another interesting method for emulsion fractionation and characterization is capillary hydrodynamic fractionation (CHDF) [245; 246]. CHDF is a method based on the differential migration of particles in capillaries under hydrodynamic conditions used for estimating emulsion droplet size and size distribution. It allows characterization and high-resolution separation of dispersed particles or droplets of varying sizes as they are carried by a carrier liquid through an open capillary with an inner diameter of 10-15 \(\upmu\)m [223]. Similarly as in the FFF methods, the separation process relies on Poiseuille flow and occurs due to the migration of unevenly sized droplets to different streamlines within the parabolic velocity profile. The fluid velocity profile in the capillary can be described by the Hagan-Poiseuille equation:  
\[d^{2}=32\eta L\frac{v}{\Delta P} \tag{14}\]  
where \(d\) is the capillary inner diameter, \(\eta\) is the viscosity of the fluid, \(L\) is the capillary length, \(v\) is the average velocity of the fluid, and \(\Delta P\) is the difference in the pressure between the capillary inlet and outlet. In CHDF, the droplet separation is also driven by the size exclusion of the droplets at the capillary wall, and colloidal forces resulting from droplet/capillary electric double layer repulsion. Larger droplets can only approach the capillary wall within a distance corresponding to their radius (\(r_{L}\)), while smaller droplets within distances \(r_{S}\ll r_{L}\)[247]. In consequence, smaller droplets are affected by a thinner exclusion layer (layer adjacent to the capillary wall) and are dragged by slower-moving regions of the flow, while larger droplets are affected by a wider exclusion layer and move more quickly along higher velocity streamlines closer to the capillary center. The droplets emerge from the capillary in order of decreasing diameter, which allows for effective fractionation of droplets based on their size. UV detectors or turbidity sensors are typically used for the detection of droplets emerging from the capillary and estimating the number of droplets in each fraction [248]. The droplet size is determined by measuring their elution time. Capillary hydrodynamic fractionation is commonly used to measure the size of particles ranging from 5 nm-3 \(\upmu\)m.  
The rate of transport of droplets through the capillary can be calculated from the ratio of capillary length to average droplet residence time. The rate of droplet transport relative to the eluant can be expressed using the separation factor (\(Rf\)), which is defined as:  
\[R_{f}=\frac{rate\ of droplet\ transport\ through\ the\ capillary}{rate\ ofeluant\ transport} \tag{15}\]  
The eluant transport rate through the capillary is established by measuring the mean elution time of a marker with a known molecular size, such as sodium dichromate. In both capillary hydrodynamic fractionation and hydrodynamic chromatography, the separation factor exceeds one, indicating that particles generally travel faster through the capillary tube than the eluant does. This is a notable departure from classical chromatography, where particles are typically hindered during movement through the column with \(R_{f}\!<\!1\). In flow-based separations, although a maximum value for \(R_{f}\) is theoretically 2 when particlesmove precisely at the center, practical values tend to be lower due to retarding effects exerted by capillary walls on particle velocity. Droplet elution times in CHDF are also influenced by factors such as capillary diameter and length, eluant composition and ionic strength, and mobile phase velocity [246]. The separation factor increases with decreasing internal diameter of the capillary and its increasing length. A longer capillary provides a greater path for particle migration, facilitating better size-based separation and resulting in higher resolution.