# Rheological Study of an Extruded Fish Diet with the Addition of Hydrolyzed Protein Flour
## 1 Introduction  
The extrusion cooking of food for human and animal consumption is a unitary operation in which various products are produced from starchy raw materials, animal or vegetable origin, and oilseeds. Products for animal feed, especially for fish farming, are an example of these extruded products, which under high temperature and short time cooking conditions (HIST), mixing, shearing, and forcing the materials are carried out through a nozzle designed to form the product, processes strongly related to the rheological properties of the materials in the extruder [1].  
Since the raw materials used in animal diets have different rheological properties, their understanding can facilitate the optimization of processing methods, process control, and product quality, as well as the quality of the finished product, such as texture, flavor release, stability, appearance, among others [2]. Apparent viscosity is one of the most important rheological properties of raw materials of non-Newtonian biological origin, being a variable used for the engineering analysis of extrusion [3], mainly in aspects of the behavior of the fluid during processing. Viscosity is related to composition and process variables during extrusion [4].  
In extrusion processes, structural changes of the components occur since biopolymers such as starch and proteins are susceptible to high temperatures or mechanical stress [5]. Under suitable conditions, this increases the digestibility of the macromolecules [6]. The starch generates an increase in gelatinization and breakdown of its chains forming dextrins, and the proteins take place the unfolding of their structure and breaking of intermolecular bonds yielding peptides of different molecular weight, establishing molecular interactions between terminal groups of the protein and starch molecules. These changes that occur during the extrusion process affect the behavior of the fluid and can be measured, facilitating product quality assurance.  
Different techniques have been used to carry out rheological measurements, which vary according to whether the determination is carried out off-line or in-line. In the first case, the experimental conditions can be applied mainly through capillary rheometers; these measurements are made with higher water contents, so the determined viscosity is lower than that developed directly in an extruder [7]. With in-line measurement systems, measurement is performed by coupling a device to the extruder outlet [7; 8; 9; 10; 11; 12], achieving measurements that avoid structural changes and water loss during the height [13]. Both the cylindrical-type die (rod die) and the slit-type die (slot die) can be directly coupled to the extruder, achieving different shear rates with the screw speed, achieving broader ranges of shear rate [14; 15]. Regardless of the technique used to determine the rheological behavior under extrusion firing, it has been established that molten materials are essentially pseudoplastic whose rheological behavior can be adequately adjusted to a Power Law model [1; 15; 16]. The first rheological model proposed to explain the behavior of cereal masses melted by extrusion was Harper's [9], which assumes that the group behaves as a pseudoplastic fluid, according to the Power Law model, with dependence on change in temperature of the Arrhenius type and an exponential sensitivity to change in water content [7].  
The present work aims to study the rheological behavior of an extruded fish diet incorporating hydrolyzed protein flour processed by extrusion. The measurement was carried out in-line with a slit die rheometer, defining the rheological models and parameters that fit the process through the methods mentioned above to obtain real processing conditions for future scaling, determine the effect on the viscosity of the hydrolyzed protein system, and adjust a model of the system.