Conical Annular Nozzle Pressure Prediction and Applications to 3D Food-Printing for Dysphagia Diets

Abstract

In order to solve the dietary problems of patients with dysphagia, a mathematical model for predicting extrusion pressure is established. The predictive model parameters are determined with the aid of the finite element method, and a 3D printing nozzle capable of printing nutrient-rich sandwich food is designed according to the predictive model. Pumpkin puree and minced pork are verified according to IDDSI standards. Finally, the accuracy of the predictive model and the printing effect of the design nozzle are verified by extrusion and printing experiments, respectively. The results show that four groups of simulation experiments reveal that the extrusion pressure increases by 15.6%, 13.5%, 12.7% and 12.4%, respectively, with a 1 cm increase in nozzle length. When the nozzle length is in the range of 1–5 cm, the extrusion pressure increases with the increase of the volume flow rate in the extrusion cylinder. The extrusion speed has little correlation with the length of the nozzle outlet, but for every 1 cm³/s increase in the inlet volume flow rate, the extrusion speed increases by about 1.5%. The finite element simulation experiment determines that the parameters of the prediction model are σ₀ = 0.6, α = 1.1, m = 0.21, τ₀ = 0, β = 0.52 and n = 0.2; the error between the predictive value and the experimental value is 15%, and the printed sandwich food has smooth lines, good molding and complies with IDDSI standards.

1. Introduction

Dysphagia, or difficulty swallowing, affects millions of people worldwide, particularly the elderly and those with certain medical conditions [1,2,3,4]. It presents significant challenges in daily life, often leading to malnutrition and a reduced quality of life due to difficulty in consuming regular food [5,6,7,8,9]. The advent of 3D food-printing technology has opened new avenues for creating customized, easy-to-swallow foods that cater to the specific needs of dysphagia patients [10,11,12].

3D food-printing has been applied to develop various dysphagia-friendly foods, such as meat analogs, fruits and vegetables, with customized textures and nutritional content [13,14]. The technology allows for the creation of bite-sized, easy-to-swallow foods that can stimulate patients’ appetites and improve their nutritional intake. Nutritional customization is essential for dysphagia diets, ensuring that patients receive adequate calories and nutrients [15]. Typically, some researchers mix a variety of ingredients and print them with a single nozzle for enough nutrients [14,16,17]. The development of 3D printed meals rich in pea protein and fibers has been reported to provide a nutritious option for dysphagia patients, enhancing the dietary fiber content and offering a high protein meal [18]. Additionally, the incorporation of isolated pea protein (IPP) in honeyed red ginseng manufactured by 3D printing has shown the potential to improve the nutritional profile and sensory attributes of the product [19].

In addition to utilizing a single nozzle for printing blended materials, 3D food-printing can also employ multiple nozzles to separately print different materials to enhance their nutritional value. It was reported that a novel multi-channel nozzle was used for accomplishing multi-material DIW (Direct Ink Writing) food-printing [20]. This technology allows for printing multiple materials without switching nozzles, thereby overcoming issues related to filament fragmentation or inconsistency during the process. Alternatively, another study reported that, in order to improve the stability of lutein, a coaxial 3D printing nozzle is used to print stuffed food, in which the core is lutein, and the shell is cornstarch paste. The results showed that the lutein retention rate of the printed food is still 70% after 21 days [21].

Textural modifications are crucial for dysphagia management, as they influence the ease of swallowing and safety from aspiration [22]. Studies have reported the successful use of 3D printing to create foods with shear-thinning properties, which are easy to swallow due to a reduction in viscosity under shear stress [23,24]. Additionally, the International Dysphagia Diet Standardization Initiative (IDDSI) framework has been employed to classify and evaluate the suitability of 3D printed foods for dysphagia patients [25].

Rheological properties, including viscosity, elasticity and yield stress, are important considerations for the extrusion of food inks and the self-supporting ability of printed objects [26]. Hydrocolloids, such as xanthan gum, gelatin and pectin, are commonly used to modify the rheological properties of food inks, enhancing their printability and structural stability [27]. The incorporation of various gums into shiitake mushroom-based inks has been shown to improve the mechanical strength and self-supporting capacity of 3D printed objects, classifying them within the IDDSI framework [21].

At present, most of the research focuses on improving the nutrition of printed foods by blending various materials or printing multiple materials with multiple nozzles [28,29,30]. Although coaxial nozzle printing has also been reported, there is still little theoretical guidance on the design of print nozzles [21]. The utilization of blended materials in food-printing may have poor taste, whereas the application of multiple nozzles in food-printing may suffer from inconsistent and high equipment costs. Consequently, there are still challenges in using a single nozzle to print food with high nutrition for dysphagia patients.

The aim of this study is to design a novel conical annular nozzle that can print a sandwich food which mainly contains dietary fiber and protein nutrients for dysphagia patients. To achieve this goal, we established a predictive model for a conical annular extrusion. The constitutive equation of pumpkin puree was determined by rheological experimentation, which employed the Finite Element Method (FEM) for calculating the characterization parameters (viz. σ₀, α, m, τ₀, β and n) of the pressure prediction model. Then, the geometric structural parameters of a conical annular nozzle were calculated by the pressure prediction model. Finally, through printing and IDDSI tests, we validated the printing effects and evaluated the printed paste consistency. In addition, this predictive model can be used not only to predict the extrusion pressure of food materials but also to other materials, which offers theoretical guidance for designing a 3D printing nozzle.

2. Theory

As shown in Figure 1, according to the assumptions of Benbow and Bridgwater [31], the extrusion pressure P is mainly composed of two parts: a die entry term P₁ and a die shear term P₂. Under the action of P₁, the material enters the die entry region, where the material undergoes extensional deformation; in the die land region, the P₂ term overcomes the friction to make the material flow in a pure shear flow along the die. D₀ is the barrel diameter; D₁ is the inner nozzle diameter, a pipe applying the filling of the piston; L and D represent the outlet length and diameter, respectively; and V is the average extrusion velocity.

As shown in Figure 2, based on spherical coordinates, a mathematical model is established for conical annular extrusion. The die entry flow field is set to be radially convergent in the region 0 < θ < θ_max and r_min < r< r_max, where θ_max, r_min and r_max are related to the orifice and barrel diameters. For the sake of analysis convenience, the assumptions are as follows:

-

The extrusion material is incompressible.

-

The extrusion material is sufficiently slow for the inertial terms to be neglected.

-

The extrusion material in the die entry is not rotational, which is prone to being stretched.

The velocity components of the angular directions Φ and θ are, respectively, assumed to be zero in the spherical coordinates. The velocity in the radial direction, then, becomes a function of the radial position, r. Basterfield et al. [32] reported that the plastic strain rate of the material flowing through an orifice die is given by

$${\dot{\gamma }}_{\mathrm{p}}=\sqrt{3}\omega {\displaystyle \frac{r_{\min }^2}{r^3}}$$

(1)

where r is the radial coordinate and ω is the velocity at the entrance to the die, viz.

$$\omega ={\displaystyle \frac{V{\sin }^2{\theta }_{\max }}{2\left(1-\cos {\theta }_{\max }\right)}}$$

(2)

Furthermore, we assume the plastic strain rate is a single-valued function of stress.

$$s=f\left({\dot{\gamma }}_{\mathrm{p}}\right)$$

(3)

The stress balance equation based on the spherical coordinate system is given by

$${\displaystyle \frac{\partial }{{\partial }_{rr}}}{\sigma }_{rr}+{\displaystyle \frac{2}{r}}{\sigma }_{rr}-{\displaystyle \frac{1}{r}}\left({\sigma }_{\phi \phi }+{\sigma }_{\theta \theta }\right)=0$$

(4)

where σ_rr a radial stress; σ_ΦΦ is an azimuth stress; and σ_θθ is an elevation stress.

Defining the dimensionless variables as

$$R={\displaystyle \frac{r}{r_{\min }}},S={\displaystyle \frac{s}{\Sigma }},X={\displaystyle \frac{{\sigma }_{rr}}{\Sigma }},\dot{\Gamma }={\displaystyle \frac{{\dot{\gamma }}_p{r}_{\min }}{\omega }},$$

$$f\left({\dot{\gamma }}_{\mathrm{p}}\right)=\Sigma F\left(\dot{\Gamma }\right)$$

(5)

where Σ is an appropriate stress scale.

We assume the material is subject to a Power law relationship as

$$f\left({\dot{\gamma }}_{\mathrm{p}}\right)=k{\left({\dot{\gamma }}_{\mathrm{p}}\right)}^n$$

(6)

where k is the flow consistency.

From Equations (4)–(6), we can obtain

$$X=-\sqrt{3}\left[S_0\left({\displaystyle \frac{D_0^2-D_1^2}{D^2-D_1^2}}\right)+{\displaystyle \frac{12^{\frac{n}{2}}}{3n}}\left(1-{\displaystyle \frac{1}{R^{3n}}}\right)\right]$$

(7)

where $S_0={\displaystyle \frac{s_0}{k{(\omega /r_{min})}^n}}$

Assuming the radial stress is zero at r = r_min and neglecting minor additional stresses gives

$$\begin{array}{l}F={\displaystyle {\int }_{{\theta }_0}^{{\theta }_{\max }}2\pi r_{\max }^2}\sin \theta {\sigma }_{rr}\left({\mathrm{r}}_{\max }\right)\cos \theta \mathrm{d}\theta \\ =\pi r_{\max }^2{\sigma }_{\mathrm{rr}}\left(r_{\max }\right){\sin }^2{\theta }_{\max }\end{array}$$

(8)

In the die entry region, an entry pressure P₁ gives:

$$P_1={\displaystyle \frac{4F}{\pi \left(D_0^2-D_1^2\right)}}={\displaystyle \frac{F}{\pi r_{\max }^{2}si{n}^2{\theta }_{\max }}}=-{\sigma }_{rr}\left(r_{\max }\right)$$

(9)

The following dimensionless solutions are obtained:

$$P_1=-\Sigma X\left(R_{\max }\right)$$

(10)

where

$$R_{\max }={\displaystyle \frac{D_0-D_1}{D-D_1}}$$

(11)

Giving

$$P_1=\left({\sigma }_0+\alpha V^m\right)\ln \left({\displaystyle \frac{D_0^2-D_1^2}{D^2-D_1^2}}\right)+A_S{k}_u{\left({\displaystyle \frac{2V}{D-D_1}}\right)}^n\left[1-{\left({\displaystyle \frac{D-D_1}{D_0-D_1}}\right)}^{3n}\right]$$

(12)

with

$$k_u=k{\sqrt{3}}^{n+1}$$

(13)

$$A_S={\displaystyle \frac{2}{3n}}{\left[\sin {\theta }_{\max }\left(1+\cos {\theta }_{\max }\right)\right]}^n$$

(14)

where σ₀ represents the quasi-static yield stress; α is the velocity factor; V is the average velocity of the material in the nozzle channel; m is the velocity index; D₀ is the barrel diameter; D is the diameter of the annular nozzle; and n is the shear rate index.

In the die land, due to the difficulty in determining the stress and flow pattern, it is assumed that the wall shear stress on the inner and outer surfaces of the annular die land are equal and that there is no wall slip, according to the balance of forces:

$$P_2=\left({\tau }_0+\beta V^n\right)\left({\displaystyle \frac{A_w}{A}}\right)$$

(15)

with

$$A_w=\pi L\left(D+D_1\right)$$

(16)

$$A={\displaystyle \frac{\pi \left(D^2-D_1^2\right)}{4}}$$

(17)

where, A_w represents the total wall area of the annular die, and A represents the cross-sectional area at the die exit.

From Equations (16) and (17), Equation (15) may be written in the following form.

$$P_2=4\left({\tau }_0+\beta V^n\right)\left({\displaystyle \frac{L}{D-D_1}}\right)$$

(18)

where, τ₀ is the wall shear stress at zero flow velocity, β is the velocity factor, and n is the velocity index, L is the length of the annular nozzle. In this study, the maximum conical angle θ_max of the barrel is 45°. The total extrusion pressure is then given by

$$P=\left({\sigma }_0+\alpha V^m\right)\ln \left({\displaystyle \frac{D_0^2-D_1^2}{D^2-D_1^2}}\right)+{\displaystyle \frac{2k{\left(1.2\right)}^n}{3h}}{\left({\displaystyle \frac{2V}{D-D_1}}\right)}^n\left[1-{\left({\displaystyle \frac{D-D_1}{D_0-D_1}}\right)}^{3n}\right]+4\left({\tau }_0+\beta V^n\right)\left({\displaystyle \frac{L}{D-D_1}}\right)$$

(19)

3. Materials and Methods

3.1. Raw Materials

Pumpkins with a moisture content of 75–80%, cornstarch and pork were purchased from the same supermarket (RT-Mart, Jinzhou, China). The pumpkins and cornstarch were stored in a refrigerator at 4 °C and used within three days. The pork was vacuum-sealed and stored for use at 5 °C. The parameters for the pumpkin puree mixture were: pumpkin 96.6 wt%, starch 2.9 wt%, and xanthan gum 0.2 wt%; the parameters for the minced pork mixture were: pork 50.97 wt%, water 45.9 wt%, xanthan gum 2.13 wt%, and salt 1 wt%.

3.2. Determination of Rheological Properties

The rheological properties of the material were conducted using a Discovery TA-HR-10 rheometer (TA, New Castle, DE, USA). This test was performed with parallel plate molds having a diameter of 5 cm and a gap distance of 0.2 cm. The test plate gap was set at 0.1 cm, the temperature was maintained at 25 °C, and the shear rate range was 0.1 to 90 s⁻¹. For the pumpkin puree and minced pork, the shear stress exhibited a nonlinear relationship with the shear rate, which could generally be characterized by the Power law model. However, FEM required an input of apparent viscosity variation with respect to shear rate [33].

$${\eta }_a={\displaystyle \frac{\tau }{\dot{\gamma }}}=k{\dot{\gamma }}^{n-1}$$

(20)

where η_a was apparent viscosity; τ was shear stress, Pa; γ was shear rate, s⁻¹; and k was the consistency coefficient.

3.3. IDDSI Tests

According to the IDDSI, texturally modified food can be divided into 8 levels [34]. This standard can be used to determine whether the texture of the material meets the requirements of patients with dysphagia. Fork squeeze and spoon tilt tests were performed on pumpkin puree and minced pork. A fork pressure test was performed by pressing the minced pork with a fork until the nail turned white. A spoon tilt test was carried out to test the adhesion and cohesion of the pumpkin puree.

3.4. FEM Analysis

The trend of the apparent viscosity with respect to the shear rate variation was observed, and the fitted results were used as input conditions for FEM simulation. The important parameters in the predictive model are related to the nozzle geometry and extrusion process parameters. The FEM is used to analyze the extrusion flow field to determine the extrusion pressure prediction model.

The important parameters of Equation (19) are associated with the nozzle geometry and extrusion process parameters. FEM was employed to analyze the extrusion flow field for calculating the parameters in Equation (19). It was assumed that the pumpkin puree behaved as an incompressible generalized non-Newtonian fluid, exhibiting three-dimensional isothermal flow during extrusion, while neglecting inertial forces [33].

As can be seen from Equation (19), the extrusion pressure is related to the length and diameter of the die land. To accurately determine the relationship between the extrusion pressure and the structural parameters, five groups of nozzle models with different dimensions were analyzed, with the nozzle extrusion speed set from 0.001–1 cm/s, as shown in

Table 1. Geometric structural parameters.

Parameter Setting	D (cm)	D0 (cm)	L (cm)	D1 (cm)	L/(D − D1)
Numerical value	1	3.6	1, 2, 3, 4, 5	0.5	2, 4, 6, 8, 10

.

The extrusion fluid domain was divided by tetrahedral mesh elements. Due to the small area of the nozzle region, the mesh was refined in the nozzle part to ensure mesh quality and improve computational accuracy, as shown in Figure 3.

The rheological experiment results were characterized by the printing material behavior, and the flow field was set to transient analysis during the simulation process. The ability of the material to go through the die land was related to the nozzle velocity; therefore, the inlet was set as inflow, the flow velocity was set from 0.01–1 cm/s and the outlet was set as outflow.

When extruding the pumpkin puree, a very thin molecular layer was prone to forming on the contact wall. In the numerical simulation process, the molecular layer was considered to adhere to the contact surface, which did not undergo relative movement, viz., the contact wall was no-slip (v_n = vs. = 0).

4. Results and Discussion

4.1. Rheological Properties

Both the pumpkin puree and the minced pork are selected as the extrusion materials for the inner and outer barrels, respectively. During the food-printing process, the flow resistance or deformation resistance of the paste comes from its own viscosity. Figure 4 shows the apparent viscosity of the pumpkin puree varying with the shear rate, and Equation (21) is obtained.

$${\eta }_a=249{\dot{\gamma }}^{-0.9}$$

(21)

4.2. IDDSI Test

Paste-like foods are one of the categories suitable for dysphagia diets, which are generally assessed through the IDDSI, as depicted in Figure 5. The IDDSI comprises several simple tests using common household items [25]. In this study, a spoon tilt test was employed to evaluate the cohesiveness and stickiness of the printing materials, while a fork was used to test their hardness.

Figure 5a shows that the pumpkin puree can easily slide off the spoon with less residue, indicating its lower stickiness. The pumpkin puree that fell onto the desk does not spread out, suggesting better cohesion and meeting IDDSI standards.

The minced pork, as depicted in Figure 5b, exhibits flattening, fragmentation, and deformation when pressed with a fork until the thumbnail turns white. Furthermore, it fails to regain its original shape after the fork is removed. Through this test, the minced pork complies with IDDSI standards.

4.3. Pressure Analysis

P₁, P₂ and V are obtained through FEM simulation. As shown in Figure 6, the pressure gradually decreases along the axis of the nozzle. When the paste flows through the die land from the extrusion barrel, the rate of pressure gradient reduction significantly accelerates. This is because the cross-sectional area of the die land is smaller, leading to a pronounced increase in the shearing action between the materials, which results in a more significant pressure drop. Furthermore, the pressure P₁ within the extrusion barrel is much greater than the pressure P₂ within the die land. This is because the diameter of the extrusion cylinder is larger than the diameter of the mold ground, which means that the volume of the material per unit distance increases significantly, which makes it easy to form a backlog, and the pressure P₂ in the work area is small, which makes the material flow slowly in the mold work area, and the upper end of the not extruded material gradually go through a static solidification phenomenon because the flow rate is too slow or even stopped. As a result, the fluidity of the material in the extrusion cylinder gradually decreases after entering the flow channel.

The influence of the die land length on extrusion pressure, as shown in Figure 7: when L = 1 cm, the pressure P₁ increases by approximately 20% compared to P₂. With each additional 1 cm increase in length, the pressure increment is observed to be 15.6%, 13.5%, 12.7% and 12.4%, respectively. This phenomenon can be attributed to a significant decrease in apparent viscosity under shear thinning effects when the die land is longer, thereby enhancing flowability and facilitating better filling of the die land area.

As shown in Figure 8, as the length of the die land is 1–5 cm, the total extrusion pressure P is positively correlated with the volume flow rate of the inlet. Additionally, the extrusion pressure gradually increases with an increase in the volume flow rate. It should be noted that when the volume flow rate of the inlet is less than 1 cm³/s, there is a significant variation in extrusion pressure. This suggests that if the extrusion velocity of the nozzle is too small, the paste in the die land will flow slowly, resulting in extrusion blockage. In cases where the length of the die land remains constant and the inlet volume flow rate varies from 1 to 10 cm³/s, with a rising inlet volume flow rate, the extrusion pressure increases first and then decreases. The reason is an increase in flow velocity due to higher inlet volume rates, indicating the paste is easier to extrude, the kinetic energy consumed by the flow of the same distance decreases, and the pressure gradient also decreases.

4.4. Velocity Analysis

The paste exhibits different velocity characteristics with the change in the nozzle diameter [35]. Along the axial direction, the diameter of the die entrance gradually diminishes, leading to an escalation in flow velocity. When entering the die land, the flow velocity tends to be constant.

As shown in Figure 9, the flow velocity in the barrel is relatively low and has no significant change, since the volume of the paste in the barrel is much larger than that of the die land, resulting in the movement distance of the paste in the die land per unit time being larger than that in the barrel. However, in contrast, the variation of the flow velocity in the central region is particularly obvious.

Numerical simulation of the different die land lengths shows that these lengths are different; the distribution of the flow velocity, however, is relatively consistent, and the average extrusion velocity curve is flat, as shown in Figure 10. It can be observed that there is no significant correlation between the length of the die land L and the flow velocity V, indicating that the extrusion velocity is less affected by the die land length. In addition, when the nozzle structure parameters remain constant, the average extrusion velocity increases by approximately 1.5 cm/s for every 1 cm³/s increase in the inlet volume flow rate.

As discussed, the die land length has a negligible effect on the extrusion velocity. However, the extrusion velocity of the paste is greatly influenced by the inlet volumetric flow rate, and these are positively correlated. The research by Gómez Blanco Juan C. et al. indicates that an increase in volumetric flow rate during the 3D printing process can accelerate the printing speed of the 3D printer [36].

4.5. Characterization Parameters

The characterization parameters of the material in Equation (19) were calculated based on the data obtained from the simulation. σ₀ is calculated by setting L/(D − D1) = 0. τ₀ is the slope of P versus L/(D − D1) = 0 at zero velocity. Finally, α, β, m and n are as shown in

Table 2. The characterization parameters of the pumpkin puree.

Characterization Parameters	Pumpkin Puree
σ0 (MPa)	0.6
α (MPa sm m−m)	1.1
m	0.21
τ0 (MPa)	0
β (MPa sn m−n)	0.52
n	0.2

.

These parameters were substituted into Equation (19) to determine the mathematical model:

$$P=\left(0.6+1.1V^{0.21}\right)\ln \left({\displaystyle \frac{D_0^2-25}{D^2-25}}\right)+0.86{\left({\displaystyle \frac{2V}{D-5}}\right)}^{0.19}\left[1-{\left({\displaystyle \frac{D-5}{D_0-5}}\right)}^{0.57}\right]+2.08V^{0.2}\left({\displaystyle \frac{L}{D-5}}\right)$$

(22)

5. Nozzle Design and Print Test

5.1. The Nozzle Structure

As shown in Figure 11, a novel conical annular nozzle was designed, which consists of a stepper motor, gear transmission device, fixed bearing, nozzle, leading screw, screw nut, inner nozzle and outer nozzle. The inner nozzle is coaxial with the outer nozzle to achieve a sandwich printing filament composed of pumpkin puree and minced pork. The inner nozzle was a straight pipe without any outlet resistance, and the paste was squeezed through an air pump affording a pressure of 0.2–0.4 MPa. Considering that the inner nozzle is relatively easy to extrude through air pressure, this paper does not intend to discuss this in depth. The extrusion workflow of the outer nozzle is as follows: first, the pre-configured paste was put into the outer nozzle, and the lead screw was rotated through gear transmission driven by a stepper motor; then, the lead screw drove the screw nut to enable the nozzle to extrude the pumpkin puree.

Based on Equation (22), the motor torque T, the leading screw pitch S and other printer construction parameters are calculated as follows in

Table 3. Structural parameters.

Item	Value
T (N·m)	0.42
S (cm/r)	0.3
D (cm)	1
D0 (cm)	3.6
D1 (cm)	0.5
L (cm)	1.5

.

In order to investigate Equation (22)’s feasibility, the pumpkin puree was extruded according to the experimental requirements as above. Figure 12 shows the average values of extrusion pressure for a nozzle velocity of 0.1 cm/s together with one set of predictions obtained by Equation (22). The error bars indicate an experimental value error range of 15%. It can be seen that an error below 15% between the calculated value and the experimental value demonstrates that the prediction method is feasible. The significant error and fluctuation observed in the results may be attributed to the algorithm used in the FEM, the material ratio, and the production process.

5.2. Print Test

The printing velocity was set at 2 cm/s, and the print layer height was set to 0.4 cm. Figure 13 illustrates the impact of the sandwich filament after 3D printing. The inner minced pork and the outer pumpkin puree were well-formed with smooth and uniform lines, showing no excessive stretching or breakage. Notably, there were no blockages during the printing process. In summary, based on the predictive model, the nozzle design proves feasible. Furthermore, this model can also be applied to predict extrusion pressure for other materials.

6. Conclusions

A conical annular pressure prediction model is established, and the model parameters are determined by FEM. Based on this prediction model, a nozzle for printing sandwich food is designed, which can provide nutritious and palatable food for patients with dysphagia. The nozzle structural parameters are determined through this prediction model, and good results are obtained during the printing process. The following conclusions are drawn from this paper:

(1)

A predictive model for the extrusion pressure of the conical annular nozzle is established, and the characterization parameters are determined by FEM. The error between the calculated value and the experimental value is within 15%.

(2)

Increasing the length of the die land is prone to increase the pressure loss within the extrusion barrel, but it has almost no effect on the flow velocity. Furthermore, the inlet volume flow rate has a significant impact on both the average velocity and the extrusion pressure positively related to it. In particular, an increase of 1 cm/s in the inlet volume flow rate leads to a corresponding increase of 1.5 cm/s in the average extrusion velocity.

(3)

A novel conical annular nozzle whose structural parameters were calculated by the predictive model was designed for dysphagia patients. Through the printing test, the printed food has a smooth and uniform shape, and the quality of the pork mince filling is good. Both pumpkin puree and minced pork meet IDDSI standards.

The research outcomes aim to offer theoretical value and a reference for the study of foods for patients with dysphagia. The 3D food-printing nozzle designed based on the screw extrusion theory presented in this paper can produce pureed foods that comply with the IDDSI, and these foods can also serve as experimental samples for clinical research. Although this predictive model is proven to be suitable for pumpkin puree, its applicability to other cementitious materials still needs to be explored. In addition, the printing accuracy of the nozzle in this paper is also insufficient and needs in-depth research in the future.