Interfacial heat transfer through a natural protective fibrous architecture: a wild silkworm cocoon wall

Abstract

The wild Antheraea pernyi silkworm cocoon is a thin and light-weight structure, yet it has shown effective thermal insulation characteristics against extreme temperature fluctuations, which meet the demands of humans for lighter materials with higher thermal resistance. We present a two-dimensional computational fluid dynamics model of this unique fibrous cocoon structure to simulate the heat transfer process through the cocoon wall. The model is able to predict the temperature field inside the cocoon reasonably well. The results of the model also show that the mineral crystals present in the outer layers of the Antheraea pernyi cocoon can increase air flow resistance and decrease the effect of natural convection, which further reduces the heat transfer through the cocoon wall effectively. This has practical significance for the development of thermal functional textiles and composite structures.

Keywords

composites performance structure-properties

In nature, very thin and light-weight cocoons can protect wild silkworms from harsh weather conditions and other environmental adversaries, while supporting their metabolic activity. The silkworm cocoon is a porous multilayer structure constructed from continuous twin silk filaments (fibroin) bonded by silk gum (sericin). A compact cocoon is formed when a silkworm, along with spinning, wraps the bave around its body through a gyrating motion of its head and cyclically bending and stretching of its body with different shapes in a programmed manner.^1,2 It has been found that as silk spinning continues, the silk filaments become finer and stronger and the crystallinity and the molecular orientation of silk polymer increase.^3,4 The silk filaments are also known to be laid more closely towards the end of spinning, making the inner shell (known as pelade) the hardest and smoothest with stronger mechanical properties.^5–7 Although the multilayered and graded structure has shown superior mechanical protection functions, including improving the toughness of the structure, enhancing energy absorption property due to the wave impedance matching of different plies^8,9 and shock absorbance as a composite composed of different materials,¹⁰ its function as an interfacial heat transfer barrier remains unclear. Understanding the thermal insulation properties of the wild silkworm cocoon may inspire the design process for light-weight protective materials and structures.

In a recent study, Zhang et al.¹¹ examined the thermal properties of four different types of silkworm cocoons and revealed that the inner temperature of wild silkworm cocoons showed significant thermal damping characteristics against sudden changes in cocoon outer temperature. In particular, the wild Chinese tasar silkworm Antheraea pernyi (A. pernyi) cocoon (Figure 1(a)) exhibited a higher level of thermal buffer over the domesticated Bombyx mori (B. mori) cocoon, presumably due to the more stringent requirements for protection in the wild. At the outer layers of this cocoon type, cubic mineral crystals that had been identified as calcium oxalates were found on the silk fiber surfaces or stacked in the pores between the layers (Figure 1(b)).¹² The role played by these crystals in the thermal insulation of this unique cocoon structure remains unclear.

Figure 1.

The cocoon and cocoon wall morphology. (a) The A. pernyi cocoon (the white scale bar is 10 mm). (b) Scanning electron microcopy (SEM) image of the outer surface of the cocoon wall (inset shows the mineral crystals). (c) SEM image of the cross-section of the cocoon wall.

Avazov¹³ recently reported a mathematical model to calculate the temperature at different positions in the thickness directions of domestic silk cocoon B. mori shell exposed to infrared (IR) radiation. The model considered heat absorption of cocoon and pupae, thermal conductivity of the cocoon wall, and the temperature gradient between cocoon walls and the inner and outer environment. However, the structure details of the B. mori cocoon were not defined nor investigated. As a porous heat transfer medium, the A. pernyi cocoon consists of solid components (silk fiber fibroin and sericin) with irregular shape, different size and distribution. The unique fibrous structure of this wild cocoon may play a significant role in enhancing its thermal insulation function. During the cocoon building process, the pores between the silk filaments vary significantly in the through-thickness direction and these pores can be either interconnected or disconnected.¹⁴ Within the pores, gas and/or liquid can fill the space. The porous cocoon material therefore can be seen as a two-phase (gas–solid or liquid–solid) or three-phase (gas, liquid and solid) material mixture, through which heat and mass flux can transfer. In this work, the cocoon wall structure was defined according to the actual structure of A. pernyi and factors such as temperature, pressure and porosity have been studied by numerical simulation. The effect of mineral crystals deposited on the outer layers of the cocoon has also been investigated.

Experimental details

Wild A. pernyi cocoons collected from Northeast China were used in this study. The length and the width of the A. pernyi cocoons were about 50 and 26 mm, respectively.

Scanning electron microscopy

The cocoon wall surfaces and cross-sections were observed by a Supra 55 VP scanning electron microscope after sputter coating with gold. The cross-section was obtained by embedding the cocoon wall into an epoxy matrix and then ground wet through 80, 240, 600, 1200 and 4000 grit silicon carbide abrasive paper.

Temperature monitoring

The temperature was measured both inside and outside the cocoon (about 10 mm away from the outer surface) using two needle-type temperature probes (ICT SFM).¹¹ Each temperature probe is 1.3 mm in diameter and 35 mm in length, with two sensors located 15 mm apart (the first sensor is 7 mm from the needle tip). For each measurement, one temperature probe was placed into the cocoon through the proximal end from which the moth usually escapes and the other probe was attached onto the outer surface of the cocoon. The sensors were deliberately uncovered and the data were recorded every second.

To study the heat transfer properties of the A. pernyi cocoon under warm conditions, the temperature measurements were conducted in an oven (Binder). The cocoons were translocated from the ambient environment to the oven with different isothermal temperature settings (at 37℃, 45℃ and 50℃, respectively). The temperature probe in the cocoon was used to measure the temperature profiles inside the cocoon, while the temperature probe outside the cocoon was used to measure the surrounding temperature profiles. Three cocoon samples were tested for each type of measurement and the standard deviations were indicated in the graphs as error bars. The initial temperature of the oven was about 17℃. After the oven was turned on, a gradual rise of temperature was introduced until the temperature reached the set value. When the temperature of the oven was set at 37℃, 45℃, and 50℃, the durations of the experiment were taken as 900, 1200 and 1400 s, respectively.

Heat transfer through fibrous media

Geometrical configurations

In order to simulate the heat transfer process through the A. pernyi cocoon wall, the commercial computational fluid dynamics (CFD) code CFX 15.0 from ANSYS Inc.¹⁵ was used in the simulation, which is based on a finite volume method and a non-structured solver. A two-dimensional (2D) model was built to simulate the heat transfer process through the A. pernyi cocoon wall. It was based on a small rectangular piece of cocoon wall that takes approximately 8 hours for numerical calculation. However, a detailed simulation of the entire cocoon structure with CFX will take much longer due to the large volume, which is not a practical solution. Furthermore, it is important to resolve the geometry and the flow to acquire a close-to-grid independent solution in order to obtain reliable results in CFX simulations.¹⁶ Based on the similarity of fiber cross-section morphology,⁵ the silkworm cocoon cross-section was simplified into three main sections in the model, that is, the outer section, the middle section and the inner section (Figure 1(c)). The silk fibers in each section have identical geometrical configuration and were arranged in a regular manner. The model did not distinguish the silk fibroin from the silk sericin. In each section, the cross-section of silk fibers was set as an ellipse shape with different sizes. The parameters used to define the cocoon structure include the length and the width of the cross-section of silk fibers, the gap distance between two adjacent fibers along the length direction (x-axis) and along the width direction (y-axis), and the total number of rows in each section. All the parameters were defined according to the average measurement data from the scanning electron microscopy (SEM) image. These geometrical parameters are summarized in Table 1. The thickness of the cocoon model (along the y-axis direction) is 450 µm, which is similar to the real cocoon.¹¹ The width of the model (along the x-axis direction) was set as 600 µm. The geometrical configuration of the cocoon wall models is shown in Figure 2. In addition to the cocoon wall (in the middle), a space with thickness of 100 µm was defined to simulate the environment inside the cocoon (upper part) and a space with thickness of 100 µm was defined to simulate the environment outside the cocoon (lower part). When the temperature outside the cocoon is higher than the temperature inside the cocoon, the direction of the heat flux is from the exterior to the interior of the cocoon. Compared with silk fibroin and silk sericin, the content of the mineral crystals is trivial. However, the mineral crystals roughen the surface of the silk fibers that have significant influence on the air flow around them. In order to investigate the functions of the mineral crystals, numerous embossments were added onto the surface of silk fibers in the outer surface section of the cocoon wall to model the crystals in model B (Figure 2(b)), while no crystals were considered in model A (Figure 2(a)). The comparison between these two models can show the influence of the mineral crystals in the heat transfer process very well. The porosity of the cocoon model was set as 66%, which is in accordance with the experimental data 0.67 ± 0.030.¹⁷

Figure 2.

Geometrical configuration of the two-dimensional model: (a) without consideration of crystals on the outer surface; (b) with consideration of crystals.

Table 1.

The geometrical data used for model predictions

	Width (µm)	Length (µm)	Width direction gap distance (µm)	Length direction gap distance (µm)	Total number of rows
Inner section	10	80	5	15	5
Middle section	11	40	9	20	12
Outer section	20	92	16	36	4

In the mesh process, the minimum size of the single grid was controlled to be no less than 4.4 × 10⁻⁷ m; the maximum size of the single grid was controlled to be no more than 8.8 × 10⁻⁵ m. The mesh results show that the number of the elements is 101,247 and the number of nodes is 201,864.

Mathematical formulation

For the heat transport through the fibrous cocoon matting, mechanisms such as thermal conduction, convection, radiation and latent heat caused by phase changes can affect the heat transfer process simultaneously. For simulation, the following assumptions were introduced: the porous fibrous matting is homogeneous in fiber arrangement and material properties; the air is continuous gas; no shrinking or expansion occurs.

Under current experimental conditions, the latent heat can be neglected since no water vapor evaporated or condensed. In addition, the temperature difference between the oven and the cocoon was not so high to transfer large quantity of radiant heat; therefore, for simplification, the radiation was neglected in the numerical calculations. Thermal conduction and thermal convection play important roles in this heat transfer process and, based on the conservation of heat energy, the energy equation can be expressed as below:¹⁸

c ν \partial T / \partial t = \underset{Convection}{\underset{︸}{- ɛ uc ν a \nabla T}} + \underset{Conduction}{\underset{︸}{λ \nabla 2 T}}

(1)

where

c ν

is the effective volumetric heat capacity of the fibrous matting, J/(m³ K);

c ν a

is the effective volumetric heat capacity of the air, J/(m³ K); ɛ is the porosity of fibrous matting, dimensionless; λ is the effective thermal conductivity of the fibrous matting, W/(m K); u is the air transferring velocity, m/s; T is the temperature, K; t is time, s.

For the numerical simulation, thermal conduction and convection were considered as the main contributing factors to the heat transfer process, which is described in Equation (1). The initial temperature in the models was taken from the temperature value in the beginning of each experiment. The boundary conditions are also shown in Figure 2. The surrounding temperatures vary with time and can be described by $T (t)$ . The opening temperatures were taken from the experimental data and the average static pressure of the outlet was set as zero. The 2D model was built based on the cross-section of the cocoon wall. In order to ensure the model is be able to show the thermal characteristics of the entire cocoon, the two sides of the model in the x-axis direction were set as “symmetry”. This kind of setting can make the 2D model act as a real three-dimensional (3D) cocoon similarly.

The initial and boundary conditions are shown in Equation (2):

T | t = 0 = T 0

(2a)

T | t \geq 0, y = 0 = T (t)

(2b)

where T₀ is the temperature of the cocoon at the initial time (K).

In the numerical simulation process, the advection scheme was set to be “high resolution” and the residual target was set to be 0.00001. At each time step, the residual target was realized after about 200 iterations

Physical parameters of silk fibers

For the current experimental conditions, the silk fibers and air have major effects on the heat transfer process. Silk is composed of silk fibroin and sericin.¹⁹ Different from the B. mori cocoon, the silk fibroin of the A. pernyi cocoon constitutes about 90% of the silk,²⁰ which is more than the ratio of the B. mori cocoon. Compared with silk fibroin and sericin, the weight of the crystals is trivial. Therefore, in the model, in order to calculate the density of the silk, the silk was defined with 90% silk fibroin and 10% sericin by weight roughly. The silk fibroin and the sericin are supposed to be connected closely and no air exists between them.

Density

The density of the silk fibroin is 1350 kg/m³,^21,22 and the density of the silk sericin is 1383 kg/m³.²³ As a result, the density of the silk was calculated as

ρ silk = (0.90 / ρ fibroin + 0.10 / ρ serioin) - 1

(3)

where

ρ fibroin

is the density of silk fibroin, kg/m³;

ρ sericin

is the density of sericin, kg/m³.

The result of this equation, 1353 kg/m³, was used as the density of the silk. The density of calcium oxalate, 2120 kg/m³, was used as the density of mineral crystals.²⁴

Heat capacity

The heat capacity of the silk fibroin was calculated by the following equation from Hu et al.:²⁵

C p (T) = 134 + 3.696 T

(4)

When T equals 300 K, the heat capacity of the silk fibroin is 1243 J/(kg K). Since the silk fibroin is the main component of the silk, the heat capacity of the silk fibroin was used as the heat capacity of the silk.

The heat capacity of the mineral crystals is 1043 J/(kg K).²⁶

Thermal conductivity

The effective thermal conductivity $λ (x, t)$ of porous media is influenced by its constituents in solid, liquid and gas phases and therefore is a function of many parameters, such as porosity, water content, saturation degree, phase change of water. Tong et al.²⁷ developed an effective thermal conductivity model for simulation of thermo-hydro-mechanical processes of the porous media. Their calculation is listed as follows:

λ s - g = η 1 (1 - ɛ) λ s + η 1 ɛ λ g + (1 - η 1) λ s λ g / (ɛ λ s + (1 - ɛ) λ g)

(5)

where

η 1

is the coefficient that depends only on the pore structure of the solid–gas mixture, and can be calculated by

η 1 = 0.0692 ɛ - 0.7831; λ s - g

is the thermal conductivity of the composite material, W/(m K);

λ s

is the thermal conductivity of the silk, W/(m K);

λ g

is the thermal conductivity of the air, W/(m K).

In our previous work, the thermal conductivity of the A. pernyi cocoon was measured.¹¹ Since the thermal conductivity changed with the temperature, the average value was used for modeling, which is 0.05 W/(m K). This value is from the cocoon, which is a composite material. When the temperature is 293 K, the pressure is 101,325 Pa and the thermal conductivity of air is 0.0265 W/(m K).²⁸

Therefore, the thermal conductivity of the silk can be calculated similarly by Equation (5) and the value of 0.41 W/(m K) was used for the model.

The thermal conductivity of the mineral crystals, 0.22 W/(m K), was used in the model.¹¹

Simulation results and discussion

Heat transfer through the cocoon wall

After the cocoon was located into the oven with isothermal setting temperature (37℃, 45℃ and 50℃, respectively), the temperature inside the oven (outside the cocoon) increased rapidly at first; when the oven temperature reached the temperature that was about 5℃ lower than the setting temperature, the temperature increasing rate decreased and more time was needed to reach the isothermal setting temperature. Figure 3 shows the temperature profiles of the inner temperature from both model B and the experimental data (temperature both inside the cocoon and outside the cocoon). The inner temperature profiles of the cocoon from experiments are similar to the outer temperature profiles of the cocoon at first. As the outer temperature increased rapidly, the temperature difference between the interior and exterior of the cocoon increased. More heat flux was driven by the increasing temperature difference in the early stage of heating, which led to the rapid increase of the inner temperature. With the reduction of the oven temperature increasing rate, after a period of time, the temperature difference between the interior and the exterior of the cocoon decreased and the change of inner temperature slowed down. Theoretically, the temperature inside the cocoon will reach the temperature outside the cocoon in the end (infinite time). For the experiments conducted in this work, due to the limited time, the temperature difference between outside and inside the cocoon was 1.01℃ (when the oven temperature was set at 37℃), 2.17℃ (when the oven temperature was set at 45℃) and 1.85℃ (when the oven temperature was set at 50℃). The inner temperature of the cocoon was lower than the outer temperature of the cocoon, showing the thermal buffer function exhibited by the cocoon structure. The calculated cocoon inner temperature from model B agreed well with the experimental data.

Figure 3.

Prediction results from model B in comparison with experimental data for oven isothermal setting at (a) 37℃; (b) 45℃; (c) 50℃.

During the initial heat transfer period up to 420 s, the calculated data were slightly lower than the actual data. This may be because the extra radiant heat transfer between the oven and the cocoon was neglected in the model. The radiant heat can be transferred from the object with high temperature to the object with low temperature,^29,30 and the heat flux by thermal radiation is affected by the temperature difference between these two objects.³¹ At the initial heat transfer stage, the temperature difference between the oven and the cocoon was larger, which led to considerable heat flux by thermal radiation and caused the model results to deviate from the experimental data. With the increase of heat transfer time, the temperature difference between calculated data and actual data became less due to the fact that the temperature difference between the cocoon and the inner surface of the oven chamber reduced and the heat transferred by thermal radiation decreased too, which could be consequently ignored. At the end of the experimental period, especially in Figures 3(b) and (c), the temperature data in model B were slightly higher than the experimental results. The tortuosity of the simplified cocoon model is less than the real cocoon. Kou et al.³² studied the relationship between the effective thermal conductivity and the tortuosity of the porous material by using the fractal theory and found that the effective thermal conductivity of porous media decreases with the increase of tortuosity. Therefore, the less tortuous nature of the cocoon model can lead to more heat transfer by convection and make the temperature inside the cocoon close to that of the surroundings.

Figure 4 shows the temperature field in the cross-section of the A. pernyi cocoon at different moments (t = 0 s, t = 120 s, t = 420 s, t = 1200 s, respectively) from model B when the temperature of the oven was set at 45℃. It can be found that the temperature difference is larger in the cocoon wall cross-section during the initial heat transfer stage (up to 420 s, Figures 4(b) and (c)) than the final stage (Figure 4(d)). At the initial stage, the temperature difference between inside and outside the cocoon was more significant and therefore more heat was transferred, that is, the temperature gradient in the cross-section of the A. pernyi cocoon at different locations was larger. In other words, the temperature in the inner layer of the cross-section was lower than the temperature in the middle and outer layers. With the increase of time, the temperature difference between the inside and outside the cocoon decreased and the temperature gradient in the cross-section of the A. pernyi cocoon at different locations decreased, too.

Figure 4.

The temperature field in the cross-section of the A. pernyi cocoon wall at different times (t = 0 s, t = 120 s, t = 420 s, t = 1200 s, respectively) from model B (oven isothermal setting was 45℃).

The temperature was inhomogeneous in the cross-section of the cocoon wall and was affected by the location of silk fibers. To use the temperature contour when the time was 120 s as an example, in the cross-section of the cocoon, especially in the outer layer of the cocoon, more temperature changes appeared and the boundaries of isotherms were not straight lines. In general, the temperature in the windward direction of the silk fiber is higher than the temperature in the leeward direction of the same silk fiber; the isotherm in the gap between the adjacent silk fibers in the x-directions is towards the positive y direction (the direction towards the inner cocoon). That is due to the air flow through the cocoon wall that affects the temperature field of the cocoon and the difference of the thermal properties between the air and silk. Analogously, when a stream of warm air flows across a flat micro channel, the temperature on the front face is also higher than the temperature on the rear face.³³

In model B, the embossments are built on the silk fiber surface of the cocoon outer section to model the real crystals, while no similar embossments are built in model A. That is the only difference between model A and model B. Therefore, the comparison of the results from model A and model B benefit the research on the function of crystals to the heat transfer process. Taking the oven temperature setting 45℃ as an example, the temperature results from model A and model B are compared in Figure 5. The calculated data of inner temperature from model B agree well with experimental data with small variation, which is discussed in Figure 3. With the same inputs of the initial and boundary conditions in model B, the calculated inner temperature data from model A are much higher and do not fit the experimental data. It indicates that the mineral crystals can increase the thermal resistance of the cocoon wall. The thermal conductivity of mineral crystals is 0.22 W/(m K),¹¹ while the thermal conductivity of the air is only 0.0265 ± 0.0003 W/(m K),²⁸ which means that the conductive heat flux through the cocoon wall should be higher in model B than model A. However, under real circumstances, due to the temperature difference between the outer and inner surfaces of the cocoon wall, the air flows in the connected pores of the cocoon wall, which can lead to much convective heat flux. The convective heat flux occupies much of the ratio of the total heat flux. The crystals cause higher thermal resistance of the cocoon wall because their existence affects the state of air flow and decreases the heat flux by convection, even when the volume proportion of crystal over the cocoon wall is only 0.2% in the model. Therefore, it is essential to research the micro-flow field within the cocoon wall, which is influenced by the cocoon structure, especially the mineral crystals.

Figure 5.

Inner temperature comparison between model predictions and experimental data (oven isothermal setting was 45℃).

Air flow through the cocoon wall

During the heat transfer process, the temperature inside the cocoon was always different from the surrounding temperature. The temperature difference can cause the pressure difference of the air and drive the air flow from a higher pressure location to a lower pressure location, which is natural convection. In the cocoon wall, the path for the air flow was along the connected pores of the cocoon. Figure 6 shows the streamline at 1200 s when the temperature of the oven was set at 45℃. The streamline shows the speed and path of the air flowing through the cocoon. For the unique A. pernyi cocoon, the streamline was strongly affected by the porous structure. The velocity is higher in the smaller gap of the cocoon wall and is much slower near the surface of silk fibers due to the influence of viscosity. Furthermore, a number of streamlines end in the cocoon wall, signifying the loss of kinetic energy while air travelled. The decreased kinetic energy of the air during flow is possibly caused by the friction between air and silk fibers and the turbulence of the air travelling through the cocoon.

Figure 6.

The velocity of air flow through the A. pernyi cocoon wall at 1200 s from model B (oven isothermal setting was 45℃).

The crystals are located on the surface of the outer section of silk fibers. Although the dimension of the crystals is far lower than that of the fibers, their existence can roughen the surface of the silk fibers, which may influence the state of the air flow around them. In order to verify whether the crystals can affect the micro-flow field within the cocoon wall, the total pressure difference across the outer layer of the cocoon was compared between model A and model B. The total pressure is the sum of static pressure and dynamic pressure. The total pressure difference across the outer layer of the cocoon indicates the mechanical energy loss due to the air flow through the wall. Points a and b were defined according to the illustrative graphs shown in Figure 2, where point a is located outside the cocoon and point b is located between the outer and middle layers of the cocoon wall. Figure 7 shows the total pressure difference between point a and point b when the temperature of the oven was set at 45℃. At the early stage of the heat transfer process, the total pressure difference was higher; with the increase of heat transfer time, the total pressure difference decreased and the total pressure difference was nearly constant finally. In the beginning of the heat transfer process, the total pressure difference between the surrounding and the interior of the cocoon was high, causing the mass of air flowing in the cocoon wall and transporting the heat by convection. That is also one of the reasons why the inner temperature increased rapidly in the early stage. With the increase of heat transfer time, the temperature difference between the surrounding and the interior of the cocoon decreased. As a result, the total pressure difference decreased and the air flow declined.

Figure 7.

The total pressure difference between point a and point b indicated in Figure 2 (oven isothermal setting was 45℃).

In Figure 7, the comparison of the cocoon outer section from model A and model B shows higher total pressure difference for the model with crystals. This signifies that the existence of crystals can cause more mechanical energy loss as the air flows through. One reason for this is that the crystals increase the contact area between air and silk fibers, which increases the friction loss at the interface; the other reason is that the air is easier to disturb when flowing along the rough surface of the silk fibers caused by the crystals, with more mechanical energy loss due to the collision of air molecules. Affected by the crystals, the flow resistance of the cocoon wall is enhanced effectively, which prevents excess air flowing through the cocoon wall and reduces the convectional heat flux of the air through the cocoon wall.

Conclusions

The thermal insulation and heat transfer process of a wild A. pernyi silk cocoon under warm conditions was investigated both experimentally and numerically. The cocoon shows significant thermal buffer against environmental temperature changes. Based on the unique structure of this type of cocoon, a 2D CFD model was generated. From both the experimental results and numerical predictions, it can be found that the mineral crystals in the outer layers of cocoon walls can enhance the air flow resistance effectively, which prevents air flowing in the cocoon wall; therefore, most of the heat flux transferred by thermal convection can be reduced. The existence of mineral crystals can enhance the shielding of the cocoon against thermal attack and promote the survival chance of the A. pernyi pupa under extreme weather conditions.

Footnotes

Funding

This work was supported by the Australian Research Council (ARC project DP 120100139).

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