**2. Fundamentals**

The basic principle of wick-debinding is the phenomenon called capillarity, which is a spontaneous flow of liquid into small pores. This effect occurs because of the attractive forces between the liquid and the solid surface of the pores and the surface tension of the liquid. The attraction of the liquid to the surface causes the adhesion of the liquid and the solid, which results in the liquid wetting the surface. The wetting is characterized by a wetting angle, which depends on the interactions between the liquid phase, the solid phase

1990) or wick-debinding. A wicking agent can be in the form of a porous solid substrate plate or in the form of a loose powder or granulate. The granular form offers a gentle physical support for samples, regardless of their shape, and thus prevents certain flaws, such as distortion and cracking. The capillary extraction is uniform over the entire surface of the green body, which ensures that debinded parts also have, as much as possible, a uniform structure after the wick-debinding. A solid plate does not offer so many benefits; however it has one advantage over the granular form of wicking agent, i.e., there are fewer practical problems when handling the compacts after the debinding. The wick-debinded parts do not

Fig. 1. Wick-debinding on a porous plate. The molten binder is extracted from the green

Fig. 2. Wick-debinding in a embedment of porous powder or granulate. The molten binder

The wicking embedment can be utilized with great success in either the high- or the lowpressure injection molding. However, its use is more beneficial in the low-pressure variant,

The basic principle of wick-debinding is the phenomenon called capillarity, which is a spontaneous flow of liquid into small pores. This effect occurs because of the attractive forces between the liquid and the solid surface of the pores and the surface tension of the liquid. The attraction of the liquid to the surface causes the adhesion of the liquid and the solid, which results in the liquid wetting the surface. The wetting is characterized by a wetting angle, which depends on the interactions between the liquid phase, the solid phase

have to be cleaned and are simply transferred to the sintering furnace.

body into the porous supporting plate.

is extracted in all directions from the green body.

where the debinding is a more delicate operation.

**2. Fundamentals** 

and the atmosphere. The smaller the wetting angle the better is the wetting and the liquid easily spreads over the surface.

Fig. 3. Sketch of a droplet of liquid on a solid surface showcasing the wetting phenomenon, characterized by the wetting angle (Φ). When a liquid wets a surface it spreads over it.

An interesting phenomenon occurs when the liquid is inside a small pore. When the liquid wets the surface of a small pore at a certain angle (Φ), the surface becomes concavely curved as is sketched in Fig 4. Any curved liquid surface causes a pressure difference across the interface (Δ*P*c = *P*V - *P*L) between the liquid and the surrounding atmosphere.

Fig. 4. The liquid, that wets the surface, inside a small, cyllindrical pore forms a concave spherical surface that causes a pressure difference between the liquid phase.

The equilibrium pressure difference is described by the Laplace-Young equation:

$$
\Delta P\_c = P\_L - P\_V = \mathcal{Y}\left(\frac{1}{R\_1} + \frac{1}{R\_2}\right) \tag{1}
$$

where *ΔP*c [Pa] is the pressure difference between the liquid phase and the air phase, *γ* [N/m] is the surface tension, and *R*1 and *R*2 are the principal radii of curvature. As the capillary surface is concave towards the atmosphere, the liquid pressure is lower than that of the atmosphere, possibly reaching negative values, which is called a tensile stress inside the liquid (Bouzid et al., 2011).

In the case of a small, cylindrically shaped, pore channel the surface of the liquid is symmetrical and *R*1 = *R*2 = *R* . On small scales gravity is not strong enough to significantly

Wick Debinding – An Effective Way

components of velocity.

of Solving Problems in the Debinding Process of Powder Injection Molding 93

The flow through an idealized single, long, circular, pore channel is described by the Hagen-Poiseuille equation (4), which is also an exact solution of the Navier-Stokes equations with certain assumptions, such as steady state, axisymmetric flow with no radial and swirl

> 2 32

*d P*

where *q* [m/s] is the flux or flow per area, *ΔP* [Pa] is the pressure difference between the ends of the pore channel, *μ* [Pa s] is the viscosity and *L* [m] is the length of the pore channel. The smaller the pore, the larger the viscous drag. This generally means that small pores present a high resistance to flow. Again, like in the case of using equation (3), the Hagen-Pouseille equation is due to the extremely complex shapes of pore channels in real systems, inappropriate for calculations, but nevertheless it demonstrates that despite the high capillary pressures, liquid transport through small pores can be slow. However, regardless of the complexity of pore channels, the flow of a liquid through porous material can be

*K P*

where *q* [m3/ (m2 s)] is the volumetric flux, *K* [m2] is the parameter called permeability, *η* [Pa

The law was formulated in the 19th century by the French engineer Henry Darcy based on the results of water flow through sand (Richardson & Harker, 2002). It is a constitutive equation with a similar meaning for fluid flow as Ohm's law for the electricity and Fourier's law for the conductive heat transfer. Darcy's law has been experimentally confirmed on many different material combinations and is considered well proven. It has also been

The permeability (*K*) is a characteristic parameter of a porous substance that depends on the size, shape and interconnectedness of the individual pore channels and on the fractional porosity. The complex shape of pore channels makes a permeability difficult to calculate or

Many empirical equations have been used to determine the permeability from basic powder-compact properties, such as particle diameter (*d*), specific surface (*S*) and fractional

> 3 <sup>2</sup> <sup>2</sup> 5 1 *<sup>E</sup> <sup>K</sup>*

 4 2 <sup>2</sup> 90 1 *E d <sup>K</sup>*

porosity (*E*). Some of them are listed below (Bao & Evans, 1991; German, 1987):

successfully described by a simple equation called the Darcy's law:

s] is the viscosity and *P* [Pa] is the pressure gradient.

derived from the Navier-Stokes equations.

predict from basic principles.

*<sup>q</sup> <sup>L</sup>* (4)

*q* (5)

*S E* (6)

*E* (7)

influence the shape of the liquid surface so the surface has a spherical shape. If the wetting angle is considered the curvature in the small, tube-shaped, pore channel can be reasoned from Fig. 4:

$$R = \frac{d}{2\cos(\Phi)}\tag{2}$$

Combining equations (1) and (2) we obtain a correlation between the capillary pressure, the wetting angle and the pore diameter:

$$
\Delta P\_c = \frac{4\chi\cos(\Phi)}{d} \tag{3}
$$

From equation 3 it is clear, that the capillary pressure is inversely proportional to the pore diameter. Because the capillary pressure is larger for smaller pores, the liquid is forced to move from the larger to the smaller pores. So in the equilibrium state the liquid would fill the smallest pores of the system. The main idea of wick-debinding is to get a green body, heated to the temperature where the binder is molten, in contact with a material that has finer pores than the pores of the green body. Capillarity would then cause the binder to move from the green body into the material in the contact.

The wetting angle must be quite small for practical use. If the surface is not wetted by the liquid (Φ > 90°) then cos(Φ) has a negative value, which means that the capillary pressure would be opposite and the liquid would not enter the porous media.

In any case, in a real system the porous media consist of pores of different sizes and shapes. Even for a green body made of packed monosized spherical particles there are voids of different sizes and shapes. However, real powders are composed of particles that are different in size and shape, which leads to an even more complex pore structure and a wider size distribution of pores. A labyrinth of interconnected voids is present in the green body and also in the wicking agent. Because of the complexity of real systems, the equation (3) is difficult to use directly. However, in real systems it has been experimentally observed that the liquid enters a porous body with a front (Bao & Evans, 1991; Somasundram, 2008) and a single value of characteristic capillary pressure at the front can be successfully used.

Another important thing to consider in the debinding is the kinetics of the process. It is important, from a practical point of view, that the process is reasonably fast. The kinetics of wick-debinding, besides capillary pressure, also depends on the resistance to flow through the porous media. Each individual channel has a certain resistance - a viscous drag that limits the velocity at which the liquid is flowing through.

The motion of liquid substances is generally described by the Navier-Stoker equations, which arise from applying Newton's second law to fluid motion. However, these equations are too complicated for practical use in describing debinding phenomena since the shape of the liquid surface would present boundary conditions that are too complex. However, with the development of computer software for liquid mechanics and because of the constant increase in computer power it is possible that accurate simulations of debinding will be developed in the future. Nevertheless, a simplified theoretical approach in dealing with the phenomena of debinding has produced satisfactory results.

influence the shape of the liquid surface so the surface has a spherical shape. If the wetting angle is considered the curvature in the small, tube-shaped, pore channel can be reasoned

2 cos

Combining equations (1) and (2) we obtain a correlation between the capillary pressure, the

4 cos 

From equation 3 it is clear, that the capillary pressure is inversely proportional to the pore diameter. Because the capillary pressure is larger for smaller pores, the liquid is forced to move from the larger to the smaller pores. So in the equilibrium state the liquid would fill the smallest pores of the system. The main idea of wick-debinding is to get a green body, heated to the temperature where the binder is molten, in contact with a material that has finer pores than the pores of the green body. Capillarity would then cause the binder to

The wetting angle must be quite small for practical use. If the surface is not wetted by the liquid (Φ > 90°) then cos(Φ) has a negative value, which means that the capillary pressure

In any case, in a real system the porous media consist of pores of different sizes and shapes. Even for a green body made of packed monosized spherical particles there are voids of different sizes and shapes. However, real powders are composed of particles that are different in size and shape, which leads to an even more complex pore structure and a wider size distribution of pores. A labyrinth of interconnected voids is present in the green body and also in the wicking agent. Because of the complexity of real systems, the equation (3) is difficult to use directly. However, in real systems it has been experimentally observed that the liquid enters a porous body with a front (Bao & Evans, 1991; Somasundram, 2008) and a

single value of characteristic capillary pressure at the front can be successfully used.

Another important thing to consider in the debinding is the kinetics of the process. It is important, from a practical point of view, that the process is reasonably fast. The kinetics of wick-debinding, besides capillary pressure, also depends on the resistance to flow through the porous media. Each individual channel has a certain resistance - a viscous drag that

The motion of liquid substances is generally described by the Navier-Stoker equations, which arise from applying Newton's second law to fluid motion. However, these equations are too complicated for practical use in describing debinding phenomena since the shape of the liquid surface would present boundary conditions that are too complex. However, with the development of computer software for liquid mechanics and because of the constant increase in computer power it is possible that accurate simulations of debinding will be developed in the future. Nevertheless, a simplified theoretical approach in dealing with the

*<sup>d</sup> <sup>R</sup>* (2)

*Pc <sup>d</sup>* (3)

from Fig. 4:

wetting angle and the pore diameter:

move from the green body into the material in the contact.

limits the velocity at which the liquid is flowing through.

phenomena of debinding has produced satisfactory results.

would be opposite and the liquid would not enter the porous media.

The flow through an idealized single, long, circular, pore channel is described by the Hagen-Poiseuille equation (4), which is also an exact solution of the Navier-Stokes equations with certain assumptions, such as steady state, axisymmetric flow with no radial and swirl components of velocity.

$$q = \frac{d^2 \Delta P}{32 \,\mu\text{L}}\tag{4}$$

where *q* [m/s] is the flux or flow per area, *ΔP* [Pa] is the pressure difference between the ends of the pore channel, *μ* [Pa s] is the viscosity and *L* [m] is the length of the pore channel.

The smaller the pore, the larger the viscous drag. This generally means that small pores present a high resistance to flow. Again, like in the case of using equation (3), the Hagen-Pouseille equation is due to the extremely complex shapes of pore channels in real systems, inappropriate for calculations, but nevertheless it demonstrates that despite the high capillary pressures, liquid transport through small pores can be slow. However, regardless of the complexity of pore channels, the flow of a liquid through porous material can be successfully described by a simple equation called the Darcy's law:

$$q = -\frac{K\nabla P}{\eta} \tag{5}$$

where *q* [m3/ (m2 s)] is the volumetric flux, *K* [m2] is the parameter called permeability, *η* [Pa s] is the viscosity and *P* [Pa] is the pressure gradient.

The law was formulated in the 19th century by the French engineer Henry Darcy based on the results of water flow through sand (Richardson & Harker, 2002). It is a constitutive equation with a similar meaning for fluid flow as Ohm's law for the electricity and Fourier's law for the conductive heat transfer. Darcy's law has been experimentally confirmed on many different material combinations and is considered well proven. It has also been derived from the Navier-Stokes equations.

The permeability (*K*) is a characteristic parameter of a porous substance that depends on the size, shape and interconnectedness of the individual pore channels and on the fractional porosity. The complex shape of pore channels makes a permeability difficult to calculate or predict from basic principles.

Many empirical equations have been used to determine the permeability from basic powder-compact properties, such as particle diameter (*d*), specific surface (*S*) and fractional porosity (*E*). Some of them are listed below (Bao & Evans, 1991; German, 1987):

$$K = \frac{E^3}{5S^2\left(1 - E\right)^2} \tag{6}$$

$$K = \frac{E^4 d^2}{90(1 - E)^2} \tag{7}$$

Wick Debinding – An Effective Way

molding step (German, 2003).

binder, is shown in Fig. 6.

al., 2000; Cetinel et al., 2010).

disruption of the powder skeleton.

shape, solid content and the inter-particle forces.

of Solving Problems in the Debinding Process of Powder Injection Molding 95

Besides the kinetics of the capillary-extraction process it is crucial that the powder compact of green body retains its shape after the process has been completed and no flaws are introduced. One of the most critical moments in the process is the point when the binder melts. At this stage the compact becomes quite weak and soft. This is especially critical in the case of low-pressure injection molding, where only one component binder i.e., paraffin wax, is used. It is because of a characteristic known as the yield stress that the green body retains its shape. The suspension behaves like a rigid body below the yield stress and flows like a liquid above the yield stress. The yield stress is mostly governed by the particle size,

However, a large yield stress is undesirable for the molding step, since it results in a low moldability of the suspension (German, 1990). Suspensions with a high yield stress must have high powder content, which also increases viscosity, which is again undesirable in the

Fortunately, the yield stress of the molded green body can be significantly larger than the yield stress of the suspension before molding. This is because the particles rearrange during molding and solidification into a denser configuration - a consequence of the shrinkage of the binder after solidification. An increased attractive inter-particle interaction occurs in the denser form (Dakskobler & Kosmač, 2009). Ideally the process does not reverse during remelting. If the inter-particle forces are high enough, then the particle arrangement will not change; instead the expanding binder will be exuded from the body, while the particle arrangement remains intact. A series of photographs of a LPIM sample, taken with an optical microscope during heating from below to above the melting temperature of the

A molten paraffin binder exudes out of the green body. This happens without any

The extent of the exudation effect depends on the amount of low-melting point wax in the body. During the melting the volume of the wax increases by 15%. The effect is most pronounced in the low-pressure injection molding where the amount of wax is large – around 60 vol%. In high-pressure molding the amount of wax is around 10% – 30%.The large amount of wax is an important factor that explains why in LPIM extreme difficulties are encountered when a wicking agent is not used. In the HPIM process the yield strength during melting does not pose that big a problem, because the additional high-melting point polymer ensures that the particles are held in position. It has been shown that the yield stress of molded parts can also increase with the storage time after the molding (Novak et

Water from a humid environment can penetrate the green body and interfere with the bonds between surfactant molecules and the surface of the particles. The strength of the inter-particle forces increases, which leads to a significant increase in the yield strength. This effect can be made even faster, if the molded bodies are soaked in water (Novak et al., 2000). Wicking embedment offers another benefit. It guarantiees a gentle physical support for the parts. If the debinding takes place on a hard substrate there is danger that certain flaws will occur, as schematically presented in the sketch in Fig. 7. The suspended parts of the green

$$K = 190 \left( \frac{E^2}{S} \right)^{2.42} \tag{8}$$

These permeability correlations have been tuned for a forced flow through the porous material, i.e. , the flow of liquid that is pushed through the material by applying an external pressure. However, the permeability can be significantly different in the case of capillary extraction, where the liquid is sucked out of green body by capillary forces.

The wicking agent must extract the liquefied binder from the green body, which is itself a porous body. If the molten binder is removed from the green compact then a new surface must be formed in the interior of that compact. This new surface, which initially appears in larger pores, causes a capillary pressure in the opposite direction and resists extraction. A competition for the binder emerges between the two porous media. Only the smaller pores of the wicking agent might have a capillary suction that is strong enough to exceed the capillary pressure of the green body. The liquid then travels into the wicking agent only through these pores. In contrast, if the liquid were to be forced by the external pressure through the wicking agent it would travel mostly through larger pores, which present a smaller resistance.

The measured permeability, or that calculated from equations 6-8, could be significantly higher than in the case of capillary extraction. This means, that conventional methods of measuring permeability, such as measuring the forced gas flow through a sample of a porous material, cannot be used to determine the permeability for the capillary-extraction phenomenon. The mismatch between the forced flow and the capillary-extraction permeability is especially large in the granular form of the wicking agent. A characteristic case for porous material in the form of large granules with a fine porosity is schematically presented in Fig 5. If the fluid is forced through such a material the permeability would appear much larger than if this granulate was extracting the liquid from another porous material, for which a strong capillary pressure is required.

Fig. 5. In the capillary extraction the liquid flows only through smaller pores inside the granulae, wheras in the case of liquid flow forced by external pressure the majority of flow would be between the granulae.

<sup>190</sup> 

These permeability correlations have been tuned for a forced flow through the porous material, i.e. , the flow of liquid that is pushed through the material by applying an external pressure. However, the permeability can be significantly different in the case of capillary

The wicking agent must extract the liquefied binder from the green body, which is itself a porous body. If the molten binder is removed from the green compact then a new surface must be formed in the interior of that compact. This new surface, which initially appears in larger pores, causes a capillary pressure in the opposite direction and resists extraction. A competition for the binder emerges between the two porous media. Only the smaller pores of the wicking agent might have a capillary suction that is strong enough to exceed the capillary pressure of the green body. The liquid then travels into the wicking agent only through these pores. In contrast, if the liquid were to be forced by the external pressure through the wicking agent it would travel mostly through larger pores, which present a

The measured permeability, or that calculated from equations 6-8, could be significantly higher than in the case of capillary extraction. This means, that conventional methods of measuring permeability, such as measuring the forced gas flow through a sample of a porous material, cannot be used to determine the permeability for the capillary-extraction phenomenon. The mismatch between the forced flow and the capillary-extraction permeability is especially large in the granular form of the wicking agent. A characteristic case for porous material in the form of large granules with a fine porosity is schematically presented in Fig 5. If the fluid is forced through such a material the permeability would appear much larger than if this granulate was extracting the liquid from another porous

Fig. 5. In the capillary extraction the liquid flows only through smaller pores inside the granulae, wheras in the case of liquid flow forced by external pressure the majority of flow

*<sup>E</sup> <sup>K</sup>*

extraction, where the liquid is sucked out of green body by capillary forces.

material, for which a strong capillary pressure is required.

would be between the granulae.

smaller resistance.

2.42 <sup>2</sup>

*S* (8)

Besides the kinetics of the capillary-extraction process it is crucial that the powder compact of green body retains its shape after the process has been completed and no flaws are introduced. One of the most critical moments in the process is the point when the binder melts. At this stage the compact becomes quite weak and soft. This is especially critical in the case of low-pressure injection molding, where only one component binder i.e., paraffin wax, is used. It is because of a characteristic known as the yield stress that the green body retains its shape. The suspension behaves like a rigid body below the yield stress and flows like a liquid above the yield stress. The yield stress is mostly governed by the particle size, shape, solid content and the inter-particle forces.

However, a large yield stress is undesirable for the molding step, since it results in a low moldability of the suspension (German, 1990). Suspensions with a high yield stress must have high powder content, which also increases viscosity, which is again undesirable in the molding step (German, 2003).

Fortunately, the yield stress of the molded green body can be significantly larger than the yield stress of the suspension before molding. This is because the particles rearrange during molding and solidification into a denser configuration - a consequence of the shrinkage of the binder after solidification. An increased attractive inter-particle interaction occurs in the denser form (Dakskobler & Kosmač, 2009). Ideally the process does not reverse during remelting. If the inter-particle forces are high enough, then the particle arrangement will not change; instead the expanding binder will be exuded from the body, while the particle arrangement remains intact. A series of photographs of a LPIM sample, taken with an optical microscope during heating from below to above the melting temperature of the binder, is shown in Fig. 6.

A molten paraffin binder exudes out of the green body. This happens without any disruption of the powder skeleton.

The extent of the exudation effect depends on the amount of low-melting point wax in the body. During the melting the volume of the wax increases by 15%. The effect is most pronounced in the low-pressure injection molding where the amount of wax is large – around 60 vol%. In high-pressure molding the amount of wax is around 10% – 30%.The large amount of wax is an important factor that explains why in LPIM extreme difficulties are encountered when a wicking agent is not used. In the HPIM process the yield strength during melting does not pose that big a problem, because the additional high-melting point polymer ensures that the particles are held in position. It has been shown that the yield stress of molded parts can also increase with the storage time after the molding (Novak et al., 2000; Cetinel et al., 2010).

Water from a humid environment can penetrate the green body and interfere with the bonds between surfactant molecules and the surface of the particles. The strength of the inter-particle forces increases, which leads to a significant increase in the yield strength. This effect can be made even faster, if the molded bodies are soaked in water (Novak et al., 2000).

Wicking embedment offers another benefit. It guarantiees a gentle physical support for the parts. If the debinding takes place on a hard substrate there is danger that certain flaws will occur, as schematically presented in the sketch in Fig. 7. The suspended parts of the green

Wick Debinding – An Effective Way

**3. Overview of theoretical work** 

more than a single mechanism.

drops by around 15% during melting (Gorjan et al., 2010).

in liquid form, leaving behind a binder-free region.

substrate can deform.

of Solving Problems in the Debinding Process of Powder Injection Molding 97

body could bend or crack and point pressure areas where the green body rests on the solid

Because of the complexity of the capillary system in the porous green body and the wicking agent the accurate and general theoretical model is difficult to obtain. Since the systems can be quite different, the extraction can also show different behaviour. The existing theoretical models predict different behaviors during the debinding and many even contradict each other. The basis of all models is Darcy's law and some form of capillary-pressure description. One of the first to theoretically describe the process of wick debinding for injection-molded samples was German (German, 1987), who in 1987 proposed a model, where he assumed that the binder is extracted from a molded compact as a continuous body

A partially debinded compact should, therefore, have a characteristic binder distribution with a binder-saturated region near the contact with the wicking powder and a region with no binder on the other side. A sharp border between these regions should be present – a sign of the trailing front of the molten binder. This model is simple and has frequently been used as a basis for research in wick debinding. Monte-Carlo simulations of binder removal based on German's assumptions have also been conducted (Shih & Houring, 2001; Lin & Houring, 2005). These simulations focused on binder penetration in the wicking embedment and examined the case where pieces are not completely surrounded by the embedment.

However, German's model has been criticized, on the basis of experimental data. Contradicting this model, many researchers observed that the binder is uniformly distributed inside the body at all stages of the debinding process (Liu, 1999; Bao & Evans, 1991; Vetter et al., 1994; Kim et al., 1999; Somasundram, 2008). There is also the question of how the air can enter behind the trailing front into the binder-free region if the molded pieces are completely surrounded by the wick (Somasundram, 2008). Furthermore, the debinding rate does not correspond well with some experiments (Vetter et al., 1994). It has also been observed that the permeability in a wick embedment can have important effects and can be a limiting factor, rather than the flow through a sample, as was suggested in German's model [Vetter et al., 1994; Somasundram, 2008]. With more precise examinations of the binder-removal rate it has been confirmed that wick-debinding must take place via

One clearly observable effect, for example, is a rapid decrease in the binder content at the beginning of the process. This has been attributed to the pressure arising from the thermal expansion of the binder [Somasundram, 2008, Gorjan et al., 2010]. Before the debinding process, molded parts contain binder in the solid state, then during the melting a large, and relatively sudden, expansion of the binder occurs. For example, the density of the paraffin

With further studies of the kinetics of capillary extraction it has been found that the molten binder inside the body exists in different states, a differentiation based on the position inside the body. It can behave as a 'mobile binder' located in the larger voids between the powder

Fig. 6. Exudation of the paraffin-wax binder during heating above the melting point of the paraffin, as observed with optical microscope. The photograph a) shows the state before the melting, b) shows the first molten paraffin exuding from the green body, c) shows the situation 1 minute after the b) and d) shows state 10 min after the b).

Fig. 7. Green bodies with a complex shape can pose difficulties if they are debinded on a solid substrate. Small areas on which the green body rests on the substrate (1 and 2) can be deformed due to the large compressive stress. Suspended parts of the body can bend due to gravity or even crack at the point where the tensile stress is the highest (3). The wicking embedment can successfully reduce these flaws, since the support pressure is well spread over the green body's surface.

body could bend or crack and point pressure areas where the green body rests on the solid substrate can deform.
