Heat Pipe Wick Properties

Figure 1. Sintered test slugs are used to measure wick properties

Wick properties of interest in heat pipe design include:

• Porosity
• Pore Size
• Permeability
• Thermal Conductivity

The properties of sintered wicks are normally measured on cylindrical samples; see Figure 1.

Porosity in heat pipe wicks

A wick has the following two extensive properties:

1. Bulk Volume: Total volume (voids plus wick)
2. Pore Volume: Volume of the voids in the bulk volume

The porosity, an intensive property, is the fraction of the wick that can be filled with fluid:

Porosity is normally calculated in a simple manner.  The bulk volume of the sample is measured.  The sample is then weighed.  The weight of a solid slug would be

Where ρ_SolidSlug is the density of the sintered material (i.e., copper).  The porosity is then calculated by comparing the measured weight with the calculated slug solid weight.

The typical porosity for a sintered wick is around 45%.  Some wicks fabricated from filamentous powder can have porosities as high as 70%.

Figure 2. SEM photo of sintered copper powder. The two arrows show examples of the bridges forming between the spherical particles.

To measure the thermal conductivity, a sintered slug is heated on one side and cooled on the other.  The temperature drop and heat flow can be used to calculate the thermal conductivity.

Pore Size

The pore size is a measure of the capillary pumping capability – the smaller the pore size, the higher pressure the wick can supply. As discussed in How a Heat Pipe Wick Operates, the capillary pressure is given by:

Where
ΔP_c      Capillary pumping capability
σ          Surface tension
r_c          Pore radius
They can be rearranged to solve for the pore radius:

To find the pore radius, the test slug is saturated with a liquid of known pore radius, with a small amount of liquid on top of the slug.  The air pressure below the slug is continuously increased until the first air bubble appears on the top of the slug.  This bubble point pressure across the slug, and the surface tension can then be used to calculate the largest pore radius in the wick sample.

Permeability

The permeability measures how easy it is to flow fluid through the wick.  It is calculated using Darcy’s law, which says that the flow rate is linearly proportional to the pressure drop through the wick.  For flow through a porous slug, Darcy’s law is:

where:
Q_Dot  Volumetric flow rate, m³
ΔP       Pressure Drop across the slug, Pa
μ_L        Liquid viscosity, kg/(m s)
k_Wick    Wick permeability, an intrinsic property of the wick, m².
A_Wick   Wick area, measured perpendicular to the liquid flow direction, m²
L_Slug      Porous slug length, m
This can be rearranged to solve for the wick permeability:

Figure 3. Test apparatus to measure wick pore size and permeability.

Relationship Between Pore Size and Permeability

The ideal heat pipe wick would have a small pore size (to maximize the capillary pumping capability), and a high permeability (to minimize the liquid pressure drop).  Unfortunately, these two properties are mutually exclusive. As the pore size decreases, the permeability also decreases much more quickly. The wick selected for any given heat pipe is a tradeoff between pore size and permeability.
The Anderson Curve, shown in Figure 4, shows the experimental relationship between pore size and permeability:

with the permeability K in m², and the pore size r_c in m.  It holds for sintered and screen wicks between 1 micron Loop Heat Pipe wicks and very coarse sintered or screen wicks.

Figure 4. Anderson curve relating pore size and permeability.