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The replication casting process is used for manufacturing open-pore aluminum foams with advanced performances, such as stability and repeatability of foam structure with porosity over 60%. A simple foam structure model based on the interaction between sodium chloride solid particles poorly wetted by melted aluminum, which leads to the formation of air pockets (or “air collars”), is proposed for the permeability of porous material. The equation for the minimum pore radius of replicated aluminum foam is derived. According to the proposed model, the main assumption of the permeability model consists in a concentration of flow resistance in a circular aperture of radius _{min}. The permeability of aluminum open-pore foams is measured using transformer oil as the fluid, changing the fractions of initial sodium chloride. Measured values of minimum pore size are close to theoretically predicted ones regardless of the particle shape. The expression for the permeability of replicated aluminum foam derived on the basis of the “bottleneck” model of porous media agrees well with the experimental data. The obtained data can be applied for commercial filter cells and pneumatic silencers.

Open-pore metal sponges offer a wide range of possible applications, such as heat-exchangers, fuel cells, filtering processes,

Replication casting can provide the advanced performances such as stability and repeatability of foam structure. Briefly, the process can be described by the following steps. The porous bed of preheated NaCl particles is infiltrated with molten metal. The resulting composite after solidification can be shaped into the desirable form, and then salt is subsequently removed by dissolution in water. Infiltration can be actuated by vacuum suction [

A similar technology was applied commercially by Composite Materials Ltd. (Ekaterinburg, Russia). Here, granular sodium chloride is preheated in a special furnace and is then cast into the mold. Molten aluminum infiltrates the salt bed by vacuum suction. The technology reduces production costs significantly and facilitates the manufacture of a variety of porous cast aluminum items, mainly filter cells and pneumatic silencers.

The main characteristic that determines the dimensions and features (wall thickness, surface area) of porous casting is permeability ^{3}/s) is an average volumetric flow rate through the porous medium, Δ^{2}) of the porous medium perpendicularly to the direction of fluid flow.

The permeability

Let us assume that NaCl granules are of spherical shape with the uniform radius

After solidification of the metal and dissolution of NaCl, the porous medium consists of cavities, shaped by parent NaCl granules connected through the air collars (_{min} where _{min} is the internal radius of an air collar (see

Air collars formation due to infiltration of melted metal into the layer of NaCl granules.

Porous structure model.

The shape of the air collar is described by Laplace’s Equation:
_{at} − P_{ac} +_{at}_{ac}

Since the radii of the air collar’s curvatures are in mutually perpendicular planes, Laplace’s Equation (2) can be rearranged to:

The angle β (^{2} + 2_{min} = −2

The simultaneous solution of Equations (4) and (5) gives the equation for the minimum pore radius of replicated aluminum foam:

We used the model of thermal conductivity of a granular medium in vacuum [_{min} [

A similar “bottleneck” model was applied to derive the permeability of replicated aluminum foam in [

We can consider the pressure drop Δ_{r}_{min}.

We can divide the porous media into slabs of thickness 2

Because the air collar is located in the zone of contact between grains, the number of apertures of radius _{min} for one grain defined as coordination number

Each sphere is in contact with _{min} in one slab along the macroscopic flow direction:

The number of spheres contained in one slab is given by:

Let us suppose that isobars are corresponding with planes, perpendicular to the direction of filtration. Then the loss of pressure in each slab is Δ_{n}

We assume a homogeneous distribution of the pressure loss along the flow direction. Then, we calculate the combined loss of pressure through a porous medium (contained

The solution of Equations (1), (8) and (12) leads to the expression for permeability of replicated aluminum foam:

Replicated aluminum foam was produced by the process described in Reference [

The porosity of NaCl bed varied from 50% up to 65% (in case of the compaction by vibration). The gauge DV8009-Kc of the membrane type with an error of 2.5% was used to estimate the pressure vacuum.

The resulting Al-NaCl composite with monolithic Al casting head was extracted from the mold after solidification. The total height of castings ranged from 120 to 140 mm with 20–40 mm metal head. In fact the height of metal head is irrelevant to the determination of the hydrostatic pressure. Samples of one inch diameter and 10 mm height were cut from the bottom part of the composite (10 mm from bottom surface). Sodium chloride was subsequently removed by dissolution in water. The hydrostatic pressure was determined individually for each casting. The contribution of the hydrostatic pressure is in the range of 2% to 14%.

The photomicrograph of the flat surface of replicated foam (

Photomicrograph of flat surface of replicated foam.

Relation between aperture radius and NaCl particle size (

The aperture radius between the big pores corresponding to the radius of the air collar and the minimum pore radius of replicated aluminum foam was calculated using _{min}=

_{min} in comparison with theoretical calculations by Equation (5). Data of capillary interaction of molten aluminum alloys with inorganic salts are given in [^{2}.

The set up for measuring the permeability of replicated aluminum foam is shown in _{o} from a standard measuring flask) flowed through the porous sample. The measured value of viscosity of the oil was 0.0216 Pa·s ± 2.5% (at 20 °С). The height of the liquid column changed from _{2} to _{1} during filtration. Minimum filtration time was equal to 100 s at the highest value of permeability and was measured three times for each experimental condition.

Set up for measuring the permeability of porous sample.

The reduction of the liquid column according to Darcy’s law is given by the Equation (1) in the differential form:
_{o} is the sectional area of the measuring flask. After this, Equation (14) is integrated:

Permeability of replicated aluminum.

Micrograph of real foam samples.

Measured values of average minimum pore size are close to theoretically predicted ones, regardless of the particle shape. Because of their fragmental shape some particles are interconnected with sharp angle to flat, others with flat to flat angle. Subsequently, the minimum pore size varies over a wide range, but the average value is close to that calculated by Equation (6). Therefore, Equation (6) can be applied easily for the estimation of the minimum pore size of replicated aluminum foam. Equations (6) and (13) are consequently solved. Predictions of Equation (13) are in compliance with experiment (_{min})^{2}) [

The agreement with experiments is found to be very satisfying, especially due to the consecutive application of two models.

A model describing the interaction between solid particles poorly wetted by molten metal with the associated formation of an “air collar” has been developed. The derived expression for the internal radius of the air collar that is equal to the minimum pore radius in replicated aluminum foam, _{min} presented in Equation (6), represents experimental data very well (

The expression for the permeability of replicated aluminum foam derived on the basis of the “bottleneck” model of a porous medium also agrees well with the experimental data. The expression can be applied successfully to design porous castings for filtering and noise reduction.