ASTM F2952-22

Standard Guide for Determining the Mean Darcy Permeability Coefficient for a Porous Tissue Scaffold

SIGNIFICANCE AND USE
4.1 This document describes the basic principles that need to be followed to obtain a mean value of the Darcy permeability coefficient for structures that consist of a series of interconnected voids or pores. The coefficient is a measure of the permeability of the structure to fluid flowing through it that is driven by a pressure gradient created across it.  
4.2 The technique is not sensitive to the presence of closed or blind-end pores (Fig. 1).
FIG. 1 Schematic of the Different Pores Types Found in Tissue Scaffolds. Fluid Flow Through the Structure is via the Open Pores  
4.3 Values of the permeability coefficient can be used to compare the consistency of manufactured samples or to determine what the effect of changing one or more manufacturing settings has on permeability. They can also be used to assess the homogeneity and anisotropy of tissue scaffolds. Variability in the permeability coefficient can be also be indicative of:  
4.3.1 Internal damage within the sample, for example, cracking or permanent deformation.  
4.3.2 The presence of large voids, including trapped air bubbles, within the structure.  
4.3.3 Surface effects such as a skin formed during manufacture.  
4.3.4 Variable sample geometry.  
4.4 This test method is based on the assumption that the flow rate through a given sample subjected to an applied pressure gradient is constant with time.
Note 1: If a steady-state flow condition isn’t reached, then this could be due to structural damage (that is, crack formation or the porous structure deformed as a result of the force being placed upon it by the fluid flowing through it). Sample deformation in the form of stretching (bowing) can also occur for less resilient structures as a result of high fluid flow rates. This topic is discussed in more detail in Section 7.  
4.5 Care should be taken to ensure that hydrophobic materials are fully wetted out when using water or other aqueous-based liquids as permeants.  
4.6 Conventionally, the p...
SCOPE
1.1 This guide describes test methods suitable for determining the mean Darcy permeability coefficient for a porous tissue scaffold, which is a measure of the rate at which a fluid, typically air or water, flows through it in response to an applied pressure gradient. This information can be used to optimize the structure of tissue scaffolds, to develop a consistent manufacturing process, and for quality assurance purposes.  
1.2 The method is generally nondestructive and non-contaminating.  
1.3 The method is not suitable for structures that are easily deformed or damaged. Some experimentation is usually required to assess the suitability of permeability testing for a particular material/structure and to optimize the experimental conditions.  
1.4 Measures of permeability should not be considered as definitive metrics of the structure of porous tissue scaffolds and should complement measures obtained by other investigative techniques, for example, scanning electron microscopy, gas flow porometry, and micro-computer X-ray tomography (Guides F2450, F2603, and F3259).  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Mar-2022
• ICS: 11.100.99 - Other standards related to laboratory medicine
• Technical Committee: F04 - Medical and Surgical Materials and Devices
• Drafting Committee: F04.42 - Biomaterials and Biomolecules for TEMPs

Relations

• Refers: ASTM F2603-06(2020) - Standard Guide for Interpreting Images of Polymeric Tissue Scaffolds
• Effective Date: 01-Aug-2020
• Refers: ASTM F2450-18 - Standard Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue-Engineered Medical Products
• Effective Date: 15-Nov-2018
• Refers: ASTM F3259-17 - Standard Guide for Micro-computed Tomography of Tissue Engineered Scaffolds
• Effective Date: 01-May-2017
• Refers: ASTM D737-04(2016) - Standard Test Method for Air Permeability of Textile Fabrics
• Effective Date: 01-Jul-2016
• Refers: ASTM F2603-06(2012) - Standard Guide for Interpreting Images of Polymeric Tissue Scaffolds
• Effective Date: 01-Oct-2012
• Refers: ASTM D737-04(2012) - Standard Test Method for Air Permeability of Textile Fabrics
• Effective Date: 01-Jul-2012
• Refers: ASTM F2450-10 - Standard Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue Engineered Medical Products
• Effective Date: 01-Mar-2010
• Refers: ASTM F2450-09 - Standard Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue Engineered Medical Products
• Effective Date: 01-Jun-2009
• Refers: ASTM D737-04(2008)e1 - Standard Test Method for Air Permeability of Textile Fabrics
• Effective Date: 01-Jul-2008
• Refers: ASTM D737-04(2008)e2 - Standard Test Method for Air Permeability of Textile Fabrics
• Effective Date: 01-Jul-2008
• Refers: ASTM F2603-06 - Standard Guide for Interpreting Images of Polymeric Tissue Scaffolds
• Effective Date: 01-Dec-2006
• Refers: ASTM D2434-68(2006) - Standard Test Method for Permeability of Granular Soils (Constant Head) (Withdrawn 2015)
• Effective Date: 01-Feb-2006
• Refers: ASTM D737-04 - Test Method for Air Permeability of Textile Fabrics
• Effective Date: 01-Dec-2004
• Refers: ASTM F2450-04 - Standard Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue Engineered Medical Products
• Effective Date: 01-Nov-2004
• Refers: ASTM D2434-68(2000) - Standard Test Method for Permeability of Granular Soils (Constant Head)
• Effective Date: 01-Jan-2000

Overview

ASTM F2952-22 is the standard guide for determining the mean Darcy permeability coefficient for porous tissue scaffolds. Developed by ASTM International, this guide outlines key test methods for measuring the permeability, or the rate at which a fluid (commonly air or water) flows through a porous scaffold in response to an applied pressure gradient. Understanding the permeability coefficient is vital for optimizing the design, manufacturing process, and quality assurance of tissue scaffolds used in biomedical applications. The method is generally nondestructive and non-contaminating, ensuring that sample integrity is maintained throughout testing.

Key Topics

• Darcy Permeability Coefficient: This measures the resistance of a scaffold material to fluid flow, governed by the structure’s interconnected open pores. Accurate measurement helps assess consistency and identify structural changes due to damage or manufacturing variations.
• Open vs. Closed Pores: The method assesses flow only through open (interconnected) pores, as closed or blind-end pores do not contribute to overall permeability.
• Sample Suitability: Not all samples are ideal - highly deformable or easily damaged scaffolds may not be suitable for permeability testing, and initial experimentation may be needed to ensure valid results.
• Complementary Techniques: Permeability measurements should not be the sole metric for scaffold assessment and are best used in conjunction with imaging (e.g., scanning electron microscopy, micro-CT) and porometry data to provide a complete structural profile.
• Experimental Considerations: Factors such as sample geometry, material hydrophobicity, mounting technique, and fluid selection (air or water) can all influence results and should be carefully controlled.
• Data Interpretation: Attention must be paid to possible hysteresis (differences during cycles of increasing and decreasing pressure) and deviations from ideal Darcy behavior to ensure valid, reproducible data.

Applications

• Tissue Engineering: Permeability coefficients inform scaffold design, particularly for tissues requiring efficient nutrient and waste exchange, such as in regenerative medicine and tissue-engineered medical products.
• Manufacturing Quality Control: By comparing permeability values, manufacturers can assess batch consistency, optimize processing parameters, and detect defects such as cracks, voids, or inconsistent porosity.
• Research & Development: Scientists use permeability data to evaluate new scaffold materials, study the effects of degradation over time, and tailor scaffolds for specific cell or tissue requirements.
• Failure Analysis: Variability in permeability may indicate internal damage, trapped air, or geometric inconsistencies, aiding in diagnostics and process improvement.

Related Standards

ASTM F2952-22 should be used alongside other relevant testing and characterization standards to ensure comprehensive evaluation of tissue scaffolds:

• ASTM F2450: Guide for assessing microstructure of polymeric scaffolds
• ASTM F2603: Guide for interpreting images of polymeric tissue scaffolds
• ASTM F3259: Guide for micro-computed tomography of tissue engineered scaffolds
• ASTM F3510: Guide for characterizing fiber-based constructs for tissue-engineered medical products
• ASTM D2434: Test methods for measurement of hydraulic conductivity of coarse-grained soils
• API RP-27: Recommended practice for determining permeability of porous media

Conclusion

ASTM F2952-22 provides a standardized approach for measuring the mean Darcy permeability coefficient in porous tissue scaffolds, supporting biomedical product development, process optimization, and quality assurance. By following this guide and considering complementary analytical techniques, stakeholders can ensure reliable measurement and interpretation of scaffold permeability, leading to improved performance in tissue engineering and related fields.

Keywords: ASTM F2952-22, Darcy permeability coefficient, tissue scaffold permeability, porous materials, quality control, tissue engineering scaffolds, permeability test method, scaffold characterization.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: F2952 − 22
Standard Guide for
Determining the Mean Darcy Permeability Coefficient for a
Porous Tissue Scaffold
This standard is issued under the fixed designation F2952; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This guide describes test methods suitable for determin-
D737 Test Method for Air Permeability of Textile Fabrics
ing the mean Darcy permeability coefficient for a porous tissue
D2434 Test Methods for Measurement of Hydraulic Con-
scaffold, which is a measure of the rate at which a fluid,
ductivity of Coarse-Grained Soils
typicallyairorwater,flowsthroughitinresponsetoanapplied
F2450 Guide for Assessing Microstructure of Polymeric
pressure gradient.This information can be used to optimize the
Scaffolds for Use in Tissue-Engineered Medical Products
structure of tissue scaffolds, to develop a consistent manufac-
F2603 Guide for Interpreting Images of Polymeric Tissue
turing process, and for quality assurance purposes.
Scaffolds
1.2 The method is generally nondestructive and non- F3259 Guide for Micro-computed Tomography of Tissue
contaminating. Engineered Scaffolds
F3510 Guide for Characterizing Fiber-Based Constructs for
1.3 The method is not suitable for structures that are easily
Tissue-Engineered Medical Products
deformed or damaged. Some experimentation is usually re-
quired to assess the suitability of permeability testing for a
3. Terminology
particular material/structure and to optimize the experimental
3.1 Definitions of Terms Specific to This Standard:
conditions.
3.1.1 tortuosity, n—the ratio of the actual path length
through connected pores to the Euclidean distance (shortest
1.4 Measures of permeability should not be considered as
linear distance).
definitivemetricsofthestructureofporoustissuescaffoldsand
should complement measures obtained by other investigative
4. Significance and Use
techniques, for example, scanning electron microscopy, gas
4.1 This document describes the basic principles that need
flow porometry, and micro-computer X-ray tomography
to be followed to obtain a mean value of the Darcy permeabil-
(Guides F2450, F2603, and F3259).
ity coefficient for structures that consist of a series of intercon-
1.5 This standard does not purport to address all of the
nected voids or pores. The coefficient is a measure of the
safety concerns, if any, associated with its use. It is the
permeability of the structure to fluid flowing through it that is
responsibility of the user of this standard to establish appro-
driven by a pressure gradient created across it.
priate safety, health, and environmental practices and deter-
4.2 The technique is not sensitive to the presence of closed
mine the applicability of regulatory limitations prior to use.
or blind-end pores (Fig. 1).
1.6 This international standard was developed in accor-
4.3 Values of the permeability coefficient can be used to
dance with internationally recognized principles on standard-
compare the consistency of manufactured samples or to deter-
ization established in the Decision on Principles for the
mine what the effect of changing one or more manufacturing
Development of International Standards, Guides and Recom-
settings has on permeability. They can also be used to assess
mendations issued by the World Trade Organization Technical
the homogeneity and anisotropy of tissue scaffolds. Variability
Barriers to Trade (TBT) Committee.
in the permeability coefficient can be also be indicative of:
4.3.1 Internal damage within the sample, for example,
cracking or permanent deformation.
This guide is under the jurisdiction of ASTM Committee F04 on Medical and
Surgical Materials and Devices and is the direct responsibility of Subcommittee
F04.42 on Biomaterials and Biomolecules for TEMPs. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved April 1, 2022. Published April 2022. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2014. Last previous edition approved in 2014 as F2952 – 14. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/F2952-22. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2952 − 22
FIG. 1 Schematic of the Different Pores Types Found in Tissue Scaffolds.
Fluid Flow Through the Structure is via the Open Pores
4.3.2 The presence of large voids, including trapped air 5. Characterization and the Structural Features of Tissue
bubbles, within the structure. Scaffolds
4.3.3 Surface effects such as a skin formed during manu-
5.1 Porous tissue scaffolds are typically manufactured from
facture.
polymers and ceramics and consist of a network of connected
4.3.4 Variable sample geometry.
voids through which cells, macromolecules such as growth
4.4 This test method is based on the assumption that the factors, and small molecules such as nutrients and dissolved
flow rate through a given sample subjected to an applied gases can move (1). The material used to create the scaffold
pressure gradient is constant with time. may disappear over time, either as a result of enzyme activity
NOTE 1—If a steady-state flow condition isn’t reached, then this could
or some other degradation processes (for example, hydrolysis).
be due to structural damage (that is, crack formation or the porous
The time-dependent permeability of tissue scaffolds to dis-
structuredeformedasaresultoftheforcebeingplaceduponitbythefluid
solved gases and solutes is critical to their function, particu-
flowing through it). Sample deformation in the form of stretching
larly for high levels of cell occupancy due to the demands for
(bowing)canalsooccurforlessresilientstructuresasaresultofhighfluid
oxygen and nutrients as well as the need to remove waste
flow rates. This topic is discussed in more detail in Section 7.
products.
4.5 Care should be taken to ensure that hydrophobic mate-
rials are fully wetted out when using water or other aqueous- 5.2 Therearemanymethodsavailableforcharacterizingthe
based liquids as permeants.
structural features of scaffolds (Guides F2450 and F3510), but
these can be time consuming, expensive to use, and can result
4.6 Conventionally,thepressuredifferentialcreatedacrossa
in permanent damage or contamination to the scaffold.
sample is measured as a function of both increasing and
decreasing flow rates. An alternative approach, which may be 5.3 Mostinvestigatorsreportsomemeasureofporesizeand
practically easier to create, is to apply a range of different
an estimate of the scaffold porosity (2, 3). However, there are
pressure differentials across the sample and measure the significant practical issues associated with these measure-
resultant flow of fluid through it. The hysteresis that occurs
ments. Techniques such as mercury porosimetry and gas flow
during a complete cycle of increasing flow rate followed by a
porometry are used to estimate pore size distributions which
progressive decrease in flow rate can provide an excellent typically differ by an order of magnitude due to differences in
measure of the behavioural consistency of the matrix. Signifi-
the underlying physics of the techniques (Guide F2450).
cant hysteresis in the measured pressure differential during Despite the shortfalls of these techniques, both can be used to
increasing and decreasing flow rates can indicate the existence
infer a useful amount of information regarding the structure of
of induced damage in the structure, the fact that the material is the scaffold. Both porosimetry and porometry represent the
behaving viscoelastically, or is suffering from permanent
scaffold structure as a distribution of differently sized parallel-
plastic deformation. Some guidance on how to identify which sided pores, that is, the model assumes a simple structure that
of these factors is responsible for hysteresis is provided in
is equivalent to the more complicated structures usually
Section 7. manufactured where the pores are not parallel-sided and not of
uniform diameter.
4.7 It is assumed that Darcy’s law is valid. This can be
established by plotting the volume flow through the specimen 5.4 Electron and other microscopies are extensively used to
against the differential pressure drop across the specimen. This
image scaffolds, but the data that these techniques produce is
plot should be linear for Darcy’s law to apply and a least- often challenging to interpret without some undefinable level
squares fit to the data should pass through the origin. It is not
of uncertainty (that is, quantifying the dimensions of typically
uncommon for such plots to be nonlinear which may indicate
that the structure does not obey Darcy’s law or that the range
ofpressuresappliedistoobroad.Thistopicisfurtherdiscussed
The boldface numbers in parentheses refer to the list of references at the end of
in Section 7. this standard.
F2952 − 22
FIG. 2 Example of a Plot of Flow Rate versus Pressure Differential
irregularly shaped and sized structural features). The same 6.2 In its simplest form, the permeability coefficient, k,of
arguments apply to tomographic methods such as magnetic the scaffold can be determined by measuring the flow of fluid
resonanceimagingandmicro-computertomography(µCT);for through the material in a given time under a known pressure
example, calculations based on the analysis of a series of gradient using Darcy’s law (5), that is,
scaffold images obtained from a tomographical method such as
2kA P 2 P
~ !
b a
Q 5 (1)
µCT will depend on how well the boundaries of the voids or
µL
pores can be defined, on the instrument resolution in the x, y
which states that the flow rate (Q,(m /s)) through the
and z planes, and the methodology used to obtain dimensional
material is directly proportional to the cross-sectional area (A,
information (Guide F3259). Nevertheless, many groups have
(m )) and the pressure drop (P – P , (Pa)) and inversely
pursued quantitative analysis of pore size distributions in
b a
proportional to the viscosity of fluid (µ, (Pa.s)) and the length
polymeric (3)andbioceramic (4)matricesinrecognitionofthe
(L, (m)) over which the pressure drop occurs.
important correlation between this parameter and tissue in-
growth.
6.3 The permeability coefficient, k, is then derived from the
slope of a linear plot of flow rate versus pressure drop where
5.5 Theporesinatissuescaffoldtypicallyconsistofaseries
the slope is forced to pass through the origin (see Fig. 2).
ofirregularlyshapedvoids thatcanbeconnectedtoeachother
both by partial fusion and connecting channels (connects).
6.4 The SI units of the coefficient are m .
Through pores provide a path through the scaffold from one
6.5 Permeability coefficients are used in assessing soils,
side to the other (see Fig. 1), and are the primary routes for
filters, and other porous materials (Test Methods D737 and
fluid penetration into the scaffold. The dimensions of a given
D2434) and have also been used to characterize polymeric
pore can be difficult to define due to, for example, merging of
scaffoldsandhardtissues,forexample,cancellousbone (6-11).
adjacent cavities that result in fenestrations or “windows”
forming in the void walls. Blind-end and closed-pores, al-
7. Methodology
though not contributing to measures of fluid permeability, play
an important role in gas diffusion through the structure.
7.1 Obtainingreliablevaluesforthepermeabilitycoefficient
involves a degree of experimental optimization to ensure that a
6. The Darcy Permeability Coefficient
range of flow rates and pressure differentials can be measured.
Clearly, it is advantageous to measure a range of flow rates and
6.1 The Darcy permeability coefficient is a measure of the
pressure differentials to improve the reliability of the Darcy
resistance of a porous material to flow of a fluid through it that
coefficient,butthiscanproducenonlinearplotsforreasonsthat
isgovernedbythedimensionsanddensityofopen(orthrough)
are discussed in Section 8. This will require some experimen-
pores and by the tortuosity of the structure.
tation to optimize the sample geometry and to select the most
appropriate fluid, typically air or water, for a given structure/
sample geometry and material type. Subsections 7.3 and 7.4
The terminology for scaffold structure is not well defined. The term “pore” is
describe the features that are required in an experimental
widely used to mean a void, a window in a void, or a conduit connecting two or
more voids together. system in order to obtain robust estimates of the coefficient.
F2952 − 22
7.2 Reliably determining the pressure differential across the both cases the practical considerations are the same: how to
scaffoldandmeasuringtheflowratethroughitarefundamental apply a progressively increasing pressure gradient without
aspects of permeability testing. In practice, the sensitivity of significantly deforming the sample or letting fluid flow around
theapparatususedtomeasurepressurewilllimitthemagnitude it.
of the pressure gradient that can be used for a given sample
geometry. 8. Practical Considerations
7.3 Gas-Based Systems: 8.1 There are many experimental configurations that can be
7.3.1 Fig. 3 shows a schematic representation of apparatus used to generate the flow rate and pressure differential mea-
that can be used to measure the flow of gas, in this case surements required to determine Darcy’s permeability coeffi-
compressed air, through a disc-like sample mounted in a cient. It is not uncommon to observe a degree of nonlinearity
commercially available filter holder that can be purchased in a in plots of flow rate versus differential pressure, particularly
range of sizes. when investigating a new sample, whether it is manufactured
7.3.2 The rate of flow through the sample is measured by a fromadifferentmaterialorproduc
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F2952 − 14 F2952 − 22
Standard Guide for
Determining the Mean Darcy Permeability Coefficient for a
Porous Tissue Scaffold
This standard is issued under the fixed designation F2952; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This guide describes test methods suitable for determining the mean Darcy permeability coefficient for a porous tissue scaffold,
which is a measure of the rate at which a fluid, typically air or water, flows through it in response to an applied pressure gradient.
This information can be used to optimize the structure of tissue scaffolds, to develop a consistent manufacturing process, and for
quality assurance purposes.
1.2 The method is generally non-destructivenondestructive and non-contaminating.
1.3 The method is not suitable for structures that are easily deformed or damaged. Some experimentation is usually required to
assess the suitability of permeability testing for a particular material/structure and to optimize the experimental conditions.
1.4 Measures of permeability should not be considered as definitive metrics of the structure of porous tissue scaffolds and should
complement measures obtained by other investigative techniques e.g., techniques, for example, scanning electron microscopy, gas
flow porometry, and micro-computer x-rayX-ray tomography (ASTM(Guides F2450, F2603, and F3259).
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D4525D737 Test Method for Air Permeability of Rocks by Flowing AirTextile Fabrics (Withdrawn 2022)
D2434 Test Methods for Measurement of Hydraulic Conductivity of Coarse-Grained Soils
F2450 Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue-Engineered Medical Products
F2603 Guide for Interpreting Images of Polymeric Tissue Scaffolds
F3259 Guide for Micro-computed Tomography of Tissue Engineered Scaffolds
F3510 Guide for Characterizing Fiber-Based Constructs for Tissue-Engineered Medical Products
This test method guide is under the jurisdiction of ASTM Committee F04 on Medical and Surgical Materials and Devices and is the direct responsibility of Subcommittee
F04.42 on Biomaterials and Biomolecules for TEMPs.
Current edition approved March 1, 2014April 1, 2022. Published April 2014April 2022. Originally approved in 2014. Last previous edition approved in 2014 as
F2952 – 14. DOI: 10.1520/F2952-14.10.1520/F2952-22.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F2952 − 22
2.2 American Petroleum Institute (API) Document:
RP-27 Recommended Practice for Determining Permeability of Porous Media
3. Terminology
3.1 Definitions:Definitions of Terms Specific to This Standard:
3.1.1 tortuosity, n—the ratio of the actual path length through connected pores to the Euclidean distance (shortest linear distance).
4. Significance and Use
4.1 This document describes the basic principles that need to be followed to obtain a mean value of the Darcy permeability
coefficient for structures that consist of a series of interconnected voids or pores. The coefficient is a measure of the permeability
of the structure to fluid flowing through it that is driven by a pressure gradient created across it.
4.2 The technique is not sensitive to the presence of closed or blind-end pores (Fig. 1).
4.3 Values of the permeability coefficient can be used to compare the consistency of manufactured samples or to determine what
the effect of changing one or more manufacturing settings has on permeability. They can also be used to assess the homogeneity
and anisotropy of tissue scaffolds. Variability in the permeability coefficient can be also be indicative of:
4.3.1 Internal damage within the sample e.g., sample, for example, cracking or permanent deformation.
4.3.2 The presence of large voids, including trapped air bubbles, within the structure.
4.3.3 Surface effects such as a skin formed during manufacture.
4.3.4 Variable sample geometry.
4.4 This test method is based on the assumption that the flow rate through a given sample subjected to an applied pressure gradient
is constant with time.
NOTE 1—If a steady state steady-state flow condition isn’t reached, then this could be due to structural damage (i.e., (that is, crack formation or the porous
structure deformed as a result of the force being placed upon it by the fluid flowing through it). Sample deformation in the form of stretching (bowing)
can also occur for less resilient structures as a result of high fluid flow rates. This topic is discussed in more detail in Section 7.
4.5 Care should be taken to ensure that hydrophobic materials are fully wetted out when using water or other aqueous-based
liquids as permeants.
4.6 Conventionally, the pressure differential created across a sample is measured as a function of both increasing and decreasing
flow rates. An alternative approach, which may be practically easier to create, is to apply a range of different pressure differentials
across the sample and measure the resultant flow of fluid through it. The hysteresis that occurs during a complete cycle of
FIG. 1 Schematic of the Different Pores Types Found in Tissue Scaffolds.
Fluid Flow throughThrough the Structure is via the Open Pores
F2952 − 22
increasing flow rate followed by a progressive decrease in flow rate can provide an excellent measure of the behavioural
consistency of the matrix. Significant hysteresis in the measured pressure differential during increasing and decreasing flow rates
can indicate the existence of induced damage in the structure, the fact that the material is behaving viscoelastically, or is suffering
from permanent plastic deformation. Some guidance on how to identify which of these factors areis responsible for hysteresis is
provided in Section 7.
4.7 It is assumed that Darcy’s law is valid. This can be established by plotting the volume flow through the specimen against the
differential pressure drop across the specimen. This plot should be linear for Darcy’s law to apply and a least squares least-squares
fit to the data should pass through the origin. It is not uncommon for such plots to be non-linearnonlinear which may indicate that
the structure does not obey Darcy’s law or that the range of pressures applied is too broad. This topic is further discussed in Section
7.
5. CharacterisationCharacterization and the Structural Features of Tissue Scaffolds
5.1 Porous tissue scaffolds are typically manufactured from polymers and ceramics and consist of a network of connected voids
through which cells, macromolecules such as growth factors, and small molecules such as nutrients and dissolved gases can move
(1). In most cases, the The material used to create the scaffold willmay disappear over time, either as a result of enzyme activity
or some other degradation processes (e.g., (for example, hydrolysis). The time-dependent permeability of tissue scaffolds to
dissolved gases and solutes is critical to their function, particularly for high levels of cell occupancy due to the demands for oxygen
and nutrients as well as the need to remove waste products.
5.2 There are many methods available for characterizing the structural features of scaffolds (ASTM(Guides F2450-10), and
F3510), but these can be time-consuming, time consuming, expensive to use, and can result in permanent damage or contamination
to the scaffold.
5.3 Most investigators report some measure of pore size and an estimate of the scaffold porosity (2, 3). However, there are
significant practical issues associated with these measurements. Techniques such as mercury porosimetry and gas flow porometry
are used to estimate pore size distributions which typically differ by an order of magnitude due to differences in the underlying
physics of the techniques (ASTM(Guide F2450). Despite the shortfalls of these techniques, both can be used to infer a useful
amount of information regarding the structure of the scaffold. Both porosimetry and porometry represent the scaffold structure as
a distribution of differently sized parallel-sided pores i.e., pores, that is, the model assumes a simple structure that is equivalent
to the more complicated structures usually manufactured where the pores are not parallel-sided and not of uniform diameter.
FIG. 2 Example of a Plot of Flow Rate versus Pressure Differential
The last approved version of this historical standard is referenced on www.astm.org.
Available from American Petroleum Institute (API), 1220 L. St., NW, Washington, DC 20005-4070, http://www.api.org.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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5.4 Electron and other microscopies are extensively used to image scaffolds, but the data that these techniques produce is often
challenging to interpret without some undefinable level of uncertainty (i.e., (that is, quantifying the dimensions of typically
irregularly shaped and sized structural features). The same arguments apply to tomographic methods such as magnetic resonance
imaging and micro-computer tomography (μCT),(μCT); for example, calculations based on the analysis of a series of scaffold
images obtained from a tomographical method such as μCT will depend on how well the boundaries of the voids or pores can be
defined, on the instrument resolution in the x,y and z planes, and the methodology used to obtain dimensional information.
information (Guide F3259). Nevertheless, many groups have pursued quantitative analysis of pore size distributions in polymeric
(3) and bioceramic (4) matrices in recognition of the important correlation between this parameter and tissue ingrowth.
5.5 The pores in a tissue scaffold typically consist of a series of irregularly shaped voids that can be connected to each other both
by partial fusion and connecting channels (connects). Through pores provide a path through the scaffold from one side to the
other,other (see Fig. 1)), and are the primary routes for fluid penetration into the scaffold. The dimensions of a given pore can be
difficult to define due to, for example, merging of adjacent cavities that result in fenestrations or ‘windows’“windows” forming
in the void walls. Blind-end and closed-pores, although not contributing to measures of fluid permeability, play an important role
in gas diffusion through the structure.
6. The Darcy Permeability Coefficient
6.1 The Darcy permeability coefficient is a measure of the resistance of a porous material to flow of a fluid through it that is
governed by the dimensions and density of open (or through) pores and by the tortuosity of the structure.
6.2 In its simplest form, the permeability coefficient, k, of the scaffold can be determined by measuring the flow of fluid through
the material in a given time under a known pressure gradient using Darcy’s law (5)), i.e.,that is,
2kA P 2 P
~ !
b a
Q 5 (1)
μL
3 2
which states that the flow rate (Q, (m /s)) through the material is directly proportional to the cross-sectional area (A, (m )) and
the pressure drop (P – P , (Pa)) and inversely proportional to the viscosity of fluid (μ, (Pa.s)) and the length (L, (m)) over which
b a
the pressure drop occurs.
6.3 The permeability coefficient, k, is then derived from the slope of a linear plot of flow rate versus pressure drop where the slope
is forced to pass through the origin (see Fig. 2).
6.4 The SI units of the coefficient are m .
6.5 Permeability coefficients are routinely used in assessing soils soils, filters, and other porous materials (ASTM (Test Methods
D4525D737-08 and D2434RP-27)) and have also been used to characterisecharacterize polymeric scaffolds and hard tissues e.g.,
tissues, for example, cancellous bone (6-911).
7. Methodology
7.1 Obtaining reliable values for the permeability coefficient involves a degree of experimental optimization to ensure that a range
of flow rates and pressure differentials can be measured. Clearly, it is advantageous to measure a range of flow rates and pressure
differentials to improve the reliability of the Darcy coefficient, but this can produce non-linearnonlinear plots for reasons that are
discussed in Section 8. This will require some experimentation to optimize the sample geometry and to select the most appropriate
fluid, typically air or water, for a given structure/sample geometry and material type. SectionsSubsections 7.3 and 7.4 describe the
features that are required in an experimental system in order to obtain robust estimates of the coefficient.
7.2 Reliably determining the pressure differential across the scaffold and measuring the flow rate through it are fundamental
aspects of permeability testing. In practice, the sensitivity of the apparatus used to measure pressure will limit the magnitude of
the pressure gradient that can be used for a given sample geometry.
The terminology for scaffold structure is not well defined. The term pore“pore” is widely used to mean a void, a window in a void, or a conduit connecting two or more
voids together.
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7.3 Gas-basedGas-Based Systems:
7.3.1 Fig. 3 shows a schematic representation of apparatus that can be used to measure the flow of gas, in this case compressed
air, through a disc-like sample mounted in a commercially available filter holder that can be purchased in a range of sizes.
7.3.2 The rate of flow through the sample is measured by a gas flow meter. These devices are commercially available for different
ranges of flow rate. Care should be taken to ensure that the flow meter used is appropriate for the flow rates used to avoid potential
measurement inaccuracies. The pressure upstream of the sample, P , is measured and used together with a measured value for
b
atmospheric pressure (P ) to determine the pressure gradient (P – P ) required by Eq 1.
a b a
7.4 Liquid-basedLiquid-Based Systems:
7.4.1 Fig. 4 shows an experimental configuration that measures the flow of a liquid, such as water, through a porous tubular
scaffold sample. The apparatus consistconsists of a circulating pump, which is used to generate an internal pressure within the
circuit,circuit (P ). P is the measured value of atmospheric pressure. The internal pressure that develops within the circuit is very
b a
dependent on the permeability of the scaffold and its geometry, but is usually sufficiently high that any chan
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