them
18-01-2008, 12:31 AM
I hope nobody objects to this experiment in space and time?
For edit
Dimensionless numbers in rheology
Deborah number
When the rheological behaviour of a material includes a transition from elastic to viscous as the time scale increase (or, more generally, a transition from a more resistant to a less resistant behaviour), one may define the relevant time scale as a relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called Deborah number. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.
Note that the Deborah number is relevant for materials that flow on long time scales (like a Maxwell fluid) but not for the reverse kind of materials (like the Voigt or Kelvin model) that are viscous on short time scales but solid on the long term.
Reynolds number
In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it is used to identify different flow regimes, such as laminar or turbulent flow.
It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flowrates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
Typically it is given as follows:
http://upload.wikimedia.org/math/9/6/0/960f13bf62a84bfaa0d4137a29a45b92.png
where:
* vs - mean fluid velocity, [m s-1]
* L - characteristic length, [m]
* μ - (absolute) dynamic fluid viscosity, [N s m-2] or [Pa s]
* ν - kinematic fluid viscosity: ν = μ / ρ, [m² s-1]
* ρ - fluid density, [kg m-3].
Space and Time in the Plant Cell Wall: Relationships between Cell Type, Cell Wall Rheology and Cell Function
Background:
The biomechanical behaviour of plant cells depends upon the material properties of their cell walls and, in many cases, it is necessary that these properties are quite specific. Additionally, physiological regulation may require that target cells responding to hormonal signals or environmental factors are able to modulate these characteristics.
Argument: This paper uses a rheological analysis of creep of elongating sunflower (Helianthus annuus) sunflower hypocotyls to demonstrate that the mechanical behaviour of plant cell walls is complex and involves multiple layered processes that can be distinguished from one another by the time-scale over which they lead to a change in tissue dimensions, their sensitivity to pH and temperature, and their responses to changes in spatial arrangement of the cell wall brought about by treatment with high Mr PEG. Furthermore, it appears possible to regulate individual rheological processes, with limited effect on others, in order to modulate growth without affecting tissue structural integrity. It is proposed that control of the water content of the cell wall and therefore the space between cell wall polymers may be one mechanism by which differential regulation of cell wall biomechanical properties is achieved. This hypothesis is supported by evidence showing that enzyme extracts from growing tissues can cause swelling in cell wall fragments in suspension.
Implications: The physiological implications of this complexity are then considered for growing tissues, stomatal guard cells and abscission cells. It is noted that, in each circumstance, a different combination of mechanical properties is required and that differential regulation of properties affecting behaviour over different time-scales is often necessary.
Key words: Helianthus annuus, cell wall, rheology, growth, stomata, abscission
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Sunflowers.jpg/800px-Sunflowers.jpg
Key word
INTRODUCTION: SPACE AND TIME
Space
It has been established that the physical properties of synthetic polymers are substantially affected by spatial constraint of the macromolecular components, so that behaviour of plastics can be controlled by addition of low molecular weight molecules known as plasticizers to maintain separation (Ward and Hadley, 1993). Thompson (2005) noted that spacing within plant cell walls, particularly between cellulose microfibrils, may be of similar importance. This was suggested by the finding that incorporation of pectins and various hemicelluloses into cellulose pellicles produced by Acetobacter resulted in composites which were weaker and more extensible than pellicles of pure cellulose (Chanliaud and Gidley, 1999; Whitney et al., 1999). In the plant cell wall, microfibril separation may be affected by a number of factors including cross-linking polysaccharides tethering microfibrils together or holding them apart (or indeed a balance between the two) and spacing by interpenetrating polysaccharides. However, the water content of the wall will also have a substantial effect on separations. This has two important consequences:
1. The cell wall matric potential and the relationship between matric potential and water content may be important in determining cell wall properties.
2. The importance of cell wall spacing can be tested by alteration of matric potential using polyethylene glycol (PEG). PEG with Mw > 4000 cannot penetrate plant cell walls (Carpita et al., 1979), and so treatment with PEG 6000 in solution alters their water potential by reducing their water content.
Thompson (2005) demonstrated that PEG solutions with osmotic pressures of 3·0 MPa substantially reduced the long-term creep of frozen and thawed sunflower hypocotyls at pH 5·0 and similar behaviour has been found using solutions with an osmotic pressure of 1·0 MPa.
Time
In the field of rheology, it is also understood that the mechanical properties observed are dependent upon the time frame of observation. One important element of this is that the dividing line between solid and fluid behaviour is not absolute, with behaviour becoming more and more fluid over longer time-scales. This is described using the ‘Deborah number’, which is the ratio of the relaxation time of the material to the observation time; the smaller the value, the more fluid the behaviour observed (Scott Blair, 1969). It is named for a line from the Song of Deborah in Judges 5, which can be translated as ‘the mountains flowed before the Lord’ (although the King James Bible uses the less apposite ‘melted’). Over geological time-scales many rocks can be treated as fluids.
A good example of the importance of this idea in plant physiology is tissue growth, when the plant's structure must exhibit solid behaviour over short time-scales, but behave in a more fluid fashion over longer periods for the cell walls to stretch and allow permanent extension.
This paper will show that characterization of plant cell walls involves a number of separate rheological elements acting over different time-scales and which are differentially affected by cell wall water content, heat treatment and pH suggesting that multiple physical or chemical processes are involved. Examples of particular tissues or cells where correct function depends upon specific control of individual biomechanical elements will then be considered.
http://www.artquotes.net/masters/vangogh/vangogh_sunflowers1888.jpg
Jascha Heifetz plays Rondo by Mozart - YouTube
For edit
Dimensionless numbers in rheology
Deborah number
When the rheological behaviour of a material includes a transition from elastic to viscous as the time scale increase (or, more generally, a transition from a more resistant to a less resistant behaviour), one may define the relevant time scale as a relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called Deborah number. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.
Note that the Deborah number is relevant for materials that flow on long time scales (like a Maxwell fluid) but not for the reverse kind of materials (like the Voigt or Kelvin model) that are viscous on short time scales but solid on the long term.
Reynolds number
In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it is used to identify different flow regimes, such as laminar or turbulent flow.
It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flowrates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
Typically it is given as follows:
http://upload.wikimedia.org/math/9/6/0/960f13bf62a84bfaa0d4137a29a45b92.png
where:
* vs - mean fluid velocity, [m s-1]
* L - characteristic length, [m]
* μ - (absolute) dynamic fluid viscosity, [N s m-2] or [Pa s]
* ν - kinematic fluid viscosity: ν = μ / ρ, [m² s-1]
* ρ - fluid density, [kg m-3].
Space and Time in the Plant Cell Wall: Relationships between Cell Type, Cell Wall Rheology and Cell Function
Background:
The biomechanical behaviour of plant cells depends upon the material properties of their cell walls and, in many cases, it is necessary that these properties are quite specific. Additionally, physiological regulation may require that target cells responding to hormonal signals or environmental factors are able to modulate these characteristics.
Argument: This paper uses a rheological analysis of creep of elongating sunflower (Helianthus annuus) sunflower hypocotyls to demonstrate that the mechanical behaviour of plant cell walls is complex and involves multiple layered processes that can be distinguished from one another by the time-scale over which they lead to a change in tissue dimensions, their sensitivity to pH and temperature, and their responses to changes in spatial arrangement of the cell wall brought about by treatment with high Mr PEG. Furthermore, it appears possible to regulate individual rheological processes, with limited effect on others, in order to modulate growth without affecting tissue structural integrity. It is proposed that control of the water content of the cell wall and therefore the space between cell wall polymers may be one mechanism by which differential regulation of cell wall biomechanical properties is achieved. This hypothesis is supported by evidence showing that enzyme extracts from growing tissues can cause swelling in cell wall fragments in suspension.
Implications: The physiological implications of this complexity are then considered for growing tissues, stomatal guard cells and abscission cells. It is noted that, in each circumstance, a different combination of mechanical properties is required and that differential regulation of properties affecting behaviour over different time-scales is often necessary.
Key words: Helianthus annuus, cell wall, rheology, growth, stomata, abscission
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Sunflowers.jpg/800px-Sunflowers.jpg
Key word
INTRODUCTION: SPACE AND TIME
Space
It has been established that the physical properties of synthetic polymers are substantially affected by spatial constraint of the macromolecular components, so that behaviour of plastics can be controlled by addition of low molecular weight molecules known as plasticizers to maintain separation (Ward and Hadley, 1993). Thompson (2005) noted that spacing within plant cell walls, particularly between cellulose microfibrils, may be of similar importance. This was suggested by the finding that incorporation of pectins and various hemicelluloses into cellulose pellicles produced by Acetobacter resulted in composites which were weaker and more extensible than pellicles of pure cellulose (Chanliaud and Gidley, 1999; Whitney et al., 1999). In the plant cell wall, microfibril separation may be affected by a number of factors including cross-linking polysaccharides tethering microfibrils together or holding them apart (or indeed a balance between the two) and spacing by interpenetrating polysaccharides. However, the water content of the wall will also have a substantial effect on separations. This has two important consequences:
1. The cell wall matric potential and the relationship between matric potential and water content may be important in determining cell wall properties.
2. The importance of cell wall spacing can be tested by alteration of matric potential using polyethylene glycol (PEG). PEG with Mw > 4000 cannot penetrate plant cell walls (Carpita et al., 1979), and so treatment with PEG 6000 in solution alters their water potential by reducing their water content.
Thompson (2005) demonstrated that PEG solutions with osmotic pressures of 3·0 MPa substantially reduced the long-term creep of frozen and thawed sunflower hypocotyls at pH 5·0 and similar behaviour has been found using solutions with an osmotic pressure of 1·0 MPa.
Time
In the field of rheology, it is also understood that the mechanical properties observed are dependent upon the time frame of observation. One important element of this is that the dividing line between solid and fluid behaviour is not absolute, with behaviour becoming more and more fluid over longer time-scales. This is described using the ‘Deborah number’, which is the ratio of the relaxation time of the material to the observation time; the smaller the value, the more fluid the behaviour observed (Scott Blair, 1969). It is named for a line from the Song of Deborah in Judges 5, which can be translated as ‘the mountains flowed before the Lord’ (although the King James Bible uses the less apposite ‘melted’). Over geological time-scales many rocks can be treated as fluids.
A good example of the importance of this idea in plant physiology is tissue growth, when the plant's structure must exhibit solid behaviour over short time-scales, but behave in a more fluid fashion over longer periods for the cell walls to stretch and allow permanent extension.
This paper will show that characterization of plant cell walls involves a number of separate rheological elements acting over different time-scales and which are differentially affected by cell wall water content, heat treatment and pH suggesting that multiple physical or chemical processes are involved. Examples of particular tissues or cells where correct function depends upon specific control of individual biomechanical elements will then be considered.
http://www.artquotes.net/masters/vangogh/vangogh_sunflowers1888.jpg
Jascha Heifetz plays Rondo by Mozart - YouTube