Particle size measurement: the equivalent spherical diameter

doi:10.1098/rspa.1988.0100

Cited by 194 publications

(107 citation statements)

References 6 publications

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“…ESD is the most commonly used parameter to describe size of nonspherical particles, but it provides no information about shape; to describe shape, at least 1 additional parameter (e.g., aspect ratio for a spheroid) is needed. Moreover, the dependence of ESD on the major dimension and aspect ratio differs with the physical basis of the measurement (e.g., volume, cross-sectional area, sedimentation rate) and therefore one cannot expect different methods to yield similar results (Jennings and Parslow, 1988). This attribute is clearly seen in our microscopy data for D. brightwellii, S. turris, and C. longipes (Figure 4 and 5) where, for the same population of cells that were sized, ESD calculations based on cell volume do not coincide with ESD calculations based on cross-sectional area.…”

Section: Fig 2 As Inmentioning

confidence: 99%

“…Other automated size analyzers, such as the Coulter counter, are sensitive to the particle's volume, and we would not expected results obtained by such analyzers to be identical to the LISST, particularly when nonspherical cells dominate the sample. These 2 methods, however, if done in concert, can be used to obtain information on the degree of nonsphericity of particles in the water (Jonasz 1987, Jennings andParslow 1988).…”

Section: Fig 2 As Inmentioning

confidence: 99%

“…Such inversions require assumptions about the particle's shape. Most commercial instruments report size as the equivalent spherical diameter (ESD), which refers to the diameter of a sphere that would exhibit the same physical characteristics as those exhibited by the particles in the examined sample (Jennings and Parslow 1988). It is important to keep in mind that different physical measurements are sensitive to different attributes of the particle (for example, whereas near-forward light scattering is sensitive to the particle's cross-sectional area, electrical impedance is sensitive to the particle's volume), and thus ESDs reported by one instrument may not be identical to those reported by another instrument, particularly in the case of nonspherical particles (Jennings and Parslow 1988).…”

Section: Introductionmentioning

confidence: 99%

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LISST‐100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape

Karp‐Boss

Azevedo

Boss

2007

Limnology & Ocean Methods

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Information on cell size is central to studies of phytoplankton ecology, yet in situ measurements of particle size distribution remain a challenge. The LISST‐100 (Laser In Situ Scattering and Transmissometry; Sequoia Scientific, Inc.) is one of few commercially available instruments that provide autonomous measurements of size distributions of suspended particles in situ. Its capability to size phytoplankton needs to be evaluated, however, for two reasons. First, size is not measured directly; rather, information on size is obtained from near‐forward scattering measurements that are inverted to obtain size distributions. The inversion assumes that particles are homogeneous spheres. Phytoplankton, however, display a wide range of cell shapes and their scattering behavior is likely to be different from that of spheres. Second, the LISST‐100 was originally designed for sediments and its inversion assumes an index of refraction typical of inorganic particles. We compared size and volume concentration distributions obtained by the LISST‐100 to those derived via microscopy for phytoplankton cultures of different cell sizes and shapes. Results demonstrate the success of the LISST‐100 in measuring size and volume concentrations of cells with a cell aspect ratio that is close to 1 and illustrate its limitations when nonspherical cells are present in the sample. Uses of the LISST‐100 in laboratory and field studies are discussed in light of the results from this study.

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Section: Fig 2 As Inmentioning

confidence: 99%

Section: Fig 2 As Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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LISST‐100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape

Karp‐Boss

Azevedo

Boss

2007

Limnology & Ocean Methods

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“…where m ¼ 8.6 Â 10 À 4 Pa s is the fluid viscosity constant of water at room temperature and R is the equivalent spherical radius of the mesoscopic bead, which equals to the radius of a sphere of equivalent volume 31 . The parameter v denotes the relative velocity of particle motion in water.…”

Section: Methodsmentioning

confidence: 99%

Impact tolerance in mussel thread networks by heterogeneous material distribution

Qin

Buehler

2013

Nat Commun

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The Mytilidae, generally known as marine mussels, are known to attach to most substrates including stone, wood, concrete and iron by using a network of byssus threads. Mussels are subjected to severe mechanical impacts caused by waves. However, how the network of byssus threads keeps the mussel attached in this challenging mechanical environment is puzzling, as the dynamical forces far exceed the measured strength of byssus threads and their attachment to the environment. Here we combine experiment and simulation, and show that the heterogeneous material distribution in byssus threads has a critical role in decreasing the effect of impact loading. We find that a combination of stiff and soft materials at an 80:20 ratio enables mussels to rapidly and effectively dissipate impact energy. Notably, this facilitates a significantly enhanced strength under dynamical loading over 900% that of the strength under static loading.

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“…As an example of the empirical correlation between LD and IA, Li et al [34] A more fundamental basis for the validation of LD by means of IA lays in the fact, that both in the process of forward light scattering as in the analysis of grey-scale images the instrument response relates to the projected area of the particles [23,25,32,35]. Since in LD the latter varies in function of their orientation, the classic Cauchy theorem explains that the expected projected area of a randomly oriented convex body is one quarter of its total surface area [36,37]. Additionally, Gabas et al [38] suggested the lowest and highest number weighted diffraction diameter to relate to the minimum and maximum particulate projected area, respectively.…”

Section: Introductionmentioning

confidence: 99%

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Tinke¹,

Carnicer

Govoreanu³

et al. 2008

Powder Technology

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A systematic study has been described on the laser diffraction (LD) and static image analysis (SIA) of rectangular particles [1]. To rule out powder sampling, sample dispersion and particle orientation as a possible root cause for differences in size distribution profile, powder samples were initially immobilized by means of a dry disperser onto a glass plate. For a defined region of the glass plate the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles were measured by LD and optical microscopy, respectively. Correlation between LD and SIA could be demonstrated considering the scattering intensity of the individual particles as the most dominating factor. For both spherical and rectangular particles, theory explains the latter to relate to the square of their projected area. In traditional LD, the size distribution profile is dominated by the maximum projected area of the particles (A), and the diffraction diameters of a rectangular particle with length L and breadth B are perceived by the LD instrument to correspond by approximation with spheres having a diameter of ∅ L and ∅ B , respectively. Weighting for differences in scattering intensity between spherical and Page 3 of 56 rectangular particles exlains each rectangular particle to contribute to the overall LD volume probability distribution proportional to A 2 /L and A 2 /B. Accordingly, for rectangular particles this scattering intensity weighted diffraction diameter (SIWDD) concept explains an overestimation of their shortest dimension and an underestimation of their longest dimension. For this study various samples have been analysed with the longest dimension of the particles ranging from ca. 10 to 1000 µm. For a variety of pharmaceutical powders all with a different rectangular particle size and shape, the demonstrated correlation between LD and SIA aims to facilitate the user in a better validation of LD methods based on SIA data.

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Particle size measurement: the equivalent spherical diameter

Cited by 194 publications

References 6 publications

LISST‐100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape

LISST‐100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape

Impact tolerance in mussel thread networks by heterogeneous material distribution

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

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