The Viscosity of Suspensions of Spheres: A Note on the Particle Interaction Coefficient

Manley, R. St. John; Mason, S. G.

doi:10.1139/v54-096

Cited by 29 publications

(8 citation statements)

References 4 publications

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“…They would have to be, on average, one diameter apart to constitute 7% of the volume of the suspetiding sievetube sap. Particles which are pt-esent at even this concentration have been found to cause an inct-ease in viscosity, r-elative to that of the suspending fluid, of only 10-40%, Eor exatnple, polystyt-ene latex particles, average diameter 0.87/nn, at a concentration of 4,8% by volume, gave a viscosity of 1.37 times that of the suspenditig fluid alone (Saundet-s, 1961); glass spheres, avetage diatneter 5 /an, at a concentration of 6.4%, gave a t-elative viscosity of 1,206 (Manley & Mason, 1954); glass spheres, average diameter 130 /an, at a concentration of 5%, gave a relative viscosity of 1,145 (Vand, 1948b). The equation deduced by Vand (1948a):…”

Section: Discussionmentioning

confidence: 99%

Analysis of particle motion in sieve tubes of Heracleum

Barclay

Johnson

1982

Plant Cell & Environment

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We have cine-filmed the random motion of ixiicroscopic particles, tnostly starch grains frotn rupt-ured plastids, in sieve tubes of Heracleum friantegcizzianum L, and H. sphondylium Sotiitn, and Lev, Our ftame-by-fratne analysis of the positions of the particles shows that they move tnuch less than calculated when genetally accepted estitnates for the viscosity of sieve-tube sap are inserted in the Stokes-Einstein and other equations for Brownian tnotion. Our analysis of a film, of similar particles, made by previous workers leads us to disagree with their conclusion that particle movement in sieve tubes was preater than should be expected for otdinaty Browtiian motion. Particles iti their liltn atid iti ours moved less than expected even when we allow for the possibility that the particles are restricted by cell walls and by each other. We suggest thai the particles tnove less than expected because the viscosity of sieve-tube sap may be higher than has been assutned by physiologists,

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Section: Discussionmentioning

confidence: 99%

Analysis of particle motion in sieve tubes of Heracleum

Barclay

Johnson

1982

Plant Cell & Environment

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“…Several authors have computed the value of the pair hydrodynamic interaction coefficient β 2 , but there is no agreement. Guth and Simha [3] obtained a β 2 value of 14.1; Saito [4] obtained β 2 of 2.5; Vand [5] obtained β 2 of 7.349; Manley and Mason [6] obtained β 2 of 10.05; Batchelor and Green [7] obtained a β 2 value of 5.2 by assuming a random particle distribution and neglecting Brownian motion. Several closed form expressions have also been proposed in the literature for the relative viscosity of concentrated suspensions of hard spheres.…”

Section: Non-dilute Suspensionsmentioning

confidence: 99%

New Generalized Viscosity Model for Non-Colloidal Suspensions and Emulsions

Pal

2020

Fluids

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The viscous behavior of solids-in-liquid suspensions and liquid-in-liquid emulsions of non-Brownian solid particles and liquid droplets dispersed in Newtonian liquids is thoroughly discussed and reviewed. The full concentration range of the dispersed particles/droplets is covered, that is, 0<ϕ<ϕm, where ϕ is the volume fraction of inclusions (particles or droplets) and ϕm is the maximum packing volume fraction of inclusions. The existing viscosity models for suspensions and emulsions are evaluated using a large pool of experimental viscosity data on suspensions and emulsions. A new generalized model for the viscosity of suspensions and emulsions is proposed and evaluated. The model takes into consideration the influence of shear-induced aggregation of particles and droplets. It also includes the effect of the droplet-to-matrix viscosity ratio λ on the viscosity of emulsions. In the limit of high ratio of droplet viscosity to matrix viscosity (λ→∞), the model reduces to the suspension viscosity model. The proposed model uncovers some important and novel characteristics of suspension systems rarely discussed heretofore in the literature. The model is validated using twenty sets of experimental viscosity data on solids-in-liquid suspensions and twenty-three sets of experimental viscosity data on liquid-in-liquid emulsions.

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“…T~L We wish next to consider the doublet concentration in a binary system where al/a2 < 2. Equation [6] gives the collision frequency per particle; the collision frequency per unit volume F 1 2 is given by fl27zl. Thus for collisions between k different species uniformly dispersed, the total number of two-body collisions of all types in unit time and unit volume is given by the factor 3 appearing since each collision has been counted twice under the summation sign.…”

Section: Steady State Concentmfion Of Doz~blefsmentioning

confidence: 99%

“…If c2 is the volume fraction of t y p e 3 spheres in the suspension, ~a 2~n p / 6 = cz, whence by substitution in equation [5] The present paper deals with an experimental study of interactions in binary suspensions of rigid spheres of different diameter ratios and in suspensions of air bubbles of approximately equal size. These experiments were carried out to extend the earlier observations (ti), t o test equation [6], and to attempt to resolve the question of whether or not the two spheres of a doublet come into true physical contact. Although the question of contact remains incompletely answered, a number of interesting and, it is believed, significant observations were made which have application to theories of viscosity and coagulation of suspensions and colloidal dispersions.…”

Section: Introductionmentioning

confidence: 99%

Particle Motions in Sheared Suspensions Iii.: Further Observations on Collisions of Spheres

Manley¹,

Mason²

1955

Can. J. Chem.

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Two-body interactions between glass spheres of diameters n, and a2 caused by velocity gradients vary with al/ap. When I < al/a2 < 2 , well-dehned collisions similar to those previo~~sly reported for spheres of equal size can be observed. Fair agreement is found between the experimentally observed and calc~llated collision frequencies over a range of particle concentrations and velocity gradients. \i'hen al/a? > 2 the particles are separated a t all times and the phenomena of interaction are Inore complex. Single air bubbles rotate a t the same angular velocity as rigid spheres. When two air bubbles of equal size are bro~lght into collision a d o~~b l e t is formed; instead of the mirror-image separation observed with neutral rigid spheres, the do~tblet continues to rotate for as many as 60 rotations before coalescence occurs. Less f r e q~~e n t l y a do~tblet with distinct particle separation is observed. Periods of rotation of both types of doublet and certain details of the rotational orbit of a d o~~b l e t of touching air bubbles have been measured and compared with values predicted from Jeffery's theoretical equations for rigid ellipsoids. Apart from their intrinsic interest, the phenomena described are of importance in theories of viscosity and coag~~lation of suspensions and colloidal dispersions. INTRODUCTIONIn an earlier paper (5), the two-body collisions of rigid neutral spheres of equal size suspended in a liquid subjected to a velocity gradient were described in some detail. I t was shown experimentally that in a simple field of fluid shear described by [I] u = Gy, v , w = O where u, v, and w are the respective velocities along the X-, Y-, and Z-axes and G is the rate of shear, two spheres can approach one another along an undisturbed rectilinear path parallel to the X-axis until they come into apparent collision at the rate 121 f = 4a3nG/3[31 = 8 c G / r . Here, f denotes the number of collisions per particle per unit time, a the particle diameter, n the number of particles per unit volume of suspension, and c the volume of particles in the suspension.The doublet formed by two colliding spheres rotates about the Z-axis a t a constant angular velocity [41 a = G/2 until it reaches the mirror image through the Y-Z plane of the initial position of contact; the two particles then separate.LManzrscript received J a n z~a r y 17, 1955.

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The Viscosity of Suspensions of Spheres: A Note on the Particle Interaction Coefficient

Cited by 29 publications

References 4 publications

Analysis of particle motion in sieve tubes of Heracleum

Analysis of particle motion in sieve tubes of Heracleum

New Generalized Viscosity Model for Non-Colloidal Suspensions and Emulsions

Particle Motions in Sheared Suspensions Iii.: Further Observations on Collisions of Spheres

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