Date: 10 September 2020
Abstract (The abstract should not exceed 250 words).
The present paper displays the difference between the time of settling when it comes to measure sand. The correspondent
procedure was carry out thanks to a bottle, water and sand. Initially there were some calculations assuming the sand as ideal or
non-ideal case and correction its factors. After that it’s found that the minor particle would take less time that the major
particle to settle then the flux of water with sand wasn’t laminar at all thus there were some modification that changes the final
settling velocity to the ideal settling velocity using the ideal model.
Index Terms — Sand, Settl ing time, hindered settling, solids particles
I. INTRODUCTION TO STUDY CASE1
Particles may be removed from the atmosphere by
deposition onto floors, walls, and other surfaces. Particles
settle under the influence of gravity where the settling (or
terminal) velocity is broadly proportional to the square of
the diameter[1]. therefore, airborne nanoparticles will fall
out much more slowly than larger particles and gravitation
settling will not be an effective removal process. this
potentially would have the implication of causing higher,
longer exposures. indeed, deposition of nanoparticles will
be independent of orientation and will occur as they
become trapped in the boundary layer on all surfaces,
including walls, ceilings, and floors [2]. The most
common modeling approach is to assume “Stokesian”
particles, namely, as particles move, the flow around them
is in the Stokes regime (Rep <<1, where Rep is the particle
Reynolds number). In this situation the drag force is given
by the well-known Stokes law for a moving sphere in a
fluid [1].
In this demonstration, we let settle a set of sand particles,
trying to stay inside the Stokesian/laminar regime. The
idealized settling velocity will be calculated and then
compared with the experimental settling velocity in order
to find some features that explain the difference between
both them (sphericity, porosity, flowing path, non ideal
fluid properties as density-viscosity and also interactions
particle-particle and fluid-particle.
The objective of this paper was to determine and compare
the theoretical and experimental settling velocity of sand
particles in the water. For the determination of settling
velocity sand. The water was taken from the tap and the
sand from a decorative object. For sand capture
sedimentation is usually used, principle of sedimentation is
based on physical properties of the sand, especially
1 Corresponding author:
depends on density of the sand [4]. For the experimental
measurement of the settling velocity of the sand a bottle is
taken to make a kind of filter, then the water is poured
with sand then the time is measured [5].
II.PROCEDURES FOR EXERCISE SOLUTION (IDEAL
CASE, HINDERED SETTLING CORRECTIONS)
A. Ideal case solution.
Sand was characterized in size and shape as follows:
The particles were measured, and it was obtained a
diameter of 1.00 mm, then it was calculated the sphericity
to make this correction, and it was obtained an average of
0.63.
According with this data and using the following
formulas for water properties (below) the ideal settling
velocity it’s estimated.
Temperature in Kelvin, viscosity (mu) expressed as Pa-
s.
Temperature in Celsius degrees, density (rho) as kg/m3
In this case the temperature was the average in Bogotá,
which is 20°C (293.15 K).
Finally, it is used the next equation and the it is
calculated the Reynolds number to verify that the result
corresponds to a laminar regime.
Ut=(Ψd)2(ρp-ρ)g/18µd)2(ρp-ρ)g/18µp-ρp-ρ)g/18µ)g/18µ
The value for the velocity was 0.35 m/s, however, at the
time of calculating the Reynolds number it is obtained a
number in the region of intermediate, in this case, the
formula to obtain the velocity changes to:
Ut=(3.54g0.71Dp1.14(ρp-ρ)g/18µp-ρp-ρ)g/18µ)0.71)/(ρp-ρ)g/18µf0.29µ0.43)
Solids Particles characterization: Settling for
silica sand demonstration
Óscar Camargo, Luis Camargo, Melissa Ordoñez y Laura Rincón
Universidad de la Sabana, Engineering Faculty, Chemical Engineering Dpt.
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