Nanobubbles in a Lennard-Jones Fluid

1
Nanobubbles in a Lennard-Jones Fluid

• D.I. Zhukhovitskii
• Institute for High Energy Densities JIHT

2
Introduction 1. Kinetics of the first-order
transitions is based on statistics of
nanoobjects (embryos of a new phase). 2. For
the vaporliquid ltgt liquidvapor transitions, a
cluster (nanobubble) is far from being a drop
(bubble). 3. The particles that form an
embryo are divided into the surface and internal
ones (effective phases) then, an interpolation
between small and large sizes is possible.
4. The layer of surface particles is the same
for a cluster and nanobubble.
3
5. Clusters (nanobubbles) are no casual
formations! Constituent particles are strongly
correlated.
4
Arbitrary size cluster in the effective phases
model
The size distribution of clusters
5
Effective surface tension vs. cluster size
6
Nucleation rate vs. barrier height of the
critical size cluster for mercury (red) and water
(green) vapors
7
Cluster surface energy vs. cluster radius (
g1/3) for LJ system. MD simulation (red) and
theory water (green)
8
Arbitrary size nanobubble in the effective
phases model
Here, S is the same as for a cluster but the
relation between g and gs is different.
The size distribution of nanobubbles
9
Here,
The critical size satisfies the condition
The equation of spinodal is
For small bubble sizes (gb 0),
10
Energy of bubble formation at spinodal (1) and in
its vicinity (2) vs. bubble size
11
A model of asymmetric fluctuations in a liquid
High density (bond-rich particles)
Low density (bond-deficient particles)
Density fluctuations are asymmetric.
Bond-deficient particles must have the maximum
possible number of bonds but the system must find
itself below the percolation threshold! Such
particles clusterize to form bond-deficient
clusters (BDCs). We assume that BDCs coincide
exactly with low-density regions (no stochastic
fluctuations). The number density of BDCs
comprising k bond-deficient particles is fk.. The
equimolecular size of these BDCs is g. The
number of bubbles with sizes from g to g dg in
the volume V is Ngdg. Obviously, ng ltNggt/V
fk(dg/dk)1.
12
The number density of voidusters with the
equimolar sizes from g to g dg is
The pre-exponential factor C is determined from
the relation between microscopic and macroscopic
fluctuations of the number of particles N in
volume V
13
On the other hand, thermodynamic relation reads
therefore,
We use the van der Waals equation with parameters
defined by the saturation line rather than
critical point to estimate the compressibility
Here,
is a solution of the equation with a single
parameter w nvs/nls
Eventually we find
and for the Lennard-Jones fluid at T 0.75, C
0.0114.
14
Eventually, we can write the size distribution of
nanovoids in the form
This makes it possible to calculate the void
fraction in a liquid
15
MD simulation
Particles are assumed to interact via the pair
additive potential
where
and is the
longrange component.
16
Simulation cell a droplet in an equilibrium
vapor environment
17
Definition of a cluster a particle belongs to
the cluster if it has at least one neighbor
particle at the distance less than rb, which
belongs to the same cluster.
Bond-deficient cluster (BDC) is a group of
bond-deficient particles. Definition of BDC a
particle belongs to the BDC if it has less than
bmax bonds and at least one neighbor
bond-deficient particle at the distance less than
rb, which belongs to the same BDC.
18
Typical nanobubble with a transitional size
19
Typical BDCs in a liquid and clusters in dense
gas
20
BDC distribution over the number of
bond-deficient particles for p 0
21
BDC equimolar size vs. the number of
bond-deficient particles for p 0
22
Nanobubble distribution over the equimolar size
of nanobubbles for p 0
23
(No Transcript)
24
Compressibility factor of BDCs as a function of
their volume fraction at p 0
25
Bulk and surface particle distributions over the
number of bonds
26
Bond deficiency in nanobubbles (theory)
At , the bond deficiency is
With and

, we have
Borrowing
we arrive at (1)
If
we have (2)
Equimolar size and bond deficiency of nanobubbles
(simulation)
where
Rcm is the largest distance between voiduster
center of mass and bond-deficient particle.
27
Bond deficiency as a function of the nanobubble
equimolar size
28
Nanobubble distribution over the equimolar size
for p 0.8
29
Bubble in a liquid in the vicinity of a spinodal
in the center of the drop. MD simulation yields
the spall threshold p 0.65, while a
theoretical estimation is p 0.62.
30

• Conclusions
• A nanobubble in a liquid is a region of
  bond-deficient particles .
• In the MD simulation, the maximum number of bonds
  for bond-deficient particles is dictated by the
  non-percolation condition.
• Size distribution of nanobubbles over the
  equimolar size correlates with the effective
  phases theory. Bond deficiency is the most
  important quantity for thermodynamics of
  nanoobjects.
• Pre-exponential factor in the size distribution
  of nanobubbles can be determined from the
  relation between microscopic and macroscopic
  fluctuations of the number of particles in a
  liquid.

31

• Thank you for the attension!

For more details, visit http//oivtran.ru/dmr