Studies in living porous media

130 Pages·2016·14.89 MB·English

Studies in Living Porous Media
by
Samuel Alaii Ocko
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
Massachusetts Institute of Technology 2015. All rights reserved.
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.A. .u. .h .r. .... .........
Department of Physics
August 20, 2015
Certified by. Signature redacted
L. Mahadevan
Professor
Thesis Supervisor
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Certified by.
Mehran Kardar
Professor
Thesis Supervisor
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MASSACHUSET INSTIUTE
OF TECHNOLOGY Associate Department Head for Education
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Studies in Living Porous Media
by
Samuel Alan Ocko
Submitted to the Department of Physics
on September 1, 2015, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Many biological systems need to control transport of nutrients and ventilation. Un-
like many nonliving porous media, they modify themselves to meet these demands;
they are active. Using a combination of experiment, theory, and computation, we
investigate several living porous media.
First we consider termite mounds, meter-sized structures built by insects nearly
three orders of magnitude smaller than the mounds themselves. It is widely accepted
that the purpose of these mounds is to give the colony a controlled microhabitat that
buffers the organisms from strong environmental fluctuations while allowing them to
exchange energy and matter with the outside world. However, previous work toward
understanding their functions has led to conflicting models of ventilation mechanisms
and little direct evidence to distinguish them. By directly measuring air flows inside
mounds of the Indian termite Odontotermes obesus, we show that they use diurnal
ambient temperature oscillations to drive cyclic flows inside the mound. These cyclic
flows in the mound flush out CO 2 from the nest and ventilate the colony, in a novel
example of deriving useful work from thermal oscillations. We also observe the same
diurnally-driven flows in mounds of the African termite Macrotermes michaelseni,
evidence that this is likely a general mechanism.
We then consider the problem of honeybee swarming, wherein thousands of bees
cling onto each other to form a dense cluster that may be exposed to the environ-
ment for several days. During this period, the cluster has the ability to maintain its
core temperature actively without a central controller. We suggest that the swarm
cluster is akin to an active porous structure whose functional requirement is to ad-
just to outside conditions by varying its porosity to control its core temperature.
Using a continuum model that takes the form of a set of advection-diffusion equa-
tions for heat transfer in a mobile porous medium, we show that the equalization of
an effective "behavioral pressure", which propagates information about the ambient
temperature through variations in density, leads to effective thermoregulation. Our
model extends and generalizes previous models by focusing the question of mecha-
nism on the form and role of the behavioral pressure, and allows us to explain the
vertical asymmetry of the cluster (as a consequence of buoyancy driven flows), the
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ability of the cluster to overpack at low ambient temperatures without breaking up
at high ambient temperatures, and the relative insensitivity to large variations in the
ambient temperature. Our theory also makes testable hypotheses for the response
of the cluster to external temperature inhomogeneities, and suggests strategies for
biomimetic thermoregulation.
Finally, we consider a generic model of an active porous medium where the con-
ductance of the medium is modified by the flow and in turn modifies the flow, so that
the classical linear laws relating current and resistance are modified over time as the
system itself evolves. This feedback coupling is quantified in terms of two parameters
that characterize the way in which addition or removal of matter follows a simple lo-
cal (or non-local) feedback rule corresponding to either flow-seeking or flow-avoiding
behavior. Using numerical simulations and a continuum mean field theory, we show
that flow-avoiding feedback causes an initially uniform system to become strongly
heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feed-
back leads to an immuring(wall-building) phase separation. Our results provide a
qualitative explanation for the patterning of active conducting media in natural sys-
tems, while suggesting ways to realize complex architectures using simple rules in
engineered systems.
Thesis Supervisor: L. Mahadevan
Title: Professor
Thesis Supervisor: Mehran Kardar
Title: Professor
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Introduction
In order to survive and reproduce, organisms must be able to cope with, take ad-
vantage of, and sometimes manipulate a complex physical environment. Often, much
of this complexity comes from fluids in the environment, which transport heat and
other resources to and from the organism through a complex geometry. Flow through
porous media is important in many problems in physics, biology, geology, and engi-
neering. Most studies are limited to transport through static media, and focus on
how geometry leads to permeability, and how permeability leads to flow. However, in
many living (and nonliving) systems, transport and flow can lead to the remodeling
of the medium itself. This leads to a coevolution of the medium with the flow through
it. Examples of active porous media abound in both living and nonliving systems.
In nonliving systems, drainage networks are formed through the interplay of ero-
sion, transport, and deposition [16, 24]. Higher flow velocities in channels can increase
erosion, a positive feedback mechanism that results in widening the channels further
[51]. Channels also grow and bifurcate based on groundwater flows that supply them
[1, 76], leading to hierarchical structures[69]. In fuse networks, commonly used to
model fracture, edges with too much current are broken. When an edge breaks, the
current has to redistribute itself through nearby edges, which can lead those edges to
break, leading to growing cracks and eventual catastrophic failure [17, 100]. There
are open questions regarding the statistics of failure and crack propagation.
In living systems, slime molds (Fig. 0-1(a)) form networks to efficiently connect
nutrient sources [28, 29]. The organism creates synchronized peristaltic flows to en-
hance transport [59, 5], and tubes with higher flow tend to grow at the expense of
those with less flow. These single celled organisms have been shown to solve maze
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and optimization problems [57, 74, 89, 58], but the full set of rules that leads to this
behavior is not well understood.
One example of high practical importance, and possibly the most complicated, is
the remodeling of vascular networks in animals (Fig. 0-1(b)). In 1918 it was observed
that the vasculature of the chicken embryo would not develop the same if the heart
was removed [10]. Since then, many feedback mechanisms have been observed in
vascular remodeling. Vessels enlarge as a result of currents, hypoxia, or
signaling,
and contract due to high transmural pressure; these factors can also control the
creation of new vessels [60, 73, 77, 45, 44, 82, 71]. One important unsolved problem is
how shunts are prevented [72]: if a low resistance vessel has high flows through it, it
can grow even larger, taking up more current without actually supplying any tissue.
Preventing shunts seems to require some level of upstream communication which is
not well understood.
Other examples of active porous media are insect-built structures. Bees, termites,
and ants (Fig. 0-1(c)) all build elaborate structures to create a microclimate for
the colony [92, 91, 13, 87, 8, 40, 42]. The structures created are remodeled due to
feedback from temperatures, gas concentrations, and airflows [34, 36] (Fig. 0-1(d)).
There are open questions regarding both the physiology of these structures as well as
the behavioral rules that give rise to them.
In other living porous media the animals themselves form the structure [7]. Swarm-
ing honeybees(Fig. 0-1(e)) and bivouacs of ants cluster together in groups of - 104
individuals, maintaining a relatively constant core temperature despite variations in
ambient conditions [11, 32, 31, 20]. In a very different context, some penguins hud-
dle together to reduce heat loss [98, 101], alternating which individuals are at the
center of the huddles. There are interesting questions of how the dynamics of these
assemblages are determined by the relatedness of the individuals that comprised them
[27].
These problems in living porous media exist at the interface between biology and
physics. How matter is transported through the medium is a physical question; how
the medium remodels itself is a biological one. What is required is a full understanding
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Figure 0-1: Some living porous media. a) Network formation in slime molds [89]. b)
Development of vascular networks in chicken embryo [44]. c) Randomly distributed
ant corpse clusters(top), are rearranged into piles aligned with a downwards imposed
airflow(bottom) [36]. e) Endocast showing internal geometry of Odontotermes obesus
mound [80]. e) Thermoregulation of honeybee swarm clusters(top is contracted cluster
on a cool day, bottom is well-ventilated cluster on a warm day) [11]
of the interplay between the physics of transport and the behavior of how the system
remodels itself.
For a better understanding of these systems, we ask several questions:
* How can living porous media exchange matter and energy with their environ-
ment?
" How can a medium adjust to outside conditions to regulate itself?
" What feedback mechanisms can a medium use to regulate transport and con-
ductivity?
My thesis is composed of three parts, which are steps towards answering these
questions.
1. Diurnally driven respiration of termite mounds
2. Collective thermoregulation of honeybee swarm clusters
3. Generic model of an active porous medium
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Diurnally driven respiration of termite mounds
A particularly impressive example of animal architecture is found in termites of the
subfamily Macrotermitinae. Individually only a few mm in body length, they are
well-known for their ability to build massive, complex structures [43, 91] without cen-
tral decision-making authority [95]. The resulting structure includes a subterranean
nest containing brood and symbiotic fungus, and a mound extending - 1 - 2m above
ground, which is primarily entered for construction and repair, but otherwise rela-
tively uninhabited. The mound contains conduits that are many times larger than a
termite [91], and widely viewed as a means to ventilate the nest [91]; the shape of the
mound results from some sort of interplay between building behavior, structure, and
transport.
Understanding the mechanism by which the mound works is important for both
understanding the solution the termites are approaching as well as the feedback pro-
cesses that gives rise to the structure. However, these mechanisms continue to be
debated due to the absence of direct in-situ measurements [93, 41, 42, 50].
In Chapter 1, by directly measuring diurnal variations in flow through the surface
conduits of the mounds of the species Odontotermes obesus, we show that a simple
combination of geometry, heterogeneous thermal mass and porosity allows the mounds
to use diurnal ambient temperature oscillations for ventilation. In particular, the
thin outer flute-like conduits heat up rapidly during the day relative to the deeper
chimneys, pushing air up the flutes and down the chimney in a closed convection
cell, with the converse situation at night. These cyclic flows flush out CO 2 from the
nest and ventilate the mound. We also directly measure and observe similar air flow
patterns inside the mounds of Macrotermes michaelseni, evidence that this is likely
to be a general mechanism among termite mounds.
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Collective thermoregulation of honeybee swarm clus-
ters
Honeybees are masters of cooperative thermoregulation, and indeed need to be able
to do so in multiple contexts. We focus on swarming, an essential part of colony
reproduction, where a fertilized queen and about 2,000 - 20,000 bees cling onto each
other in a swarm cluster, typically hanging on a tree branch, while scouts search
for a new hive location [79]. For up to several days, the swarm cluster regulates its
temperature by forming a dense surface mantle that envelopes a more porous interior
core. Over this period, the cluster adjusts its shape and size to allow the bees to
maintain and regulate the core temperature to within a few degrees of a homeostatic
set point of 35'C over a wide range of ambient conditions.
The swarm cluster is able to perform this thermoregulatory task and modulate
its heat loss without a centralized controller to coordinate behavior, in the absence of
any long-range communication between bees in different parts of the cluster [32, 31].
Instead, the shape and temperature profile of the swarm cluster emerges from the
interplay between heat transfer throughout the cluster and the collective behavior of
thousands of bees [7] which know only their local conditions.
In Chapter 2, we present a model for swarm cluster thermoregulation that results
from the collective behavior of bees acting based on local information, yet propagates
information about ambient temperature throughout the cluster. Our model yields
good thermoregulation and is consistent with experiments at both high and low tem-
peratures, with a cluster radius, temperature profile, and density profile qualitatively
similar to observations, and makes predictions for possible experiments.
Generic model of an active porous medium
Elements across many living and nonliving active porous media are conservation of
current, feedback that changes resistance, and stochasticity. A minimal distillation of
the common elements in these different systems corresponds to a stochastically evolv-
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ing network driven uniformly by fluxes and forces at the
boundary due to pressure,
voltage, or concentration gradients.
In Chapter 3, we consider a minimal model for this feedback coupling in terms
of two parameters that characterize the way in which addition or removal of matter
follows a simple local (or non-local) feedback rule corresponding to either flow-seeking
or flow-avoiding behavior. We show that flow-avoiding feedback causes an initially
uniform system to spontaneously channelize; flow-seeking behavior causes the system
to spontaneously form a network of walls. We can understand this behavior by
constructing a continuum model, and understanding the walling and channelization
behaviors in terms of phase separations.
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