البحوث المنشورة
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البحث (1):
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عنوان البحث:
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A Rivulet
Of A Power-Law Fluid With Constant Contact Angle Draining Down A Slowly
Varying Substrate
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رابط إلى البحث:
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Click here
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تاريخ النشر:
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May 2015
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موجز عن البحث:
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Locally
unidirectional steady gravity-driven flow of a thin rivulet of a power-law
fluid with prescribed volume flux down a locally planar substrate is
considered. First, the solution for unidirectional flow of a uniform rivulet
down a planar substrate is obtained, and then it is used to obtain the
solution for a slowly varying rivulet with prescribed constant (nonzero)
contact angle down a slowly varying substrate, specifically flow in the
azimuthal direction around the outside of a large horizontal circular cylinder.
The solution is shown to depend strongly on the value of the power-law index
of the fluid. For example, a rivulet of strongly shear-thinning fluid
“self-channels” its flow down a narrow central channel between two “levées”
of slowly moving fluid that form at its sides, and in the central channel
there is a “plug-like” flow except in a boundary layer near the substrate. On
the other hand, in a rivulet of a strongly shear-thickening fluid the
velocity profile is linear except in a boundary layer near the free surface.
Another notable qualitative departure from Newtonian behaviour is that,
whereas the mass of a rivulet of a Newtonian or a shear-thinning fluid is
theoretically infinite, the mass of a rivulet of a shear-thickening fluid is
finite.
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البحث (2):
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عنوان البحث:
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A Rivulet Of A
Power-Law Fluid With Constant Width Draining Down A Slowly Varying Substrate
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رابط إلى البحث:
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Click
here
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تاريخ النشر:
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13 August 2015
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موجز عن البحث:
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The flow of a
slowly varying rivulet of a power-law fluid with prescribed constant width
(i.e. with pinned contact lines) but slowly varying contact angle down a
slowly varying substrate, specifically the flow in the azimuthal direction
around the outside of a large horizontal circular cylinder, is described. The
solution for a rivulet of a perfectly wetting fluid (which can never have
constant width) is obtained, and it is shown that, despite having the same
local behaviour, the global behaviour of a rivulet of a non-perfectly wetting
fluid is qualitatively different from that of a rivulet with prescribed
constant contact angle but slowly varying width. Specifically, it is
described how the contact lines of a sufficiently narrow rivulet can remain
pinned as it drains all the way from the top to the bottom of the cylinder,
but how the contact lines of a wider rivulet de-pin at a critical position on
the lower half of the cylinder, and how thereafter it drains to the bottom of
the cylinder with zero contact angle and slowly varying width. How the shape
of the rivulet and the velocity within it depend on the power-law index N is
described in detail. In particular, it is shown that whereas neither the
shape of the rivulet nor the velocity within it vary monotonically with N,
its mass always decreases monotonically with N. Despite the limitations of
the power-law model, the present results provide rare analytical insight into
non-Newtonian rivulet flow, and, in particular, are a useful benchmark for
the study of rivulet flow of more realistic non-Newtonian fluids.
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المؤتمرات العلمية:
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المؤتمر (1):
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عنوان المؤتمر:
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THE
11TH EUROPEAN COATING SYMPOSIUM
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تاريخ الإنعقاد:
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09-11 September 2015
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مكان الإنعقاد:
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Eindhoven,
The Netherlands
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طبيعة المشاركة:
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Oral Presentation
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عنوان المشاركة:
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Rivulet
Flow Of A Power-Law Fluid Down A Slowly Varying Substrate
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ملخص المشاركة:
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The
gravity-driven draining of a rivulet of viscous fluid occurs in a wide
variety of practical and industrial applications, such as geophysical flow of
ice, lava and mud, and rain–wind–induced vibrations of cable-stayed bridges.
As a result, there has been a significant number of theoretical studies of
rivulet flow of a Newtonian fluid; however, despite the widespread occurrence
of non-Newtonian rheology in a wide range of practical contexts, there has
been relatively little theoretical work on rivulet flow of non-Newtonian
fluids. We consider the locally unidirectional steady gravity-driven flow of
a thin rivulet of a power-law fluid with prescribed volume flux down a
locally planar substrate. First, the solution for unidirectional flow of a
parallel-sided rivulet down a planar substrate is obtained, and then it is
used to obtain the solution for a slowly-varying rivulet with prescribed
constant (nonzero) contact angle flowing down a slowly varying substrate,
specifically flow in the azimuthal direction round the outside of a large
horizontal circular cylinder. The solution is shown to depend strongly on the
value of the power-law index of the fluid. For example, a rivulet of strongly
shear-thinning fluid “self-channels” its flow down a narrow central channel
between two “lev´ees” of slowly moving fluid that form at its sides. In
contrast, in a rivulet of a strongly shear-thickening fluid the velocity
profile is linear except in boundary layer near the free surface.We also
discuss briefly the corresponding flow of a rivulet with prescribed constant
width (i.e. pinned contact lines) but slowly varying contact angle. The flow
in this case is qualitatively different from that of a rivulet with constant
contact angle.
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المؤتمر (2):
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عنوان المؤتمر:
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THE 21ST
SIAM UKIE ANNUAL MEETING
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تاريخ الإنعقاد:
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12 January 2017
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مكان الإنعقاد:
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Glasgow, UK
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طبيعة المشاركة:
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Poster
Presentation
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عنوان المشاركة:
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Non-Newtonian
Rivulet Flow
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ملخص المشاركة:
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Gravity-driven
flow of a thin uniform rivulet of a generalised Newtonian fluid down a
vertical planar substrate is considered. We derive the parametric solution
for any generalized Newtonian fluid whose viscosity is specified as a
function of the shear rate, and the explicit solution for any generalised
Newtonian fluid whose viscosity is specified as a function of the shear
stress. We use these solutions to describe rivulet flow of a Carreau fluid
and of an Ellis fluid, highlighting the similarities and differences between
the behaviour of these two fluids.
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المؤتمر (3):
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عنوان المؤتمر:
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BRITISH
APPLIED MATHEMATICS COLLOQUIUM 2017
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تاريخ الإنعقاد:
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10-12 April 2017
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مكان الإنعقاد:
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Surrey, UK
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طبيعة المشاركة:
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Oral
Presentation
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عنوان المشاركة:
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Non-Newtonian
Effects And Taylor Dispersion In Rivulet Flow
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ملخص المشاركة:
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The
previous work by Al Mukahal et al. concerning rivulet flow of a power-law
fluid provided a rare analytical benchmark for the study of rivulet flow of
non-Newtonian fluids; however, it is of limited applicability to the flow of
more realistic non-Newtonian fluids. In this talk we consider steady
gravity-driven flow of a thin uniform rivulet of a generalised Newtonian
fluid down a vertical planar substrate. We derive the parametric solution for
any generalized Newtonian fluid whose viscosity is specified as a function of the shear rate
(including, in particular, the solution for a Carreau fluid), and the
explicit solution for any generalised Newtonian fluid whose viscosity is
specified as a function of the shear stress (including, in particular, the
solution for an Ellis fluid). These solutions are used to describe rivulet
flow of a Carreau fluid and of an Ellis fluid, highlighting the similarities
and differences between the behaviour of these two fluids. In particular, a
rivulet of a strongly shear-thinning Ellis fluid can comprise two regions
with different viscosities, with the velocity having a plug-like profile with
large magnitude in a narrow central region of the rivulet. While Taylor
dispersion has been studied extensively for pipe and channels flows of
various cross-sections, much less attention has been paid to transport in
rivulet flow.
Thus
in this talk we also investigate both the short-time advection and the
long-time dispersion of a passive solute in steady flow of a rivulet of a
Newtonian fluid and subject to a uniform shear stress on its free surface down
a vertical planar substrate. In particular, we derive the dispersion
coefficient of the solute as a function of the shear stress.
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المؤتمر (4):
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عنوان المؤتمر:
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28th Scottish Fluid Mechanics Meeting
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تاريخ الإنعقاد:
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28/05/2015
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مكان الإنعقاد:
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Glasgow, Scotland
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طبيعة المشاركة:
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Oral presentation
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عنوان المشاركة:
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A rivulet of a power-law fluid
draining down a slowly varying substrate
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ملخص المشاركة:
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The gravity-driven draining of a rivulet of viscous
fluid occurs in a wide variety of practical and industrial applications, such
as geophysical flow of ice, lava and mud, and rain–wind–induced vibrations of
cable-stayed bridges. As a result, there has been a significant number of
theoretical studies of rivulet flow of a Newtonian fluid; however, despite
the widespread occurrence of non-Newtonian rheology in a wide range of
practical contexts, there has been relatively little theoretical work on rivulet
flow of non-Newtonian fluids. We consider the locally unidirectional steady
gravity-driven flow of a thin rivulet of a power-law fluid with prescribed
volume flux down a locally planar substrate. First, the solution for
unidirectional flow of a parallel-sided rivulet down a planar substrate is
obtained, and then it is used to obtain the solution for a slowly-varying
rivulet with prescribed constant (nonzero) contact angle flowing down a
slowly varying substrate, specifically flow in the azimuthal direction round
the outside of a large horizontal circular cylinder. The solution is shown to
depend strongly on the value of the power-law index of the fluid. For
example, a rivulet of strongly shear-thinning fluid “self-channels” its flow
down a narrow central channel between two “lev´ees” of slowly moving fluid
that form at its sides. In contrast, in a rivulet of a strongly
shear-thickening fluid the velocity profile is linear except in boundary
layer near the free surface.We also discuss briefly the corresponding flow of
a rivulet with prescribed constant width (i.e. pinned contact lines) but
slowly varying contact angle. The flow in this case is qualitatively
different from that of a rivulet with constant contact angle.
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المؤتمر (5):
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عنوان المؤتمر:
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30th Scottish Fluid Mechanics meeting
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تاريخ الإنعقاد:
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19/05/2017
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مكان الإنعقاد:
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Glasgow, Scotland
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طبيعة المشاركة:
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Poster presentation
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عنوان المشاركة:
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Non-Newtonian effects and Taylor dispersion in rivulet
flow
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ملخص المشاركة:
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We consider steady
gravity-driven flow of a thin uniform rivulet of a generalised Newtonian
fluid down a vertical planar substrate. We derive the parametric solution for
any generalized Newtonian fluid whose viscosity is specified as a function of
the shear rate (including, in particular, the solution for a Carreau fluid),
and the explicit solution for any generalised Newtonian fluid whose viscosity
is specified as a function of the shear stress (including, in particular, the
solution for an Ellis fluid). These solutions are used to describe rivulet
flow of a Carreau fluid and of an Ellis fluid, highlighting the similarities
and differences between the behaviour of these two fluids. In particular, the surprisingly complicated
behaviour of strongly shear-thinning Carreau and Ellis fluids is described.
In particular, a rivulet of a strongly shear-thinning Ellis fluid can
comprise two regions with different viscosities, with the velocity having a
plug-like profile with large magnitude in a narrow central region of the
rivulet. While Taylor dispersion has been studied extensively for pipe and
channels flow of various cross-sectional shapes, much less attention has been
paid to transport in rivulet flow. We investigate both the short-time
advection and the long-time Taylor dispersion of a passive solute in steady
unidirectional flow of a thin rivulet of a Newtonian fluid down a vertical
planar substrate and subject to a uniform shear stress on its free surface.
In particular, we derive the enhanced dispersion coefficient of the solute as
a function of the shear stress.
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المؤتمر (6):
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عنوان المؤتمر:
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Flow 17
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تاريخ الإنعقاد:
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3-5/07/2017
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مكان الإنعقاد:
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Paris, France
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طبيعة المشاركة:
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Poster presentation
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عنوان المشاركة:
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Non-Newtonian effects and Taylor dispersion in rivulet
flow
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ملخص المشاركة:
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Rivulet flows arise in a wide variety of practical
contexts, including industrial coating, heat exchangers and various
biological contexts, as well as in microfluidics. For example, recently
Herrada et al. [1] proposed a technique for producing microbubbles with a
controlled size from the breakup of a rivulet in a microfluidic channel. More
generally, the wide variety of contexts in which they occur has led to a
considerable body of theoretical and experimental work on rivulet flow.
Inevitably most of the previous theoretical work has been focused on the flow
of a Newtonian fluid, and, despite the importance of non-Newtonian rheologies
in many practical contexts, there has been comparatively little work on the
flow of non-Newtonian fluids. An exception is our recent work on rivulet flow
of a power-law fluid [2,3]; however, it is of limited applicability to the
flow of more realistic non-Newtonian fluids. Thus in the present talk we
analyse rivulet flow of generalised Newtonian fluids. Specifically, we
consider steady gravity-driven flow of a thin uniform rivulet of a
generalised Newtonian fluid down a vertical planar substrate. We derive the
parametric solution for any
generalized Newtonian fluid whose viscosity is specified as a function
of the shear rate (including, in particular, the solution for a Carreau
fluid), and the explicit solution for any generalised Newtonian fluid whose
viscosity is specified as a function of the shear stress (including, in
particular, the solution for an Ellis fluid). These solutions are used to
describe rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting
the similarities and differences between the behaviour of these two fluids. In particular, the surprisingly complicated
behaviour of strongly shear-thinning Carreau and Ellis fluids is described.
We also demonstrate that the non-monotonic variation of the viscosity of an
Ellis fluid with the parameter that measures the degree of shear thinning
leads to a more complicated dependence of the behaviour of the rivulet on
this parameter than on the other parameters in the Carreau and Ellis models.
In particular, a rivulet of a strongly shear-thinning Ellis fluid can
comprise two regions with different viscosities, with the velocity having a
plug-like profile with large magnitude in a narrow central region of the
rivulet. While Taylor dispersion [4] in flow down pipe and channels with many
different cross-sectional shapes has been studied extensively for many years,
much less attention has been paid to transport in rivulet flow. Thus in this
talk we also investigate both the short-time advection and the long-time
dispersion of a passive solute in a thin rivulet of a Newtonian fluid subject
to a uniform shear stress on its free surface flowing down a vertical planar
substrate. In particular, we derive the enhanced dispersion coefficient of
the solute as a function of the shear stress.
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المؤتمر (7):
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عنوان المؤتمر:
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British Society of Rheology Winter Meeting 2015:
Microrheology and Microfluidics
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تاريخ الإنعقاد:
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14-15/12/2015
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مكان الإنعقاد:
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Glasgow, Scotland
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طبيعة المشاركة:
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Poster presentation
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عنوان المشاركة:
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Non-Newtonian Rivulet Flow
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ملخص المشاركة:
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Rivulet flows occur in a
variety of practical and industrial applications including, for example,
industry, biology and nature, and have been the subject of enduring
theoretical and experimental interest. In particular, there have been a
considerable number of theoretical studies of rivulet flow of a Newtonian
fluid; however, despite the widespread occurrence of non-Newtonian rheology
in many of the practical occurrences of rivulet flow, there has been
comparatively little theoretical work on rivulet flow of non-Newtonian
fluids.
In the present work, the
solution for the steady gravity-driven flow of a thin rivulet of a power-law
fluid with prescribed volume flux down a planar substrate is obtained, and
then used as a local solution to describe the flow of a slowly varying
rivulet of a power-law fluid with prescribed constant (nonzero) contact angle
but slowly varying width down a slowly varying substrate, specifically the
flow in the azimuthal direction round the outside of a large horizontal
cylinder. We demonstrate how the features of the solution are strongly
influenced by the shear-dependence of the viscosity. For example, rivulet
flow of a strongly shear-thinning fluid ”self-channels” down a narrow
central channel between two ”levées” of slowly moving fluid that form at
the sides of the rivulet, and in the central channel there is a ”plug-like”
flow except in a boundary layer near the substrate. On the other hand, in
rivulet flow of a strongly shear-thickening fluid the velocity profile is
linear except in a boundary layer near the free surface.
We also demonstrate how the
local solution (together with the corresponding local solution for a rivulet
of a perfectly wetting fluid) can also be used to describe the flow of a
slowly varying rivulet of a power-law fluid with prescribed constant
(nonzero) width (i.e. pinned contact lines) but slowly varying contact angle
down a slowly varying substrate. In particular, the global behavior of the
rivulet is shown to be qualitatively very different from that of a rivulet
with prescribed contact angle described above. Specifically, the contact
lines of a sufficiently narrow rivulet can remain pinned as it drains all the
way from the top to the bottom of the cylinder, but the contact lines of a
wider rivulet de-pin at a critical position on the lower half of the
cylinder, and thereafter it drains to the bottom of the cylinder with zero
contact angle and slowly varying semi-width. Further details of both constant
contact angle and contact width rivulets are given by Al Mukahal et al.
[1,2].
While the results described
above provide a rare analytical benchmark for the study of rivulet flow of a
power-law fluid, they are of limited applicability to the flow of more
realistic non-Newtonian fluids. Thus, we also consider the steady
unidirectional flow of a rivulet of a generalized Newtonian fluid on a
vertical substrate. Specifically, we derive the general solutions for
generalized Newtonian fluids whose viscosity is specified as a function of
either the local shear rate or the local extra stress. The features of
rivulet flow are then described for fluids of both types, namely for a
Carreau fluid and for a (generalized) Ellis fluid. In particular, the
surprisingly complicated behavior of a strongly shear-thinning Ellis fluid is
described.
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