18 Questions
What challenge arises in the mathematical formulation of multiphase flows when inter-facial surfaces are present?
Difficulty in formulating differential balances for the set of sub-regions
How can a multiphase flow be conceptually considered to overcome the challenge of differential balances?
As a field of sub-regions of single phase flow with moving and varying boundary conditions
What is the goal of employing proper averaging in a multiphase flow model?
To obtain mean values of fluid motions and eliminate local instantaneous fluctuations
What are the difficulties arising in a multiphase flow model due to large discontinuities of properties across an interface?
- Large discontinuities of properties 2. Multiple moving interfaces 3. Fluctuations of variables
Why does the differential balance not hold for the set of sub-regions in a multiphase flow?
It would violate the law of continuity
How is the unifying approach towards a multiphase flow model achieved?
By describing the local properties of the flow and obtaining macroscopic properties through averaging
What are the coefficients CD, CM, CH, CLR, and CLS in the BBO equation?
drag, virtual-mass, history, rotation-induced, and shear-induced lift coefficients
What happens to the coefficients CD, CM, CH, CLR, and CLS in the creeping flow regime when the particle is spherical?
They converge to 1 as the Reynolds number approaches 0.
What is the reduced form of the BBO equation (2.120) when the particle phase is much denser than the fluid phase?
dUp/CDRep = g + uf - Updt/(24τp)
In the MRG equation, what terms are included in the similar extension as in the BBO equation?
all relevant terms
How can the velocity field previously defined in Eqs.(2.10a) and (2.10b) be verified to satisfy mass conservation?
Irrespective of how ψ(r, θ) is expressed.
What does the Stokes streamfunction ψ(r, θ) represent in the context of the velocity field defined in Eqs.(2.10a) and (2.10b)?
The streamfunction in the velocity field.
Who proposed the drag coefficient for a rigid sphere as derived by van Dyke?
van Dyke
What is the form of van Dyke's drag coefficient for a rigid sphere?
CD = 24 Rep (Reo / (Reo + Rep))^23
What limitation is pointed out in PPKL's correction to Oseen's work?
The linearization of the advective term is not valid in the boundary layer of the sphere.
Who considered the matched asymptotic expansion of the full Navier-Stokes equations to derive a uniformly valid solution close to a sphere?
PPKL and Oseen
In the drag coefficient equation by Goldstein, what term involves Re2?
24 Rep
What transformation did van Dyke use to propose a drag coefficient that converges to infinity?
Euler transformation
Explore the challenges faced in continuum mechanics when dealing with multiphase flows, particularly in formulating differential balances for field properties. Learn how inter-facial surfaces impact the mathematical representation of the problem.
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