Functions
	meniscus (w, theta_deg, dg, sigma=1.0, n=600)

	meniscus_mean (w, theta_deg, dg, sigma=1.0, xlo=None, xhi=None)

	jurin (w, theta_deg, dg, sigma=1.0)

	max_u (s, zlo=None)

	relax (s, steps, cfl=0.15, dt_cap=None, probe=0, cb=None, ramp=0.02)

	capsule_sdf (nx, ny, nz, xm, r, z0, z1)

	jurin_scene (nx=96, ny=4, nz=112, w=16.0, plate=8.0, zp=(12.0, 100.0))

	jurin_colour (nx, ny, nz, subsdf, zi_of_x, sub=4)

	set_zero_mean_buoyancy (s, dg, ratio, wos=False)

	_channel_columns (sdf, nz)

	level_of (cc, eps, xs)

	g3_static (theta=30.0, steps=500, nx=96, ny=4, nz=112, w=16.0, plate=8.0, dg=3.0e-3, sigma=1.0, mu=0.2, ratio=10.0, datum=28.0, zp=(12.0, 100.0), flat_start=False, wos=False)

	cap_sphere (volume, theta_deg)

	cap_colour (nx, ny, nz, cx, cy, zw, R, theta_deg=90.0)

	g2_spread (theta_e=30.0, slip=0.1, steps=1500, probe=50, nx=64, nz=40, R=12.0, zw=4.25, sigma=1.0, oh=0.1, dynamic=True, wall_slip=False)

	g3_rise (theta_e=30.0, slips=(0.05, 0.3), steps=1500, nx=96, ny=4, nz=112, w=16.0, plate=8.0, dg=3.0e-3, sigma=1.0, mu=0.2, ratio=10.0, datum=28.0, zp=(12.0, 100.0), static_control=True, wall_slip=False, probe=None, lw=False)

	g4_incline (theta_a=70.0, theta_r=50.0, bo_fracs=(0.5, 0.7, 1.5, 2.5), steps=1200, nx=48, nz=32, R=8.0, zw=4.25, sigma=1.0, oh=0.2, slip=0.1)

Variables
int	PRESS_MAXIT = 300

float	DEG = math.pi / 180.0

dict	_MEN_CACHE = {}

list	args = [a for a in sys.argv[1:] if not a.startswith("--")]

str	quick = "--quick" in sys.argv

list	which = args or ["jurin"]

	theta

	steps

	flat_start

	wos

	probe

list	res = []

	sp

	wt

	am

	slip

	sl

list	d_meas = res[i][1] - res[i - 1][1]

float	d_pred = 9.0 * math.log(res[i - 1][0] / res[i][0])

	wall_slip

	slips

	lw

	False

	static_control

	True

Detailed Description

WO-V6 (rung V6) — the DYNAMIC contact angle and hysteresis: the gate battery, in Python.

Every gate prints its numbers; nothing is summarised into an adjective. The MODEL (state it with
every result, VOF_PLAN section 6):

    theta_Delta^3 = theta_e^3 + 9 Ca_cl ln(Delta/lambda),   Ca_cl = mu_l U_cl / sigma

Afkhami, Zaleski & Bussmann, JCP 228:5370 (2009). `lambda` is an EXPLICIT slip length in cells and
is never omitted from a reported number: a VoF contact line's numerical slip is proportional to the
cell size, so without it the imposed angle is silently grid-dependent.

  jurin   G3-static. CAPILLARY RISE, STATIC. Two 8-cell plates with ROUNDED ends (a capsule SDF, so
          there is no sharp 90-degree corner where |grad sdf| != 1) at QUARTER-integer placement,
          bounding a gap `w`; the periodic outer channel is a second capillary of width `w_out`.
          Both menisci rise, so the reference is the LEVEL DIFFERENCE. Jurin's
          `2 sigma cos(theta)/(drho g) (1/w - 1/w_out)` is the Bond -> 0 asymptote and is NOT the
          right reference at the Bond numbers a finite box affords; the exact reference is the
          static meniscus ODE `sigma z''/(1+z'^2)^{3/2} = drho g (z - z_ref)` with `z'(w/2) =
          cot(theta)`, solved here by shooting. Both are printed.

  spread  G2. SPREADING DROP vs Cox-Voinov. A drop released as a hemisphere on a wall with
          `theta_e = 30`: the contact radius a(t) and the apparent angle theta_app(t) are measured
          from the shape, `Ca_cl = mu (da/dt)/sigma` from the contact line's own motion, and
          `theta_app^3 - theta_e^3` is fitted against `Ca_cl`. The composition property of
          Cox-Voinov says the slope is `9 ln(a/lambda)`: the fill supplies `9 ln(Delta/lambda)` and
          the resolved hydrodynamics supply `9 ln(a/Delta)`. Tanner's `a ~ t^(1/10)` at late times
          is reported alongside.

  rise    G3-dynamics. The same plate scene from a FLAT interface, with the dynamic angle, over a
          slip sweep: the rise curve h(t), the final height against the static equilibrium, and the
          damping class (asymptotic vs oscillatory) — the two regimes Gruending et al. (AMM 86:142,
          2020) separate.

  incline G4. HYSTERESIS: a drop on a tilted wall (the wall is kept axis-aligned and GRAVITY is
          tilted, which is the same problem and keeps the SDF exact). Below the critical Bond
          number `Bo_c = cos(theta_r) - cos(theta_a)` the contact line must stay PINNED; above it
          the drop slides with the front near theta_a and the rear near theta_r.

Usage:
    PYTHONPATH=$PWD/build_cuda python tests/study/vof_wetting_dynamic.py [jurin spread rise incline]
    ... --quick        shorter runs

Function Documentation

◆ meniscus()

vof_wetting_dynamic.meniscus	(	w,
		theta_deg,
		dg,
		sigma = `1.0`,
		n = `600`
	)

The exact 2-D static meniscus in a slot of width `w` with contact angle `theta` on both
walls, in gravity `dg = drho*g`:

    sigma z''/(1 + z'^2)^{3/2} = dg (z - z_ref),    z'(0) = 0,   z'(w/2) = cot(theta)

measured from the flat far-field datum `z_ref = 0`. Shooting on z(0) (monotone: a higher
meniscus has a steeper wall slope). Returns (x, z) on [0, w/2] — the profile is symmetric.
Reduces to Jurin `z = 2 sigma cos(theta)/(dg w)` as Bond -> 0.

Definition at line 59 of file vof_wetting_dynamic.py.

References jurin().

Referenced by g3_static(), and meniscus_mean().

◆ meniscus_mean()

vof_wetting_dynamic.meniscus_mean	(	w,
		theta_deg,
		dg,
		sigma = `1.0`,
		xlo = `None`,
		xhi = `None`
	)

The MEAN interface height over x in [xlo, xhi] (default the whole slot, x measured from the
LEFT wall) — the quantity the colour-integral level read-out measures.

Definition at line 112 of file vof_wetting_dynamic.py.

References meniscus().

Referenced by g3_static().

◆ jurin()

vof_wetting_dynamic.jurin	(	w,
		theta_deg,
		dg,
		sigma = `1.0`
	)

Definition at line 126 of file vof_wetting_dynamic.py.

Referenced by g3_rise(), g3_static(), and meniscus().

◆ max_u()

vof_wetting_dynamic.max_u	(	s,
		zlo = `None`
	)

Definition at line 131 of file vof_wetting_dynamic.py.

Referenced by relax().

◆ relax()

vof_wetting_dynamic.relax	(	s,
		steps,
		cfl = `0.15`,
		dt_cap = `None`,
		probe = `0`,
		cb = `None`,
		ramp = `0.02`
	)

`ramp`: the first step is taken at `ramp * dt_cap`, because the interface-local Courant
number is read BEFORE the step and is 0 at rest — a full first step on a scene with a strong
initial capillary imbalance overshoots the Weymouth-Yue cap and the advector (correctly) throws.

Definition at line 139 of file vof_wetting_dynamic.py.

References max_u().

Referenced by g3_rise(), g3_static(), and g4_incline().

◆ capsule_sdf()

vof_wetting_dynamic.capsule_sdf	(	nx,
		ny,
		nz,
		xm,
		r,
		z0,
		z1
	)

A plate of thickness 2r centred on x = xm, spanning z in [z0, z1] with SEMICIRCULAR ends:
the distance to the segment (xm, z0+r) -> (xm, z1-r) minus r. Flat vertical faces at xm +/- r,
no sharp corner anywhere (|grad sdf| = 1 everywhere outside the axis).

Definition at line 170 of file vof_wetting_dynamic.py.

Referenced by jurin_scene().

◆ jurin_scene()

vof_wetting_dynamic.jurin_scene	(	nx = `96`,
		ny = `4`,
		nz = `112`,
		w = `16.0`,
		plate = `8.0`,
		zp = `(12.0, 100.0)`
	)

The two rounded plates. Returns (sdf, xm_gap, xm_outer, w_out, subsdf); the plate FACES sit
at quarter-integer x (WO-S finding 5: at a half-integer the wall cell's tangential MAC faces sit
on the SDF zero level and close, and the contact line cannot move). `subsdf(x, z)` is the same
SDF as a callable, for sub-cell sampling of the initial colour.

Definition at line 182 of file vof_wetting_dynamic.py.

References capsule_sdf().

Referenced by g3_rise(), and g3_static().

◆ jurin_colour()

vof_wetting_dynamic.jurin_colour	(	nx,
		ny,
		nz,
		subsdf,
		zi_of_x,
		sub = `4`
	)

C = liquid fraction of the FLUID volume of each cell (VOF_PLAN rule 2), for an interface
z = zi(x). The FLUID restriction is not cosmetic: a sub-cell of a cut wall column that is
sampled as if it were fluid drops that column's C to `eps`, and a C of 0.75 in the middle of
the liquid is a FAKE INTERFACE that the V3 cascade turns into |kappa| ~ 3e6 (measured).

Definition at line 203 of file vof_wetting_dynamic.py.

Referenced by g3_rise(), and g3_static().

◆ set_zero_mean_buoyancy()

vof_wetting_dynamic.set_zero_mean_buoyancy	(	s,
		dg,
		ratio,
		wos = `False`
	)

`force_z = g (rho_bar - rho)` with `g = dg/(rho_l - rho_g)`: the buoyancy that produces the
prescribed `drho g` AND has zero volume mean.

THIS IS THE FIX THAT MAKES THE JURIN SCENE WORK, and the defect it removes is what WO-S's G4
measured. The obvious "zero in the gas, -dg in the liquid" form (`[dg/(ratio-1), -dg/(1-1/ratio)]`,
which is what WO-S used) has a NON-ZERO volume mean, and in a fully periodic box a non-zero-mean
body force accelerates the whole fluid without bound (WO-Q finding 9). Worse than a drift: the
accelerating frame contributes its own `-rho a` body force, i.e. it CANCELS PART OF GRAVITY, so
the menisci relax towards a smaller level difference the longer the run goes — exactly the -83 %
WO-S recorded, with the accompanying non-decaying `max|u|`.

Definition at line 218 of file vof_wetting_dynamic.py.

Referenced by g3_rise(), and g3_static().

◆ _channel_columns()

vof_wetting_dynamic._channel_columns	(	sdf,
		nz
	)

protected

The fluid columns of the gap and of the periodic outer channel, as index arrays. EVERY fluid
column is included, cut ones too: the level read-out is eps-weighted, so the full-width mean is
what the exact identity below refers to.

Definition at line 244 of file vof_wetting_dynamic.py.

Referenced by g3_rise(), and g3_static().

◆ level_of()

vof_wetting_dynamic.level_of	(	cc,
		eps,
		xs
	)

Definition at line 259 of file vof_wetting_dynamic.py.

Referenced by g3_rise(), and g3_static().

◆ g3_static()

vof_wetting_dynamic.g3_static	(	theta = `30.0`,
		steps = `500`,
		nx = `96`,
		ny = `4`,
		nz = `112`,
		w = `16.0`,
		plate = `8.0`,
		dg = `3.0e-3`,
		sigma = `1.0`,
		mu = `0.2`,
		ratio = `10.0`,
		datum = `28.0`,
		zp = `(12.0, 100.0)`,
		flat_start = `False`,
		wos = `False`
	)

Definition at line 265 of file vof_wetting_dynamic.py.

References _channel_columns(), jurin(), jurin_colour(), jurin_scene(), level_of(), meniscus(), meniscus_mean(), relax(), and set_zero_mean_buoyancy().

◆ cap_sphere()

vof_wetting_dynamic.cap_sphere	(	volume,
		theta_deg
	)

Definition at line 333 of file vof_wetting_dynamic.py.

Referenced by cap_colour().

◆ cap_colour()

vof_wetting_dynamic.cap_colour	(	nx,
		ny,
		nz,
		cx,
		cy,
		zw,
		R,
		theta_deg = `90.0`
	)

Definition at line 339 of file vof_wetting_dynamic.py.

References cap_sphere().

Referenced by g2_spread(), and g4_incline().

◆ g2_spread()

vof_wetting_dynamic.g2_spread	(	theta_e = `30.0`,
		slip = `0.1`,
		steps = `1500`,
		probe = `50`,
		nx = `64`,
		nz = `40`,
		R = `12.0`,
		zw = `4.25`,
		sigma = `1.0`,
		oh = `0.1`,
		dynamic = `True`,
		wall_slip = `False`
	)

Definition at line 352 of file vof_wetting_dynamic.py.

References cap_colour().

◆ g3_rise()

vof_wetting_dynamic.g3_rise	(	theta_e = `30.0`,
		slips = `(0.05, 0.3)`,
		steps = `1500`,
		nx = `96`,
		ny = `4`,
		nz = `112`,
		w = `16.0`,
		plate = `8.0`,
		dg = `3.0e-3`,
		sigma = `1.0`,
		mu = `0.2`,
		ratio = `10.0`,
		datum = `28.0`,
		zp = `(12.0, 100.0)`,
		static_control = `True`,
		wall_slip = `False`,
		probe = `None`,
		lw = `False`
	)

G3-dynamics: the same plate scene from a FLAT interface, so the contact line has to travel.
The static equilibrium level difference is Jurin's, EXACTLY (see g3_static), so the gate is the
final height against it; the damping class (asymptotic vs oscillatory) is the second half of
the Gruending et al. (AMM 86:142, 2020) comparison.

Definition at line 448 of file vof_wetting_dynamic.py.

References _channel_columns(), jurin(), jurin_colour(), jurin_scene(), level_of(), relax(), and set_zero_mean_buoyancy().

◆ g4_incline()

vof_wetting_dynamic.g4_incline	(	theta_a = `70.0`,
		theta_r = `50.0`,
		bo_fracs = `(0.5, 0.7, 1.5, 2.5)`,
		steps = `1200`,
		nx = `48`,
		nz = `32`,
		R = `8.0`,
		zw = `4.25`,
		sigma = `1.0`,
		oh = `0.2`,
		slip = `0.1`
	)

The wall is kept axis-aligned and GRAVITY is tilted — the same problem, an exact SDF.
Bo = drho g V^(2/3) sin(alpha) / sigma against Bo_c = cos(theta_r) - cos(theta_a)
(ElSherbini & Jacobi 2006's retention relation in its simplest form).

Definition at line 527 of file vof_wetting_dynamic.py.

References cap_colour(), and relax().

Variable Documentation

◆ PRESS_MAXIT

int vof_wetting_dynamic.PRESS_MAXIT = 300

Definition at line 51 of file vof_wetting_dynamic.py.

◆ DEG

float vof_wetting_dynamic.DEG = math.pi / 180.0

Definition at line 52 of file vof_wetting_dynamic.py.

◆ _MEN_CACHE

dict vof_wetting_dynamic._MEN_CACHE = {}

protected

Definition at line 56 of file vof_wetting_dynamic.py.

◆ args

list vof_wetting_dynamic.args = [a for a in sys.argv[1:] if not a.startswith("--")]

Definition at line 584 of file vof_wetting_dynamic.py.

◆ quick

str vof_wetting_dynamic.quick = "--quick" in sys.argv

Definition at line 585 of file vof_wetting_dynamic.py.

◆ which

list vof_wetting_dynamic.which = args or ["jurin"]

Definition at line 586 of file vof_wetting_dynamic.py.

◆ theta

vof_wetting_dynamic.theta

Definition at line 588 of file vof_wetting_dynamic.py.

◆ steps

vof_wetting_dynamic.steps

Definition at line 588 of file vof_wetting_dynamic.py.

◆ flat_start

vof_wetting_dynamic.flat_start

Definition at line 591 of file vof_wetting_dynamic.py.

◆ wos

vof_wetting_dynamic.wos

Definition at line 593 of file vof_wetting_dynamic.py.

◆ probe

vof_wetting_dynamic.probe

Definition at line 595 of file vof_wetting_dynamic.py.

◆ res

list vof_wetting_dynamic.res = []

Definition at line 601 of file vof_wetting_dynamic.py.

◆ sp

vof_wetting_dynamic.sp

Definition at line 603 of file vof_wetting_dynamic.py.

◆ wt

vof_wetting_dynamic.wt

Definition at line 603 of file vof_wetting_dynamic.py.

◆ am

vof_wetting_dynamic.am

Definition at line 603 of file vof_wetting_dynamic.py.

◆ slip

vof_wetting_dynamic.slip

Definition at line 603 of file vof_wetting_dynamic.py.

◆ sl

vof_wetting_dynamic.sl

Definition at line 603 of file vof_wetting_dynamic.py.

◆ d_meas

list vof_wetting_dynamic.d_meas = res[i][1] - res[i - 1][1]

Definition at line 609 of file vof_wetting_dynamic.py.

◆ d_pred

float vof_wetting_dynamic.d_pred = 9.0 * math.log(res[i - 1][0] / res[i][0])

Definition at line 610 of file vof_wetting_dynamic.py.

◆ wall_slip

vof_wetting_dynamic.wall_slip

Definition at line 621 of file vof_wetting_dynamic.py.

◆ slips

vof_wetting_dynamic.slips

Definition at line 634 of file vof_wetting_dynamic.py.

◆ lw

vof_wetting_dynamic.lw

Definition at line 634 of file vof_wetting_dynamic.py.

◆ False

vof_wetting_dynamic.False

Definition at line 635 of file vof_wetting_dynamic.py.

◆ static_control

vof_wetting_dynamic.static_control

Definition at line 635 of file vof_wetting_dynamic.py.

◆ True

vof_wetting_dynamic.True

Definition at line 637 of file vof_wetting_dynamic.py.

Functions

Variables

Detailed Description

Function Documentation

◆ meniscus()

◆ meniscus_mean()

◆ jurin()

◆ max_u()

◆ relax()

◆ capsule_sdf()

◆ jurin_scene()

◆ jurin_colour()

◆ set_zero_mean_buoyancy()

◆ _channel_columns()

◆ level_of()

◆ g3_static()

◆ cap_sphere()

◆ cap_colour()

◆ g2_spread()

◆ g3_rise()

◆ g4_incline()

Variable Documentation

◆ PRESS_MAXIT

◆ DEG

◆ _MEN_CACHE

◆ args

◆ quick

◆ which

◆ theta

◆ steps

◆ flat_start

◆ wos

◆ probe

◆ res

◆ sp

◆ wt

◆ am

◆ slip

◆ sl

◆ d_meas

◆ d_pred

◆ wall_slip

◆ slips

◆ lw

◆ False

◆ static_control

◆ True