Viscoelastic free surface flows: spin coating and dynamic contact lines

Spaid, Michael; Homsy, G. M.

doi:10.1016/0377-0257(94)80073-1

Cited by 27 publications

(24 citation statements)

References 16 publications

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“…The velocity is taken to diminish from one at x = 0, but vanishes for x¿10. These conditions also satisfy Equations (15). As will be discussed below, the in uence of the initial conditions on the ensuing ow can be signiÿcant.…”

Section: Discussion and Resultsmentioning

confidence: 93%

“…; U i¿1 (x = 0; t) = 0 (15) where h(x = 0) = 0 is used. The initial conditions may generally be written as…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Note that Á 0 (0) = 1 and U 0 (0) = 8= (8 + 5 ). The solution of system (13) and (14), subject to conditions (15) and (16), is obtained by using an implicit forward ÿnite di erence scheme in time, combined with a sixth-order Runge-Kutta integration in space. It is particularly convenient in this case to treat Á x explicitly in Equation (14).…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Later, Stillwagon and Larson considered the levelling of thin ÿlms over uneven substrates during spin coating [32]. This problem was also considered by Spaid and Homsy for an Oldroyd-B uid [15]. More recently, Ruschak and Weinstein examined the gravitydriven ow of a thin ÿlm over a round-crested weir [33].…”

Section: Introductionmentioning

confidence: 96%

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Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

Khayat

Kim

Delosquer

2004

Numerical Methods in Fluids

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SUMMARYThis study examines theoretically the development of early transients for axisymmetric ow of a thin ÿlm over a stationary cylindrical substrate of arbitrary shape. The uid is assumed to emerge from an annular tube as it is driven by a pressure gradient maintained inside the annulus, and/or by gravity in the axial direction. The interplay between inertia, annulus aspect ratio, substrate topography and gravity is particularly emphasized. Initial conditions are found to have a drastic e ect on the ensuing ow. The ow is governed by the thin-ÿlm equations of the 'boundary-layer' type, which are solved by expanding the ow ÿeld in terms of orthonormal modes in the radial direction. The formulation is validated upon comparison with the similarity solution of Watson (J. Fluid Mech 1964; 20:481) leading to an excellent agreement when only 2-3 modes are included. The wave and ow structure are examined for high and low inertia. It is found that low-inertia uids tend to accumulate near the annulus exit, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the di culty faced with coating high-viscosity uids. The annulus aspect is found to be in uential only when inertia is signiÿcant; there is less ow resistance for a ÿlm over a cylinder of smaller diameter. For high inertia, the free surface evolves similarly to two-dimensional ow. The substrate topography is found to have a signiÿcant e ect on transient behaviour, but this e ect depends strongly on inertia. It is observed that the ow of a high-inertia uid over a step-down exhibits the formation of a secondary wave that moves upstream of the primary wave. Gravity is found to help the ÿlm (coating) ow by halting or prohibiting the wave growth. The initial ÿlm proÿle and velocity distribution dictate whether the uid will ow downstream or accumulate near the annulus exit.

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Section: Discussion and Resultsmentioning

confidence: 93%

“…; U i¿1 (x = 0; t) = 0 (15) where h(x = 0) = 0 is used. The initial conditions may generally be written as…”

Section: Solution Proceduresmentioning

confidence: 99%

Section: Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

Khayat

Kim

Delosquer

2004

Numerical Methods in Fluids

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“…Applications for measuring thin film thicknesses of liquids include coating processes (Ashmore et al 2008;Spaid 1994), microfluidics (Hardy et al 2009), and thin film instabilities (Oron et al 1997). Methods of measuring thin film thicknesses are atomic force microscopy (Becker et al 2002;Xu et al 2004), ellipsometry (Beaglehol 1989;Heslot et al 1992), polarized reflection microscopy (Leger et al 1988a, b), and interferometry (Kavehpour et al 2003).…”

Section: Introductionmentioning

confidence: 98%

Dynamic measurement of microfilms and nanofilms of fluids using fluorescence microscopy

et al. 2012

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The noninvasive measurement of submicron liquid film thicknesses has been one of the greatest challenges in fluid mechanics experiments. Most applications require the time-dependent measurement of thin film thickness as it varies from macroscopic to microscopic dimensions. The current techniques lack resolution and range to capture the complete characteristics of these phenomena. Here, we use fluorescence microscopy as an optical technique to investigate the thickness of micro-and nanofilms as they evolve with time. We show that this technique is capable of measuring film thicknesses on the order of nanometers to millimeters with very high spatial resolution. Experimental examples are provided to demonstrate the various potential applications of this technique.

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Transient two‐layer thin‐film flow

Pandher

Khayat

2011

Numerical Methods in Fluids

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SUMMARYThe transient two-layer thin-film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface-to-interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer.

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Viscoelastic free surface flows: spin coating and dynamic contact lines

Cited by 27 publications

References 16 publications

Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

Influence of inertia, topography and gravity on transient axisymmetric thin‐film flow

Dynamic measurement of microfilms and nanofilms of fluids using fluorescence microscopy

Transient two‐layer thin‐film flow

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