In adsorption processing terminology, what is the name for the stage-wise (multi-stage, batch-contact) mode where adsorbent and solution are contacted in successive steps and the solids are filtered off between stages?

Introduction:
Adsorption can be carried out in different modes. Besides continuous fixed-bed columns, a stage-wise or cross-current approach repeatedly contacts fresh adsorbent with solution, then separates the solids before the next stage. Knowing the terminology helps in selecting mass-transfer models and equipment.

Given Data / Assumptions:

• Process involves batch contact of adsorbent with liquid.
• Solids are removed between stages (e.g., by filtration).
• Objective is to incrementally remove solute across multiple contacts.

Concept / Approach:
This multi-stage, batch-contact method is commonly termed contact filtration. It contrasts with continuous packed-bed adsorption (breakthrough curves) and with specific modalities like ion exchange (a particular adsorption mechanism) or affinity adsorption (ligand-specific binding).

Step-by-Step Solution:
Step 1: Identify the key features: staged, batch contacts plus solid–liquid separation.Step 2: Map to the standard term used in operations texts: contact filtration.Step 3: Distinguish from fixed-bed columns and from mechanism-specific labels.

Verification / Alternative check:
Classic separations references describe cross-current adsorption as contact followed by separation, iterated over stages to approach desired solute removal.

Why Other Options Are Wrong:

• conventional adsorption: Vague; does not denote staged batch contact.
• affinity adsorption: Mechanism-specific, not an operating mode.
• ion exchange: A subtype based on charge exchange; can be run in columns.
• fixed-bed breakthrough operation: Continuous mode, not stage-wise batch.

Common Pitfalls:
Confusing operation mode (stage-wise vs continuous) with adsorption mechanism (physical, ion exchange, affinity).

Final Answer:
contact filtration